This document summarizes a statistical framework for recognizing 2D shapes represented as arrangements of curves or strokes. It presents a hierarchical model with two layers: 1) At the lower level, each curve is represented by a point distribution model describing its shape variability. Curves are assigned stroke labels. 2) At the top level, shapes are represented by the geometric arrangement of curve center points (using another point distribution model) and a string of stroke labels. Recognition involves assigning stroke labels to curves, and recovering stroke and shape deformation parameters using expectation maximization. The method is applied to Arabic handwritten character recognition.
HANDWRITTEN CHARACTER RECOGNITION USING STRUCTURAL SHAPE DECOMPOSITIONcsandit
This paper presents a statistical framework for recognising 2D shapes which are represented as
an arrangement of curves or strokes. The approach is a hierarchical one which mixes geometric
and symbolic information in a three-layer architecture. Each curve primitive is represented
using a point-distribution model which describes how its shape varies over a set of training
data. We assign stroke labels to the primitives and these indicate to which class they belong.
Shapes are decomposed into an arrangement of primitives and the global shape representation
has two components. The first of these is a second point distribution model that is used to
represent the geometric arrangement of the curve centre-points. The second component is a
string of stroke labels that represents the symbolic arrangement of strokes. Hence each shape
can be represented by a set of centre-point deformation parameters and a dictionary of
permissible stroke label configurations. The hierarchy is a two-level architecture in which the
curve models reside at the nonterminal lower level of the tree. The top level represents the curve
arrangements allowed by the dictionary of permissible stroke combinations. The aim in
recognition is to minimise the cross entropy between the probability distributions for geometric
alignment errors and curve label errors. We show how the stroke parameters, shape-alignment
parameters and stroke labels may be recovered by applying the expectation maximization EM
algorithm to the utility measure. We apply the resulting shape-recognition method to Arabic
character recognition.
LATTICE-CELL : HYBRID APPROACH FOR TEXT CATEGORIZATIONcsandit
The document proposes a new text categorization framework called LATTICE-CELL that is based on concepts lattice and cellular automata. It models concept structures using a Cellular Automaton for Symbolic Induction (CASI) in order to reduce the time complexity of categorization caused by concept lattices. The framework consists of a preprocessing module to create a vector representation of documents and a categorization module that generates the categorization model by representing the concept lattice structure as a cellular lattice. Experiments show the approach improves performance while reducing categorization time compared to other algorithms such as Naive Bayes and k-nearest neighbors.
This paper analyzes the swap rates issued by the China Inter-bank Offered Rate(CHIBOR) and
selects the one-year FR007 daily data from January 1st, 2019 to June 30th, 2019 as a sample. To fit the data,
we conduct Monte Carlo simulation with several typical continuous short-term swap rate models such as the
Merton model, the Vasicek model, the CIR model, etc. These models contain both linear forms and nonlinear
forms and each has both drift terms and diffusion terms. After empirical analysis, we obtain the parameter
values in Euler-Maruyama scheme and relevant statistical characteristics of each model. The results show that
most of the short-term swap rate models can fit the swap rates and reflect the change of trend, while the CKLSO
model performs best.
This document discusses stiffness analysis of flexible parallel manipulators. It presents the forward kinematics analysis of a 3-RRR planar parallel manipulator using genetic algorithms and neural networks to minimize positional errors. The Jacobian and platform stiffness matrices are evaluated within the defined workspace. A pseudo-rigid body model with frame and plate elements is used to analyze the flexible link configuration and compliant joints. Stiffness indices are obtained and validated using commercial finite element software. The methodology is illustrated for a 3-RRR flexible parallel manipulator to study the effects of link flexibility and joint compliance on stiffness.
3D M ESH S EGMENTATION U SING L OCAL G EOMETRYijcga
We develop an algorithm to segment a 3D surface mesh intovisually meaningful regions based
on
analyzing the local geometry ofvertices. We begin with a novel characterization of mesh vertices as
convex,concave or hyperbolic depending upon their discrete local geometry.Hyperbolic and concave
vertices are considered potential feature regionboundari
es. We propose a new region growing technique
starting fromthese boundary vertices leading to a segmentation of the surface thatis subsequently simplified
by a region
-
merging method. Experiments indicatethat our algorithm segments a broad range of 3D
model
s at aquality comparable to existing algorithms. Its use of methods that belongnaturally to discretized
surfaces and ease of implementation makeit an appealing alternative in various applications
We develop an algorithm to segment a 3D surface mesh intovisually meaningful regions based on analyzing the local geometry ofvertices. We begin with a novel characterization of mesh vertices as convex,concave or hyperbolic depending upon their discrete local geometry.Hyperbolic and concave vertices are considered potential feature regionboundaries. We propose a new region growing technique
starting fromthese boundary vertices leading to a segmentation of the surface thatis subsequently simplified by a region-merging method. Experiments indicatethat our algorithm segments a broad range of 3D models at aquality comparable to existing algorithms. Its use of methods that belongnaturally to discretized surfaces and ease of implementation makeit an appealing alternative in various applications.
Surface classification using conformal structuresEvans Marshall
This paper introduces a novel method for classifying 3D surfaces using their conformal structures. Conformal structures are intrinsic to a surface's geometry and invariant to transformations like triangulation. The paper represents a surface's conformal structure using matrices called period matrices that describe the shapes of parallelograms surfaces are conformally mapped to. An algorithm is presented to compute these conformal structures and classify surfaces based on whether they have equivalent conformal structures. This approach is more discriminating for classification than topological approaches while being more robust than methods based on exact geometry.
A SYSTEM FOR VISUALIZATION OF BIG ATTRIBUTED HIERARCHICAL GRAPHSIJCNCJournal
Information visualization is a process of transformation of large and complex abstract forms of information
into the visual forms, strengthening cognitive abilities of users and allowing them to take the most optimal
decisions. A graph is an abstract structure that is widely used to model complex information for its
visualization. In the paper, we consider a system aimed at supporting of visualization of big amounts of
complex information on the base of attributed hierarchical graphs.
HANDWRITTEN CHARACTER RECOGNITION USING STRUCTURAL SHAPE DECOMPOSITIONcsandit
This paper presents a statistical framework for recognising 2D shapes which are represented as
an arrangement of curves or strokes. The approach is a hierarchical one which mixes geometric
and symbolic information in a three-layer architecture. Each curve primitive is represented
using a point-distribution model which describes how its shape varies over a set of training
data. We assign stroke labels to the primitives and these indicate to which class they belong.
Shapes are decomposed into an arrangement of primitives and the global shape representation
has two components. The first of these is a second point distribution model that is used to
represent the geometric arrangement of the curve centre-points. The second component is a
string of stroke labels that represents the symbolic arrangement of strokes. Hence each shape
can be represented by a set of centre-point deformation parameters and a dictionary of
permissible stroke label configurations. The hierarchy is a two-level architecture in which the
curve models reside at the nonterminal lower level of the tree. The top level represents the curve
arrangements allowed by the dictionary of permissible stroke combinations. The aim in
recognition is to minimise the cross entropy between the probability distributions for geometric
alignment errors and curve label errors. We show how the stroke parameters, shape-alignment
parameters and stroke labels may be recovered by applying the expectation maximization EM
algorithm to the utility measure. We apply the resulting shape-recognition method to Arabic
character recognition.
LATTICE-CELL : HYBRID APPROACH FOR TEXT CATEGORIZATIONcsandit
The document proposes a new text categorization framework called LATTICE-CELL that is based on concepts lattice and cellular automata. It models concept structures using a Cellular Automaton for Symbolic Induction (CASI) in order to reduce the time complexity of categorization caused by concept lattices. The framework consists of a preprocessing module to create a vector representation of documents and a categorization module that generates the categorization model by representing the concept lattice structure as a cellular lattice. Experiments show the approach improves performance while reducing categorization time compared to other algorithms such as Naive Bayes and k-nearest neighbors.
This paper analyzes the swap rates issued by the China Inter-bank Offered Rate(CHIBOR) and
selects the one-year FR007 daily data from January 1st, 2019 to June 30th, 2019 as a sample. To fit the data,
we conduct Monte Carlo simulation with several typical continuous short-term swap rate models such as the
Merton model, the Vasicek model, the CIR model, etc. These models contain both linear forms and nonlinear
forms and each has both drift terms and diffusion terms. After empirical analysis, we obtain the parameter
values in Euler-Maruyama scheme and relevant statistical characteristics of each model. The results show that
most of the short-term swap rate models can fit the swap rates and reflect the change of trend, while the CKLSO
model performs best.
This document discusses stiffness analysis of flexible parallel manipulators. It presents the forward kinematics analysis of a 3-RRR planar parallel manipulator using genetic algorithms and neural networks to minimize positional errors. The Jacobian and platform stiffness matrices are evaluated within the defined workspace. A pseudo-rigid body model with frame and plate elements is used to analyze the flexible link configuration and compliant joints. Stiffness indices are obtained and validated using commercial finite element software. The methodology is illustrated for a 3-RRR flexible parallel manipulator to study the effects of link flexibility and joint compliance on stiffness.
3D M ESH S EGMENTATION U SING L OCAL G EOMETRYijcga
We develop an algorithm to segment a 3D surface mesh intovisually meaningful regions based
on
analyzing the local geometry ofvertices. We begin with a novel characterization of mesh vertices as
convex,concave or hyperbolic depending upon their discrete local geometry.Hyperbolic and concave
vertices are considered potential feature regionboundari
es. We propose a new region growing technique
starting fromthese boundary vertices leading to a segmentation of the surface thatis subsequently simplified
by a region
-
merging method. Experiments indicatethat our algorithm segments a broad range of 3D
model
s at aquality comparable to existing algorithms. Its use of methods that belongnaturally to discretized
surfaces and ease of implementation makeit an appealing alternative in various applications
We develop an algorithm to segment a 3D surface mesh intovisually meaningful regions based on analyzing the local geometry ofvertices. We begin with a novel characterization of mesh vertices as convex,concave or hyperbolic depending upon their discrete local geometry.Hyperbolic and concave vertices are considered potential feature regionboundaries. We propose a new region growing technique
starting fromthese boundary vertices leading to a segmentation of the surface thatis subsequently simplified by a region-merging method. Experiments indicatethat our algorithm segments a broad range of 3D models at aquality comparable to existing algorithms. Its use of methods that belongnaturally to discretized surfaces and ease of implementation makeit an appealing alternative in various applications.
Surface classification using conformal structuresEvans Marshall
This paper introduces a novel method for classifying 3D surfaces using their conformal structures. Conformal structures are intrinsic to a surface's geometry and invariant to transformations like triangulation. The paper represents a surface's conformal structure using matrices called period matrices that describe the shapes of parallelograms surfaces are conformally mapped to. An algorithm is presented to compute these conformal structures and classify surfaces based on whether they have equivalent conformal structures. This approach is more discriminating for classification than topological approaches while being more robust than methods based on exact geometry.
A SYSTEM FOR VISUALIZATION OF BIG ATTRIBUTED HIERARCHICAL GRAPHSIJCNCJournal
Information visualization is a process of transformation of large and complex abstract forms of information
into the visual forms, strengthening cognitive abilities of users and allowing them to take the most optimal
decisions. A graph is an abstract structure that is widely used to model complex information for its
visualization. In the paper, we consider a system aimed at supporting of visualization of big amounts of
complex information on the base of attributed hierarchical graphs.
Recognition of Persian handwritten characters has been considered as a significant field of research for
the last few years under pattern analysing technique. In this paper, a new approach for robust handwritten
Persian numerals recognition using strong feature set and a classifier fusion method is scrutinized to
increase the recognition percentage. For implementing the classifier fusion technique, we have considered
k nearest neighbour (KNN), linear classifier (LC) and support vector machine (SVM) classifiers. The
innovation of this tactic is to attain better precision with few features using classifier fusion method. For
evaluation of the proposed method we considered a Persian numerals database with 20,000 handwritten
samples. Spending 15,000 samples for training stage, we verified our technique on other 5,000 samples,
and the correct recognition ratio achievedapproximately 99.90%. Additional, we got 99.97% exactness
using four-fold cross validation procedure on 20,000 databases.
Role Model of Graph Coloring Application in Labeled 2D Line Drawing ObjectWaqas Tariq
Several researches had worked on the development of sketch interpreters. However, very few of them gave a complete cycle of the sketch interpreter which can be used to transform an engineering sketch to a valid solid object. In this paper, a framework of the complete cycle of the sketch interpreter is presented. The discussion in this paper will stress on the usage of line labeling and graph coloring application in the validation of two dimensional (2D) line drawing phase. Both applications are needed to determine whether the given 2D line drawing represent possible or impossible object. In 2008, previous work by Matondang et al., has used line labeling algorithm to validate several 2D line drawings. However, the result shows that line labeling algorithm is not sufficient, as the algorithm does not have a validation technique for the result. Therefore, in this research study, it is going to be shown that if a 2D line drawing is valid as a possible object by using the line labeling algorithm, then it can be colored using graph coloring concept with a determine-able minimum numbers of color needed. This is equal in vice versa. The expected output from this phase is a valid-labeled of 2D line drawing with different colors at each edge and ready for the reconstruction phase. As a preliminary result, a high programming language MATLAB R2009a and several primitive 2D line drawings has been used and presented in this paper to test the graph coloring concept in labeled 2D line drawing.
Unimodal Multi-Feature Fusion and one-dimensional Hidden Markov Models for Lo...IJECEIAES
The objective of low-resolution face recognition is to identify faces from small size or poor quality images with varying pose, illumination, expression, etc. In this work, we propose a robust low face recognition technique based on one-dimensional Hidden Markov Models. Features of each facial image are extracted using three steps: firstly, both Gabor filters and Histogram of Oriented Gradients (HOG) descriptor are calculated. Secondly, the size of these features is reduced using the Linear Discriminant Analysis (LDA) method in order to remove redundant information. Finally, the reduced features are combined using Canonical Correlation Analysis (CCA) method. Unlike existing techniques using HMMs, in which authors consider each state to represent one facial region (eyes, nose, mouth, etc), the proposed system employs 1D-HMMs without any prior knowledge about the localization of interest regions in the facial image. Performance of the proposed method will be measured using the AR database.
Face Alignment Using Active Shape Model And Support Vector MachineCSCJournals
The document proposes improvements to the classical Active Shape Model (ASM) algorithm for face alignment. The improvements include: 1) Combining Sobel filtering and 2D profiles to build texture models, 2) Applying Canny edge detection for enhancement, 3) Using Support Vector Machines (SVM) to classify landmarks for more accurate localization, and 4) Automatically adjusting 2D profile lengths based on image size. Experimental results on two face databases show the proposed ASM-SVM method achieves better alignment accuracy than the classical ASM and other methods.
The document provides a summary of a curriculum for teaching transformation geometry to middle school students. It discusses the objectives to have students create and relate the objects of the subject (rotations, translations, reflections) and construct operations on them. A key goal is for students to understand transformations as mappings between states (positions, headings, orientations) of figures, and later as multivariate mappings and isometric plane mappings. The curriculum uses a computer program called MOTIONS to allow students to perform and compose transformations on figures. It describes activities to help students develop understandings of transformations and their properties and operations like composition.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Study on a Hybrid Segmentation Approach for Handwritten Numeral Strings in Fo...inventionjournals
This paper presents a hybrid approach to segment single- or multiple-touching handwritten numeral strings in form document, the core of which is the combined use of foreground, background and recognition analysis. The algorithm first located some feature points on both the foreground and background skeleton images containing connected numeral strings in form document. Possible segmentation paths were then constructed by matching these feature points, with an unexpected benefit of removing useless strokes. Subsequently, all these segmentation paths were validated and ranked by a recognition-based analysis, where a well-trained two-stage classifier was applied to each separated digit image to obtain its reliability. Finally, by introducing a locally optimal strategy to accelerate the recognition process, the top ranked segmentation path survived to help make a decision on whether to accept or not. Experimental results show that the proposed method can achieve a correct segmentation rate of 96.2 percent on a large dataset collected by our own.
International Refereed Journal of Engineering and Science (IRJES)irjes
This document provides a survey of pattern recognition techniques using fuzzy clustering approaches for image segmentation. It discusses how fuzzy logic and soft computing techniques can be applied to edge detection and image segmentation problems. Specifically, it describes fuzzy clustering algorithms like fuzzy c-means clustering and hierarchical clustering that have been used for image segmentation. It also discusses other related topics like fuzzy logic in pattern recognition and image processing, and different methods for evaluating image segmentation techniques.
An Interactive Decomposition Algorithm for Two-Level Large Scale Linear Multi...IJERA Editor
This paper extended TOPSIS (Technique for Order Preference by Similarity Ideal Solution) method for solving
Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters in the righthand
side of the constraints (TL-LSLMOP-SP)rhs of block angular structure. In order to obtain a compromise (
satisfactory) solution to the (TL-LSLMOP-SP)rhs of block angular structure using the proposed TOPSIS
method, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance
function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions
of the two levels. In every level, as the measure of ―Closeness‖ dp-metric is used, a k-dimensional objective
space is reduced to two –dimentional objective space by a first-order compromise procedure. The membership
functions of fuzzy set theory is used to represent the satisfaction level for both criteria. A single-objective
programming problem is obtained by using the max-min operator for the second –order compromise operaion.
A decomposition algorithm for generating a compromise ( satisfactory) solution through TOPSIS approach is
provided where the first level decision maker (FLDM) is asked to specify the relative importance of the
objectives. Finally, an illustrative numerical example is given to clarify the main results developed in the paper.
This document summarizes a project on recognizing handwritten digits using machine learning classifiers. The researchers used the MNIST dataset and preprocessed the images before extracting features. They then applied Naive Bayes and Logistic Regression classifiers and evaluated their performance based on accuracy and confusion matrices. Logistic Regression significantly outperformed Naive Bayes. Regularization was also investigated for Logistic Regression, with cross-validation used to select the optimal regularization parameter.
Sketch recognition systems used for the development of many domains are time consuming. This is because it involves intricacies in handling the data with greater care for each domain. Present authors introduced A new approach to sketch recognition using Heuristic [1]. It compares very well with the statistical approach used in Bayesian networks[4] In this paper, we have introduced MAHI: (Machine and Human Interface) as a sketching language based on geometrical rules associated to the recognition of basic elements in its domain as the better option discussed in MAHII (Machine And Interactive Interface [2]. The recognition engine interprets the sketches based on the information obtained from the description of domains associated with the input from the user. Keywords: MAHI, MAHII, LADDER, Domain-Description, Geometrical Constraints, Multi-connected lines.
This document provides an overview of the topics covered in an advanced computer aided design course, including principles of computer graphics, CAD tools, surface modeling, parametric representation of surfaces, geometric modeling in 3D, data exchange formats and standards, and collaborative engineering. The syllabus covers points plotting, lines, Bresenham's circle algorithm, transformations, hidden surface removal, CAD system evaluation criteria, modeling techniques like wireframe, surface and solid modeling, parametric surfaces, solid modeling representations, data exchange formats like IGES and DXF, and collaborative design principles and tools.
The Framework of Image Recognition based on Modified Freeman Chain CodeCSCJournals
Image recognition of line drawing involves feature extraction and feature comparison. Works on the extraction required the representation of the image to be compared. Combining these two requirements, a framework that develops a new extraction algorithm of a chain code representation is presented. In addition, new corner detection is presented as pre-processing to the line drawing input in order to derive the chain code. This paper presents a new framework that consist of five steps namely pre-processing and image processing, new corner detection algorithm, chain code generator, feature extraction algorithm, and recognition process. Heuristic approach that is applied in the corner detection algorithm accepts input of thinned binary image and produce a modified thinned binary image consisted of J character to represent corners in the image. Using the modified thinned binary image, a new chain code scheme that is based on Freeman chain code is proposed and an algorithm is developed to generate a single chain code series that is representing the line drawing input. The feature extraction algorithm is then extracting the three pre-defined features of the chain code for recognition purpose. The features are corner properties, distance between corners, and angle from a corner to the connected corner. The explanation of steps in the framework is supported with two line drawings. The results show that the framework successfully recognizes line drawing into five categories namely not similar line drawing, and four other categories that are similar but with attributes of rotation angle and scaling ratio.
Sparse Observability using LP Presolve and LTDL Factorization in IMPL (IMPL-S...Alkis Vazacopoulos
Presented in this short document is a description of our technology we call “Sparse Observability”. Observability is the estimatability metric (Bagajewicz, 2010) to structurally determine that an unmeasured variable or regressed parameter is either uniquely solvable (observable) or otherwise unsolvable (unobservable) in data reconciliation and regression (DRR) applications. Ultimately, our purpose to use efficient sparse matrix techniques is to solve large industrial DRR flowsheets quickly and accurately.
Most other implementations of observability calculation use dense linear algebra such as reduced row echelon form (RREF), Gauss-Jordan decomposition (Crowe et. al. 1983; Madron 1992), QR factorization which can now be considered as semi-sparse (Swartz, 1989; Sanchez and Romagnoli, 1996), Schur complements, Cholesky factorization (Kelly, 1998a) and singular value decomposition (SVD) (Kelly, 1999). A sparse LU decomposition with complete-pivoting from Albuquerque and Biegler (1996) for dynamic data reconciliation observability computation was used but it is uncertain if complete-pivoting causes extreme “fill-ins” of the lower and upper triangular matrices essentially making them near-dense. There is another sparse observability method using an LP sub-solver found in Kelly and Zyngier (2008) but this requires solving as many LP sub-problems as there are unmeasured variables which can be considered as somewhat inefficient.
IMPL’s sparse observability technique uses the variable classification and nomenclature found in Kelly (1998b) given that if we partition or separate the unmeasured variables into independent (B12) and dependent (B34) sub-matrices then all dependent unmeasured variables by definition are unobservable. If any independent unmeasured variable is a (linear) function of any dependent variable then this independent variable is of course also unobservable because it is dependent on another non-observable variable.
This document presents new certified optimal solutions found by the Charibde algorithm for six difficult benchmark optimization problems. Charibde combines an evolutionary algorithm and interval-based methods in a cooperative framework. It has achieved optimality proofs for five bound-constrained problems and one nonlinearly constrained problem. These problems are highly multimodal and some had not been solved before even with approximate methods. The document also compares Charibde's performance to other state-of-the-art solvers, showing it is highly competitive while providing reliable optimality proofs.
Automatic Recognition of Isolated And Interacting Manufacturing Features In M...IJERA Editor
Manufacturing features play an important role between design information and manufacturing activities.
Recently, various efforts have been concentrated in development of automatic feature recognition systems.
However, only limited number of features could be recognized, intersecting features were generally not
involved. This paper presents a simple system, in which manufacturing features are easily detected using a
Chain of Faces and Base of Faces (CF-BF) graph. A feature is modeled by a series/parallel association of
opened Chain of Faces (OCF) or Closed chain of Faces (CCF) that rest on a Base Face (BF). The feature is
considered Perfect Manufacturing Feature (PMF) if all Faces that participate in constitution of OCF/CCF are
blank faces, else it is an Imperfect Manufacturing Feature (IMF). In order to establish news Virtual Faces to
satisfy this necessaries condition, a judicious analysis of orientation of frontier faces that rest on BF is
performed. The technique was tested on several parts taken from literature and the results were satisfying.
This document is a project submitted for a Bachelor of Engineering degree that investigates computer simulations of fractal patterns through diffusion limited growth processes. The student developed three diffusion limited aggregation (DLA) models in an attempt to more realistically simulate diffusion limited growth processes with specific reference to electro-deposition. The models included growth of more than one cluster and complete coverage of the substrate. Patterns and data produced from the models allowed calculation of fractional dimensions between one and two as expected. However, unexpected results were also observed where the relationship between log of density and log of characteristic length deviated from mathematical predictability due to impingement effects.
LITERATURE SURVEY ON SPARSE REPRESENTATION FOR NEURAL NETWORK BASED FACE DETE...csijjournal
Face detection and recognition is a challenging problem in the field of image processing. In this paper, we reviewed some of the recent research works on face recognition. Issues with the previous face recognition
techniques are , time required is more for face recognition , recognition rate and database required to store the data . To overcome these problems sparse representation based classifier technique can be used.
A review of automatic differentiationand its efficient implementationssuserfa7e73
Automatic differentiation is a powerful tool for automatically calculating derivatives of mathematical functions and algorithms. It works by expressing the target function as a sequence of elementary operations and then applying the chain rule to differentiate each operation. This can be done using either forward or reverse mode. Forward mode calculates how changes in inputs propagate through the function to influence the outputs, while reverse mode calculates how changes in outputs backpropagate to influence the inputs. Both modes require performing the computation twice - once for the forward pass and once for the derivative pass. Careful implementation is required to make automatic differentiation efficient in terms of speed and memory usage.
LEARNING SPLINE MODELS WITH THE EM ALGORITHM FOR SHAPE RECOGNITIONgerogepatton
This paper demonstrates how cubic Spline (B-Spline) models can be used to recognize 2-dimension nonrigid handwritten isolated characters. Each handwritten character is represented by a set of nonoverlapping uniformly distributed landmarks. The Spline models are constructed by utilizing cubic order of
polynomial to model the shapes under study. The approach is a two-stage process. The first stage is
learning, we construct a mixture of spline class parameters to capture the variations in spline coefficients
using the apparatus Expectation Maximization algorithm. The second stage is recognition, here we use the
Fréchet distance to compute the variations between the spline models and test spline shape for recognition.
We test the approach on a set of handwritten Arabic letters.
MIXTURES OF TRAINED REGRESSION CURVES MODELS FOR HANDWRITTEN ARABIC CHARACTER...gerogepatton
In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We proceed then, by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.
Recognition of Persian handwritten characters has been considered as a significant field of research for
the last few years under pattern analysing technique. In this paper, a new approach for robust handwritten
Persian numerals recognition using strong feature set and a classifier fusion method is scrutinized to
increase the recognition percentage. For implementing the classifier fusion technique, we have considered
k nearest neighbour (KNN), linear classifier (LC) and support vector machine (SVM) classifiers. The
innovation of this tactic is to attain better precision with few features using classifier fusion method. For
evaluation of the proposed method we considered a Persian numerals database with 20,000 handwritten
samples. Spending 15,000 samples for training stage, we verified our technique on other 5,000 samples,
and the correct recognition ratio achievedapproximately 99.90%. Additional, we got 99.97% exactness
using four-fold cross validation procedure on 20,000 databases.
Role Model of Graph Coloring Application in Labeled 2D Line Drawing ObjectWaqas Tariq
Several researches had worked on the development of sketch interpreters. However, very few of them gave a complete cycle of the sketch interpreter which can be used to transform an engineering sketch to a valid solid object. In this paper, a framework of the complete cycle of the sketch interpreter is presented. The discussion in this paper will stress on the usage of line labeling and graph coloring application in the validation of two dimensional (2D) line drawing phase. Both applications are needed to determine whether the given 2D line drawing represent possible or impossible object. In 2008, previous work by Matondang et al., has used line labeling algorithm to validate several 2D line drawings. However, the result shows that line labeling algorithm is not sufficient, as the algorithm does not have a validation technique for the result. Therefore, in this research study, it is going to be shown that if a 2D line drawing is valid as a possible object by using the line labeling algorithm, then it can be colored using graph coloring concept with a determine-able minimum numbers of color needed. This is equal in vice versa. The expected output from this phase is a valid-labeled of 2D line drawing with different colors at each edge and ready for the reconstruction phase. As a preliminary result, a high programming language MATLAB R2009a and several primitive 2D line drawings has been used and presented in this paper to test the graph coloring concept in labeled 2D line drawing.
Unimodal Multi-Feature Fusion and one-dimensional Hidden Markov Models for Lo...IJECEIAES
The objective of low-resolution face recognition is to identify faces from small size or poor quality images with varying pose, illumination, expression, etc. In this work, we propose a robust low face recognition technique based on one-dimensional Hidden Markov Models. Features of each facial image are extracted using three steps: firstly, both Gabor filters and Histogram of Oriented Gradients (HOG) descriptor are calculated. Secondly, the size of these features is reduced using the Linear Discriminant Analysis (LDA) method in order to remove redundant information. Finally, the reduced features are combined using Canonical Correlation Analysis (CCA) method. Unlike existing techniques using HMMs, in which authors consider each state to represent one facial region (eyes, nose, mouth, etc), the proposed system employs 1D-HMMs without any prior knowledge about the localization of interest regions in the facial image. Performance of the proposed method will be measured using the AR database.
Face Alignment Using Active Shape Model And Support Vector MachineCSCJournals
The document proposes improvements to the classical Active Shape Model (ASM) algorithm for face alignment. The improvements include: 1) Combining Sobel filtering and 2D profiles to build texture models, 2) Applying Canny edge detection for enhancement, 3) Using Support Vector Machines (SVM) to classify landmarks for more accurate localization, and 4) Automatically adjusting 2D profile lengths based on image size. Experimental results on two face databases show the proposed ASM-SVM method achieves better alignment accuracy than the classical ASM and other methods.
The document provides a summary of a curriculum for teaching transformation geometry to middle school students. It discusses the objectives to have students create and relate the objects of the subject (rotations, translations, reflections) and construct operations on them. A key goal is for students to understand transformations as mappings between states (positions, headings, orientations) of figures, and later as multivariate mappings and isometric plane mappings. The curriculum uses a computer program called MOTIONS to allow students to perform and compose transformations on figures. It describes activities to help students develop understandings of transformations and their properties and operations like composition.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Study on a Hybrid Segmentation Approach for Handwritten Numeral Strings in Fo...inventionjournals
This paper presents a hybrid approach to segment single- or multiple-touching handwritten numeral strings in form document, the core of which is the combined use of foreground, background and recognition analysis. The algorithm first located some feature points on both the foreground and background skeleton images containing connected numeral strings in form document. Possible segmentation paths were then constructed by matching these feature points, with an unexpected benefit of removing useless strokes. Subsequently, all these segmentation paths were validated and ranked by a recognition-based analysis, where a well-trained two-stage classifier was applied to each separated digit image to obtain its reliability. Finally, by introducing a locally optimal strategy to accelerate the recognition process, the top ranked segmentation path survived to help make a decision on whether to accept or not. Experimental results show that the proposed method can achieve a correct segmentation rate of 96.2 percent on a large dataset collected by our own.
International Refereed Journal of Engineering and Science (IRJES)irjes
This document provides a survey of pattern recognition techniques using fuzzy clustering approaches for image segmentation. It discusses how fuzzy logic and soft computing techniques can be applied to edge detection and image segmentation problems. Specifically, it describes fuzzy clustering algorithms like fuzzy c-means clustering and hierarchical clustering that have been used for image segmentation. It also discusses other related topics like fuzzy logic in pattern recognition and image processing, and different methods for evaluating image segmentation techniques.
An Interactive Decomposition Algorithm for Two-Level Large Scale Linear Multi...IJERA Editor
This paper extended TOPSIS (Technique for Order Preference by Similarity Ideal Solution) method for solving
Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters in the righthand
side of the constraints (TL-LSLMOP-SP)rhs of block angular structure. In order to obtain a compromise (
satisfactory) solution to the (TL-LSLMOP-SP)rhs of block angular structure using the proposed TOPSIS
method, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance
function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions
of the two levels. In every level, as the measure of ―Closeness‖ dp-metric is used, a k-dimensional objective
space is reduced to two –dimentional objective space by a first-order compromise procedure. The membership
functions of fuzzy set theory is used to represent the satisfaction level for both criteria. A single-objective
programming problem is obtained by using the max-min operator for the second –order compromise operaion.
A decomposition algorithm for generating a compromise ( satisfactory) solution through TOPSIS approach is
provided where the first level decision maker (FLDM) is asked to specify the relative importance of the
objectives. Finally, an illustrative numerical example is given to clarify the main results developed in the paper.
This document summarizes a project on recognizing handwritten digits using machine learning classifiers. The researchers used the MNIST dataset and preprocessed the images before extracting features. They then applied Naive Bayes and Logistic Regression classifiers and evaluated their performance based on accuracy and confusion matrices. Logistic Regression significantly outperformed Naive Bayes. Regularization was also investigated for Logistic Regression, with cross-validation used to select the optimal regularization parameter.
Sketch recognition systems used for the development of many domains are time consuming. This is because it involves intricacies in handling the data with greater care for each domain. Present authors introduced A new approach to sketch recognition using Heuristic [1]. It compares very well with the statistical approach used in Bayesian networks[4] In this paper, we have introduced MAHI: (Machine and Human Interface) as a sketching language based on geometrical rules associated to the recognition of basic elements in its domain as the better option discussed in MAHII (Machine And Interactive Interface [2]. The recognition engine interprets the sketches based on the information obtained from the description of domains associated with the input from the user. Keywords: MAHI, MAHII, LADDER, Domain-Description, Geometrical Constraints, Multi-connected lines.
This document provides an overview of the topics covered in an advanced computer aided design course, including principles of computer graphics, CAD tools, surface modeling, parametric representation of surfaces, geometric modeling in 3D, data exchange formats and standards, and collaborative engineering. The syllabus covers points plotting, lines, Bresenham's circle algorithm, transformations, hidden surface removal, CAD system evaluation criteria, modeling techniques like wireframe, surface and solid modeling, parametric surfaces, solid modeling representations, data exchange formats like IGES and DXF, and collaborative design principles and tools.
The Framework of Image Recognition based on Modified Freeman Chain CodeCSCJournals
Image recognition of line drawing involves feature extraction and feature comparison. Works on the extraction required the representation of the image to be compared. Combining these two requirements, a framework that develops a new extraction algorithm of a chain code representation is presented. In addition, new corner detection is presented as pre-processing to the line drawing input in order to derive the chain code. This paper presents a new framework that consist of five steps namely pre-processing and image processing, new corner detection algorithm, chain code generator, feature extraction algorithm, and recognition process. Heuristic approach that is applied in the corner detection algorithm accepts input of thinned binary image and produce a modified thinned binary image consisted of J character to represent corners in the image. Using the modified thinned binary image, a new chain code scheme that is based on Freeman chain code is proposed and an algorithm is developed to generate a single chain code series that is representing the line drawing input. The feature extraction algorithm is then extracting the three pre-defined features of the chain code for recognition purpose. The features are corner properties, distance between corners, and angle from a corner to the connected corner. The explanation of steps in the framework is supported with two line drawings. The results show that the framework successfully recognizes line drawing into five categories namely not similar line drawing, and four other categories that are similar but with attributes of rotation angle and scaling ratio.
Sparse Observability using LP Presolve and LTDL Factorization in IMPL (IMPL-S...Alkis Vazacopoulos
Presented in this short document is a description of our technology we call “Sparse Observability”. Observability is the estimatability metric (Bagajewicz, 2010) to structurally determine that an unmeasured variable or regressed parameter is either uniquely solvable (observable) or otherwise unsolvable (unobservable) in data reconciliation and regression (DRR) applications. Ultimately, our purpose to use efficient sparse matrix techniques is to solve large industrial DRR flowsheets quickly and accurately.
Most other implementations of observability calculation use dense linear algebra such as reduced row echelon form (RREF), Gauss-Jordan decomposition (Crowe et. al. 1983; Madron 1992), QR factorization which can now be considered as semi-sparse (Swartz, 1989; Sanchez and Romagnoli, 1996), Schur complements, Cholesky factorization (Kelly, 1998a) and singular value decomposition (SVD) (Kelly, 1999). A sparse LU decomposition with complete-pivoting from Albuquerque and Biegler (1996) for dynamic data reconciliation observability computation was used but it is uncertain if complete-pivoting causes extreme “fill-ins” of the lower and upper triangular matrices essentially making them near-dense. There is another sparse observability method using an LP sub-solver found in Kelly and Zyngier (2008) but this requires solving as many LP sub-problems as there are unmeasured variables which can be considered as somewhat inefficient.
IMPL’s sparse observability technique uses the variable classification and nomenclature found in Kelly (1998b) given that if we partition or separate the unmeasured variables into independent (B12) and dependent (B34) sub-matrices then all dependent unmeasured variables by definition are unobservable. If any independent unmeasured variable is a (linear) function of any dependent variable then this independent variable is of course also unobservable because it is dependent on another non-observable variable.
This document presents new certified optimal solutions found by the Charibde algorithm for six difficult benchmark optimization problems. Charibde combines an evolutionary algorithm and interval-based methods in a cooperative framework. It has achieved optimality proofs for five bound-constrained problems and one nonlinearly constrained problem. These problems are highly multimodal and some had not been solved before even with approximate methods. The document also compares Charibde's performance to other state-of-the-art solvers, showing it is highly competitive while providing reliable optimality proofs.
Automatic Recognition of Isolated And Interacting Manufacturing Features In M...IJERA Editor
Manufacturing features play an important role between design information and manufacturing activities.
Recently, various efforts have been concentrated in development of automatic feature recognition systems.
However, only limited number of features could be recognized, intersecting features were generally not
involved. This paper presents a simple system, in which manufacturing features are easily detected using a
Chain of Faces and Base of Faces (CF-BF) graph. A feature is modeled by a series/parallel association of
opened Chain of Faces (OCF) or Closed chain of Faces (CCF) that rest on a Base Face (BF). The feature is
considered Perfect Manufacturing Feature (PMF) if all Faces that participate in constitution of OCF/CCF are
blank faces, else it is an Imperfect Manufacturing Feature (IMF). In order to establish news Virtual Faces to
satisfy this necessaries condition, a judicious analysis of orientation of frontier faces that rest on BF is
performed. The technique was tested on several parts taken from literature and the results were satisfying.
This document is a project submitted for a Bachelor of Engineering degree that investigates computer simulations of fractal patterns through diffusion limited growth processes. The student developed three diffusion limited aggregation (DLA) models in an attempt to more realistically simulate diffusion limited growth processes with specific reference to electro-deposition. The models included growth of more than one cluster and complete coverage of the substrate. Patterns and data produced from the models allowed calculation of fractional dimensions between one and two as expected. However, unexpected results were also observed where the relationship between log of density and log of characteristic length deviated from mathematical predictability due to impingement effects.
LITERATURE SURVEY ON SPARSE REPRESENTATION FOR NEURAL NETWORK BASED FACE DETE...csijjournal
Face detection and recognition is a challenging problem in the field of image processing. In this paper, we reviewed some of the recent research works on face recognition. Issues with the previous face recognition
techniques are , time required is more for face recognition , recognition rate and database required to store the data . To overcome these problems sparse representation based classifier technique can be used.
A review of automatic differentiationand its efficient implementationssuserfa7e73
Automatic differentiation is a powerful tool for automatically calculating derivatives of mathematical functions and algorithms. It works by expressing the target function as a sequence of elementary operations and then applying the chain rule to differentiate each operation. This can be done using either forward or reverse mode. Forward mode calculates how changes in inputs propagate through the function to influence the outputs, while reverse mode calculates how changes in outputs backpropagate to influence the inputs. Both modes require performing the computation twice - once for the forward pass and once for the derivative pass. Careful implementation is required to make automatic differentiation efficient in terms of speed and memory usage.
LEARNING SPLINE MODELS WITH THE EM ALGORITHM FOR SHAPE RECOGNITIONgerogepatton
This paper demonstrates how cubic Spline (B-Spline) models can be used to recognize 2-dimension nonrigid handwritten isolated characters. Each handwritten character is represented by a set of nonoverlapping uniformly distributed landmarks. The Spline models are constructed by utilizing cubic order of
polynomial to model the shapes under study. The approach is a two-stage process. The first stage is
learning, we construct a mixture of spline class parameters to capture the variations in spline coefficients
using the apparatus Expectation Maximization algorithm. The second stage is recognition, here we use the
Fréchet distance to compute the variations between the spline models and test spline shape for recognition.
We test the approach on a set of handwritten Arabic letters.
MIXTURES OF TRAINED REGRESSION CURVES MODELS FOR HANDWRITTEN ARABIC CHARACTER...gerogepatton
In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We proceed then, by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.
This document presents a novel approach for measuring shape similarity and using it for object recognition. The key steps are:
1) Solving the correspondence problem between two shapes by attaching a descriptor called "shape context" to sample points on each shape. Shape context captures the distribution of remaining points relative to the reference point.
2) Using the point correspondences to estimate an aligning transformation between the shapes. This provides a measure of shape similarity as the matching error between corresponding points plus the magnitude of the transformation.
3) Treating recognition as a nearest neighbor problem to find the most similar stored prototype shape. The approach is demonstrated on various datasets including handwritten digits, silhouettes, and 3D objects
VARIATIONAL MONTE-CARLO APPROACH FOR ARTICULATED OBJECT TRACKINGcsandit
In this paper, we describe a novel variational Monte Carlo approach for modeling and tracking
body parts of articulated objects. An articulated object (human target) is represented as a
dynamic Markov network of the different constituent parts. The proposed approach combines
local information of individual body parts and other spatial constraints influenced by
neighboring parts. The movement of the relative parts of the articulated body is modeled with
local information of displacements from the Markov network and the global information from
other neighboring parts. We explore the effect of certain model parameters (including the
number of parts tracked; number of Monte-Carlo cycles, etc.) on system accuracy and show that
ourvariational Monte Carlo approach achieves better efficiency and effectiveness compared to
other methods on a number of real-time video datasets containing single targets.
Image similarity using symbolic representation and its variationssipij
This paper proposes a new method for image/object retrieval. A pre-processing technique is applied to
describe the object, in one dimensional representation, as a pseudo time series. The proposed algorithm
develops the modified versions of the SAX representation: applies an approach called Extended SAX
(ESAX) in order to realize efficient and accurate discovering of important patterns, necessary for retrieving
the most plausible similar objects. Our approach depends upon a table contains the break-points that
divide a Gaussian distribution in an arbitrary number of equiprobable regions. Each breakpoint has more
than one cardinality. A distance measure is used to decide the most plausible matching between strings of
symbolic words. The experimental results have shown that our approach improves detection accuracy.
Exploiting Dissimilarity Representations for Person Re-IdentificationRiccardo Satta
The document discusses person re-identification through dissimilarity representations. It proposes representing each person as a vector of dissimilarity values compared to visual prototypes, rather than traditional descriptors. This reduces storage requirements and allows extremely fast matching. The Multiple Component Dissimilarity framework is presented, which defines prototypes, and represents templates and queries as dissimilarity vectors for efficient matching in the dissimilarity space. Preliminary experiments applying this framework to a specific method show improvements in computational time and storage over the original method.
A New Method Based on MDA to Enhance the Face Recognition PerformanceCSCJournals
A novel tensor based method is prepared to solve the supervised dimensionality reduction problem. In this paper a multilinear principal component analysis(MPCA) is utilized to reduce the tensor object dimension then a multilinear discriminant analysis(MDA), is applied to find the best subspaces. Because the number of possible subspace dimensions for any kind of tensor objects is extremely high, so testing all of them for finding the best one is not feasible. So this paper also presented a method to solve that problem, The main criterion of algorithm is not similar to Sequential mode truncation(SMT) and full projection is used to initialize the iterative solution and find the best dimension for MDA. This paper is saving the extra times that we should spend to find the best dimension. So the execution time will be decreasing so much. It should be noted that both of the algorithms work with tensor objects with the same order so the structure of the objects has been never broken. Therefore the performance of this method is getting better. The advantage of these algorithms is avoiding the curse of dimensionality and having a better performance in the cases with small sample sizes. Finally, some experiments on ORL and CMPU-PIE databases is provided.
This document discusses using Constrained Local Models (CLM) for facial landmark localization and applications in pose estimation and facial expression classification. It describes:
1) How CLM models are trained using local image descriptors for each landmark region rather than a holistic texture model, and how the Subspace Constrained Mean Shift algorithm is used to fit the CLM to new images.
2) How the trained CLM can be applied to estimate head pose by inferring orientation from localized facial landmarks.
3) How facial expressions are classified based on detected Action Units (facial muscle movements) from CLM-localized landmarks.
Evaluation results are presented for the CLM landmark localization, pose estimation, and expression
MIXTURES OF TRAINED REGRESSION CURVESMODELS FOR HANDRITTEN ARABIC CHARACTER R...ijaia
In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We proceed then, by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.
2D Shape Reconstruction Based on Combined Skeleton-Boundary FeaturesCSCJournals
This paper proposes a new method for 2D shape reconstruction based on combining skeleton and boundary features. The method aims to mimic human perceptual processes by using both curvature properties of the shape boundary and structural properties of the shape skeleton. Junction points on the skeleton are used to identify likely protrusions, while boundary features like curvature, length and width are used to determine the strength of protrusions. Experiments show the reconstructed shapes match human perceptual judgments better than existing methods. The approach gives a stable reconstruction and is robust to noise.
VARIATIONAL MONTE-CARLO APPROACH FOR ARTICULATED OBJECT TRACKINGcscpconf
In this paper, we describe a novel variational Monte Carlo approach for modeling and tracking body parts of articulated objects. An articulated object (human target) is represented as a
dynamic Markov network of the different constituent parts. The proposed approach combines local information of individual body parts and other spatial constraints influenced by
neighboring parts. The movement of the relative parts of the articulated body is modeled with local information of displacements from the Markov network and the global information from other neighboring parts. We explore the effect of certain model parameters (including the number of parts tracked; number of Monte-Carlo cycles, etc.) on system accuracy and show that ourvariational Monte Carlo approach achieves better efficiency and effectiveness compared to
other methods on a number of real-time video datasets containing single targets
In this paper person identification is done based on sets of facial images. Each facial image is considered as the scattered point of logistic regression. The vertical distance of scattered point of facial image and the regression line is considered as the parameter to determine whether the image is of same person or not. The ratio of Euclidian distance (in terms of number of pixel of gray scale image based on ‘imtool’ of Matlab 13.0) between nasal and eye points are determined. The variance of the ration is considered another parameter to identify a facial image. The concept is combined with ghost image of Principal Component Analysis; where the mean square error and signal to noise ratio (SNR) in dB is considered as the parameters of detection. The combination of three methods, enhance the degree of accuracy compared to individual one.
Sparse representation based classification of mr images of brain for alzheime...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
This document discusses using a Direction-Length Code (DLC) to represent binary objects. The DLC is a "knowledge vector" that provides information about the direction and length of pixels in every direction of an object. Patterns over a 3x3 pixel array are generated to form a basic alphabet for representing digital images as spatial distributions of these patterns. The DLC compresses bi-level images while preserving shape information and allowing significant data reduction. It can serve as standard input for numerous shape analysis algorithms. Components of images are extracted from the DLC and used to accurately regenerate the original images, demonstrating the effectiveness of the DLC representation.
This document provides an overview of knowledge representation techniques and object recognition. It discusses syntax and semantics in representation, as well as descriptions, features, grammars, languages, predicate logic, production rules, fuzzy logic, semantic nets, and frames. It then covers statistical and cluster-based pattern recognition methods, feedforward and backpropagation neural networks, unsupervised learning including Kohonen feature maps, and Hopfield neural networks. The goal is to represent knowledge in a way that enables object classification and decision-making.
This document provides an overview of knowledge representation techniques and object recognition. It discusses syntax and semantics in representation, as well as descriptions, features, grammars, languages, predicate logic, production rules, fuzzy logic, semantic nets, and frames. It then covers statistical and cluster-based pattern recognition methods, feedforward and backpropagation neural networks, unsupervised learning including Kohonen feature maps, and Hopfield neural networks. The goal is to represent knowledge in a way that enables object classification and decision-making.
This document discusses face recognition using Fisher face analysis (LDA). It provides an overview of LDA and how it is used for face recognition. LDA works by finding a linear transformation that maximizes between-class variance and minimizes within-class variance to achieve better class separation. The document outlines the LDA algorithm which involves computing within-class and between-class scatter matrices to find discriminant vectors that project faces into a space where classes are well separated. It also mentions the ORL face database is used and provides references for further information.
Machine Learning Algorithms for Image Classification of Hand Digits and Face ...IRJET Journal
This document discusses machine learning algorithms for image classification using five different classification schemes. It summarizes the mathematical models behind each classification algorithm, including Nearest Class Centroid classifier, Nearest Sub-Class Centroid classifier, k-Nearest Neighbor classifier, Perceptron trained using Backpropagation, and Perceptron trained using Mean Squared Error. It also describes two datasets used in the experiments - the MNIST dataset of handwritten digits and the ORL face recognition dataset. The performance of the five classification schemes are compared on these datasets.
Performance analysis of chain code descriptor for hand shape classificationijcga
Feature Extraction is an important task for any Image processing application. The visual properties of any image are its shape, texture and colour. Out of these shape description plays important role in any image classification. The shape description method classified into two types, contour base and region based. The contour base method concentrated on the shape boundary line and the region based method considers whole area. In this paper, contour based, the chain code description method was experimented for different hand shape.
The chain code descriptor of various hand shapes was calculated and tested with different classifier such as k-nearest- neighbour (k-NN), Support vector machine (SVM) and Naive Bayes. Principal component analysis (PCA) was applied after the chain code description. The performance of SVM was found better than k-NN and Naive Bayes with recognition rate 93%.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...Waqas Tariq
Selection of inputs is one of the most substantial components of classification algorithms for data mining and pattern recognition problems since even the best classifier will perform badly if the inputs are not selected very well. Big data and computational complexity are main cause of bad performance and low accuracy for classical classifiers. In other words, the complexity of classifier method is inversely proportional with its classification efficiency. For this purpose, two hybrid classifiers have been developed by using both type-1 and type-2 fuzzy c-means clustering with cascaded a classifier. In this proposed classifier, a large number of data points are reduced by using fuzzy c-means clustering before applied to a classifier algorithm as inputs. The aim of this study is to investigate the effect of fuzzy clustering on well-known and useful classifiers such as artificial neural networks (ANN) and support vector machines (SVM). Then the role of positive effects of these proposed algorithms were investigated on applied different data sets.
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ARABIC HANDWRITTEN CHARACTER RECOGNITION USING STRUCTURAL SHAPE DECOMPOSITION
1. Signal & Image Processing : An International Journal (SIPIJ) Vol.8, No.2, April 2017
DOI : 10.5121/sipij.2017.8201 1
ARABIC HANDWRITTEN CHARACTER
RECOGNITION USING STRUCTURAL SHAPE
DECOMPOSITION
Abdullah A. Al-Shaher1
and Edwin R. Hancock2
1
Department of Computer and Information Systems, College of Business Studies,
Public Authority for Applied Education and Training, Kuwait
2
Department of Computer Science University of York, York, United Kingdom
ABSTRACT
This paper presents a statistical framework for recognising 2D shapes which are represented as an
arrangement of curves or strokes. The approach is a hierarchical one which mixes geometric and symbolic
information in a three-layer architecture. Each curve primitive is represented using a point-distribution
model which describes how its shape varies over a set of training data. We assign stroke labels to the
primitives and these indicate to which class they belong. Shapes are decomposed into an arrangement of
primitives and the global shape representation has two components. The first of these is a second point
distribution model that is used to represent the geometric arrangement of the curve centre-points. The second
component is a string of stroke labels that represents the symbolic arrangement of strokes. Hence each shape
can be represented by a set of centre-point deformation parameters and a dictionary of permissible stroke
label configurations. The hierarchy is a two-level architecture in which the curve models reside at the
nonterminal lower level of the tree. The top level represents the curve arrangements allowed by the
dictionary of permissible stroke combinations. The aim in recognition is to minimise the cross entropy
between the probability distributions for geometric alignment errors and curve label errors. We show how
the stroke parameters, shape-alignment parameters and stroke labels may be recovered by applying the
expectation maximization EM algorithm to the utility measure. We apply the resulting shape-recognition
method to Arabic character recognition.
KEYWORDS
point distribution models, expectation maximization algorithm, discrete relaxation, hierarchical mixture of
experts, Arabic scripts, handwritten characters
1. INTRODUCTION
The analysis and recognition of curved shapes has attracted considerable attention in the computer
vision literature. Current work is nicely exemplified by point distribution models [1] and
shape-contexts [2]. However, both of these methods are based on global shape-descriptors. This is
potentially a limitation since a new model must be acquired for each class of shape and this is an
inefficient process. An alternative and potentially more flexible route is to use a structural approach
to the problem, in which shapes are decomposed into arrangements of primitives. This idea was
central to the work of Marr [3]. Shape learning may then be decomposed into a two-stage process.
The first stage is to acquire a models of the variability is the distinct primitives. The second stage is
to learn the arrangements of the primitives corresponding to different shape classes.
2. Signal & Image Processing : An International Journal (SIPIJ) Vol.8, No.2, April 2017
2
Although this structural approach has found widespread use in the character recognition
community, it has not proved popular in the computer vision domain. The reason for this is that the
segmentation of shapes into stable primitives has proved to be an elusive problem. Hence, there is a
considerable literature on curve polygonalisation, segmentation and grouping. However, one of the
reasons that the structural approach has proved fragile is that it has been approached using
geometric rather than statistical methods. Hence, the models learned and the recognition results
obtained are highly sensitive to segmentation error. In order to overcome these problems, in this
paper we explore the use of probabilistic framework for recognition.
We focus on the problem of developing hierarchical shape models for handwritten Arabic
characters. These characters are decomposed into concave or convex strokes. Our statistical
learning architecture is reminiscent of the hierarchical mixture of experts algorithm. This is a
variant of the expectation maximisation algorithm, which can deal with hierarchically structured
models. The method was first introduced in 1994 by Jordan and Jacobs [4]. In its simplest form the
method models data using a doubly nested mixture model. At the top layer the mixture is over a set
of distinct object classes. This is sometimes referred to as the gating layer. At the lower level, the
objects are represented as a mixture over object subclasses. These sub-classes feed into the gating
later with predetermined weights. The parameters of the architecture reside in the sublayer, which
is frequently represented using a Gaussian mixture model. The hierarchical mixture of experts
algorithm provides a means of learning both the gating weights and the parameters of the Gaussian
mixture model.
Here our structural decomposition of 2D shapes is a hierarchical one which mixes geometric and
symbolic information. The hierarchy has a two-layer architecture. At the bottom layer we have
strokes or curve primitives. These fall into different classes. For each class the curve primitive is
represented using a point-distribution model [5] which describes how its shape varies over a set of
training data. We assign stroke labels to the primitives to distinguish their class identity. At the top
level of the hierarchy, shapes are represented as an arrangement of primitives. The representation
of the arrangement of primitives has two components. The first of these is a second point
distribution model that is used to represent how the arrangement of the primitive centre-points
varies over the training data. The second component is a dictionary of configurations of stroke
labels that represents the arrangements of strokes at a symbolic level. Recognition hence involves
assigning stroke symbols to curves primitives, and recovering both stroke and shape deformation
parameters. We present a probabilistic framework which can be for the purposes of
shape-recognition in the hierarchy. We apply the resulting shape-recognition method to Arabic
character recognition.
2. SHAPE REPRESENTATION
We are concerned with recognising a shape },...,{= 1 pwwW
rr
which consists of a set of p
ordered but unlabelled landmark points with 2D co-ordinate vectors 1w
r
, ...., pw
r
. The shape is
assumed to be segmented into a set of K non-overlapping strokes. Each stroke consists of a set of
consecutive landmark points. The set of points belonging to the stroke indexed k is kS . For each
stroke, we compute the mean position
i
kSik
k w
S
c
rr
∑∈
1
= (1)
The geometry of stroke arrangement is captured by the set of mean position vectors
},....{= 1 KccC
rr
.
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3
Our hierarchical model of the characters uses both geometric and symbolic representations of the
shapes. The models are constructed from training data. Each training pattern consists of a set of
landmark points that are segmented into strokes. We commence by specifying the symbolic
components of the representation. Each training pattern is assigned to shape class and each
component stroke is assigned to stroke class. The set of shape-labels is cΩ and the set of stroke
labels is sΩ . The symbolic structure of each shape is represented a permissible arrangement of
stroke-labels. For shapes of class cΩ∈ω the permissible arrangement of strokes is denoted by
>,...,=< 21
ωω
ω λλΛ (2)
We model the geometry of the strokes and stroke-centre arrangements using point distribution
models. To capture the shape variations, we use training data. The data consists of a set of shapes
which have been segmented into strokes. Let the th
t training pattern consist of the set of p
landmark co-ordinate vectors },......,{= 1 p
t
xxX
rr
. Each training pattern is segmented into strokes.
For the training pattern indexed t there are tK strokes and the index set of the points belonging
to the th
k stroke is t
kS . To construct the point distribution model for the strokes and stroke-centre
arrangements, we convert the point co-ordinates into long-vectors. For the training pattern indexed
t, the long-vector of stroke centres is TTt
L
TtTt
t cccX ))(,....,)(,)((= 21
rrr
. Similarly for the stroke
indexed k in the training pattern indexed t, the long-vector of co-ordinates is denoted by ktz , .
For examples shapes belonging to the class ω , to construct the stroke-centre point distribution
model we need to first compute the mean long vector
t
Tt
X
T
Y ∑∈ ωω
ω
1
= (3)
where ωT is the set of index patterns and the associated covariance matrix
T
tt
Tt
YXYX
T
))((
1
= ωω
ωω
ω −−Σ ∑∈
(4)
The eigenmodes of the stroke-centre covariance matrix are used to construct the point-distribution
model. First, the eigenvalues e of the stroke covariance matrix are found by solving the
eigenvalue equation 0|=| Ieω
ω −Σ where I is the LL 22 × identity matrix. The eigen-vector
iφ corresponding to the eigenvalue ω
ie is found by solving the eigenvector equation
ωωω
φφ iii e=Σ . According to Cootes and Taylor [6], the landmark points are allowed to undergo
displacements relative to the mean-shape in directions defined by the eigenvectors of the
covariance matrix ωΣ . To compute the set of possible displacement directions, the M most
significant eigenvectors are ordered according to the magnitudes of their corresponding
eigenvalues to form the matrix of column-vectors )|...||(= 21
ωωω
ω φφφ MΦ , where ωωω
Meee ,.....,, 21
is the order of the magnitudes of the eigenvectors. The landmark points are allowed to move in a
direction which is a linear combination of the eigenvectors. The updated landmark positions are
given by ωωω γΦ+YX =ˆ , where ωγ is a vector of modal co-efficients. This vector represents the
free-parameters of the global shape-model.
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4
This procedure may be repeated to construct a point distribution model for each stroke class. The
set of long vectors for strokes of class λ is }=|{= , λλλ
t
kktZT . The mean and covariance matrix
for this set of long-vectors are denoted by λY and λΣ and the associated modal matrix is λΦ .
The point distribution model for the stroke landmark points is λλλ γΦ+YZ =ˆ .
3. LEARNING MIXTURES OF PDM'S
In Cootes and Taylor’s method [5], learning involves extracting a single covariance matrix from the
sets of landmark points. Hence, the method can only reproduce variations in shape which can be
represented as linear deformations of the point positions. To reproduce more complex variations in
shape either a non-linear deformation or a series of local piecewise linear deformations must be
employed.
Here we adopt an approach based on mixtures of point-distributions [7]. Our reasons for adopting
this approach are twofold. First, we would like to be able to model more complex deformations by
using multiple modes of shape deformation. The need to do this may arise in a number of situations.
The first of these is when the set of training patterns contains examples from different classes of
shape. In other words, we are confronted with an unsupervised learning problem and need to
estimate both the mean shape and the modes of variation for each class of object. The second
situation is where the shape variations in the training data can not be captured by a single
covariance matrix, and a mixture is required.
Our approach is based on fitting a Gaussian mixture model to the set of training examples. We
commence by assuming that the individual examples in the training set are conditionally
independent of one-another. We further assume that the training data can be represented by a set of
shape-classes Ω. Each shape-class ω has its own mean point-pattern Yω and covariance matrix
Σω. With these ingredients, the likelihood function for the set of training patterns is
),|(),...1,(
1
ω
ω
ω Σ== ∏ ∑= Ω∈
T
t
tt YXpTtXp (5)
where ),|( ωω ΣYXp t is the probability distribution for drawing the training pattern tX from the
shape-class ω.
According to the EM algorithm, we can maximise the likelihood function above, by adopting a
two-step iterative process. The process revolves around the expected log-likelihood function
),|(ln),,|()|( )1()1()()(
1
)()1( ++
Ω∈=
+
ΣΣ∈= ∑∑ nn
t
nn
t
T
t
nn
L YXPYXtPCCQ ωωωω
ω
ω (6)
where Y
(n)
ω and Σ
(n)
ω are the estimates of the mean pattern-vector and the covariance matrix for
class ω at iteration n of the algorithm. The quantity ( ∈ | ,
(
, Σ
(
is the a posteriori
probability that the training pattern Xt belongs to the class ω at iteration n of the algorithm. The
probability density for the pattern-vectors associated with the shape-class ω, specified by the
estimates of the mean and covariance at iteration n+1 is ( |
(
, Σ
(
. In the M, or
5. Signal & Image Processing : An International Journal (SIPIJ) Vol.8, No.2, April 2017
5
maximisation, step of the algorithm the aim is to find revised estimates of the mean pattern-vector
and covariance matrix which maximise the expected log-likelihood function. The update equations
depend on the adopted model for the class-conditional probability distributions for the
pattern-vectors.
In the E, or expectation, step the a posteriori class membership probabilities are updated. This is
done by applying the Bayes formula to the class-conditional density. At iteration n+1, the revised
estimate is
,
(
, Σ
(
=
(
, Σ
( (
∑ ( |
(
, Σ
( (
∈
(7)
where
),,|(
1 )()(
1
)1( nn
T
t
t
n
YXtP
T
ωωω ωπ ∑∈= ∑=
+
(8)
3.1 Mixtures of Gaussians
We now consider the case when the class conditional density for the training patterns is Gaussian.
Here we assume that the pattern vectors are distributed according to the distribution
−∑−−
∑
=∑ −
)()()(
2
1
exp
||)2(
1
),|( )(1)()(
)(
)()( n
t
nTn
tnL
nn
t YXYXYXP ωωω
ω
ωω
π
(9)
At iteration n+1 of the EM algorithm the revised estimate of the mean pattern vector for class ω is
t
nn
T
t
t
n
XYXtPY ),,|( )()(
1
)1(
ωωω ω ∑∈= ∑=
+
(10)
while the revised estimate of the covariance matrix is
Tn
t
T
t
n
t
nn
t
n
YXYXYXtP ))()(,,|( )(
1
)()()()1(
ωωωωω ω −−∑∈=∑ ∑=
+
(11)
When the algorithm has converged, then the point-distribution models for the different classes may
be constructed off-line using the procedure outlined in Section 3. For the class ω, we denote the
eigenvector matrix by Φω.
4. HIERARCHICAL ARCHITECTURE
With the stroke and shape point distribution models to hand, our recognition method proceeds in a
hierarchical manner. To commence, we make maximum likelihood estimates of the best-fit
parameters of each stroke-model to each set of stroke-points. The best-fit parameters k
λγ of the
stroke-model with class-label λ to the set of points constituting the stroke indexed k is
),|(maxarg= γγ λ
γ
λ Φk
k
zp (12)
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6
We use the best-fit parameters to assign a label to each stroke. The label is that which has maximum
a posteriori probability given the stroke parameters. The label assigned to the stroke indexed k is
),,|(maxarg= λλ
λ
γ Φ
Ω∈
k
s
k zlPl (13)
In practice, we assume that the fit error residuals follow a Gaussian distribution. As a result, the
class label is that associated with the minimum squared error. This process is repeated for each
stroke in turn. The class identity of the set of strokes is summarised the string of assigned
stroke-labels
>,.....,=< 21 llL (14)
Hence, the input layer is initialised using maximum likelihood stroke parameters and maximum a
posteriori probability stroke labels.
The shape-layer takes this information as input. The goal of computation in this second layer is to
refine the configuration of stroke labels using global constraints on the arrangement of strokes to
form consistent shapes. The constraints come from both geometric and symbolic sources. The
geometric constraints are provided by the fit of a stroke-centre point distribution model. The
symbolic constraints are provide by a dictionary of permissible stroke-label strings for different
shapes.
The parameters of the stroke-centre point distribution model are found using the EM algorithm [8].
Here we borrow ideas from the hierarchical mixture of experts algorithm, and pose the recovery of
parameters as that of maximising a gated expected log-likelihood function for the distribution of
stroke-centre alignment errors ),|( ωω ΓΦXp . The likelihood function is gated by two sets of
probabilities. The first of these are the a posteriori probabilities ),,|( ωλωλ
ω
γλ
kk
kk zP Φ of the
individual strokes. The second are the conditional probabilities )|( ωΛLP of the assigned
stroke-label string given the dictionary of permissible configurations for shapes of class ω . The
expected log-likelihood function is given by
),|(ln)},,|(){|(= ωωωλωλ
ω
ω
ω
γλ ΓΦΦΛ ∏∑Ω∈
XpzPLPL
kk
kk
kc
(15)
The optimal set of stroke-centre alignment parameters satisfies the condition
),|(ln)},,|(){|(maxarg=*
ωωωλωλ
ω
ωω γλ ΓΦΦΛΓ ∏Γ
XpzPLP
kk
kk
k
(16)
From the maximum likelihood alignment parameters we identify the shape-class of maximum a
posteriori probability. The class is the one for which
),,|(maxarg= **
ωω
ω
ωω ΓΦ
Ω∈
XP
c
(17)
The class identity of the maximum a posteriori probability shape is passed back to the
stroke-layer of the architecture. The stroke labels can then be refined in the light of the consistent
assignments for the stroke-label configuration associated with the shape-class ω .
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7
)|),((),,|(maxarg= ωλ
λ
λγλ ΛΦ
Ω∈
kLPzPl k
lk
s
k (18)
Finally, the maximum likelihood parameters for the strokes are refined
)),,|(maxarg= *
ω
γ
γγ ΓΦ
klkk zp
r
(19)
These labels are passed to the shape-layer and the process is iterated to convergence.
5. MODELS
In this section we describe the probability distributions used to model the point-distribution
alignment process and the symbol assignment process.
5.1 Point-set Alignment
To develop a useful alignment algorithm we require a model for the measurement process. Here we
assume that the observed position vectors, i.e. iw
r
are derived from the model points through a
Gaussian error process. According to our Gaussian model of the alignment errors,
)]()(
2
1
[exp
2
1
=),|( 2 λωωλωωλλ γγ
σπσ
γ Φ−−Φ−−−Φ YzYzzp k
T
kk
rrr
(20)
where 2
σ is the variance of the point-position errors which for simplicity are assumed to be
isotropic. The maximum likelihood parameter vector is given by
))(()(
2
1
= 1
ωωωωωλγ Yzk
TTk
−Φ+ΦΦΦ − r
(21)
A similar procedure may be applied to estimate the parameters of the stroke centre point
distribution model.
5.2 Label Assignment
The distribution of label errors is modelled using the method developed by Hancock and Kittler [9].
To measure the degree of error we measure the Hamming distance between the assigned string of
labels L and the dictionary item Λ . The Hamming distance is given by
ωλω δ
iil
K
i
LH
,
1=
=),( ∑Λ (22)
where δ is the DiracDelta function. With the Hamming distance to hand, the probability of the
assigned string of labels L given the dictionary item Λ is
)],([exp=)|( ωω Λ−Λ LHkKLP pp (23)
8. Signal & Image Processing : An International Journal (SIPIJ) Vol.8, No.2, April 2017
8
where K
p pK )(1= − and
p
p
kp
−1
ln= (24)
are constants determined by the label-error probability p .
6. EXPERIMENT
We have evaluated our approach on sets of Arabic characters. Figure 1 shows some of the data used
for the purpose of learning and recognition. In total we use, 18 distinct classes of Arabic characters
and for each class there are 200 samples. The landmarks are placed uniformly along the length of
the characters. The top row shows the example pattern used for training a representative set of
shape-classes. The second row of the figure shows the configuration of mean strokes for each class.
Finally, the third row shows the stroke centre-points.
Figure 1: Raw 1 shows sample training sets. Raw 2 shows stroke mean shapes, Raw 3 shows stroke
arrangements
Figure 2: Learning convergence rate for stroke-shape classes as a function per iteration no.
Turning the attention to the learning results for 8 stroke-shape classes. Figure 2 illustrates the
average a posteriori stroke-class probabilities for different components. The different curves are
for different components shown in figure 1. It is clear from the plot that stroke-classe compnents
are convering rapidly in a few iterations.
Table 1 shows the results for a series of recognition experiments. The top raw of the table shows the
character shape class. For each shape-class, we have used 200 test patterns to evaluate the
recognition performance. These patterns are separate from the data used in training. The raws of the
table compare the recognition results obtained using a global point-distribution model to represent
9. Signal & Image Processing : An International Journal (SIPIJ) Vol.8, No.2, April 2017
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the character shape and using the stroke decomposition model described in this paper. We list the
number of correctly identified patterns. In the case of the global PDM, the average recognition
accuracy is 93.2% over the different character classes. However, in the case of the stroke
decomposition method the accuracy is 97%. Hence, the new method offers a performance gain of
some 5%.
Table 1. Recognition Rate for shape-classes (Full Character, Stroke-based arrangements )
Figure 3 examines the iterative qualities of the method. Here we plot the a posteriori class
probability as a function of iteration number when recognition of characters of a specific class is
attempted. The different curves are for different classes. The plot shows that the method converges
in about six iterations and that the probabilities of the subdominant classes tend to zero.
Figure 3. Alignment convergence rate as a function per iteration number
Figure 1. Alignment. First raw shows hierarchical strokes:(a)iteration 1, (b)iteration 2, (c)iteration 3,
(d)iteration 4, (e)iteration 5. Second raw represents character models:(a)iteration 1, (b)iteration 2, (c)iteration
3, (d)iteration 4, (d)iteration 8
Figure 4 compares the fitting of the stroke model (top row) and a global PDM (bottom row) with
iteration number. It is clear that the results obtained with the stroke model are better than those
obtained with the global PDM, which develops erratic local deformations. Finally, we demonstrate
in Figure 4 comparison of stroke decomposition and character with respect to recognition rate as a
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function of point position error. Stroke decomposition methods shows a better performance when
points are moved randomly away of their original location.
Figure 5. Recognition rate with respect to random point position.
Table 2 shows the shape-classes label replacement process for shapes segmented into 4 strokes.
The table clearly shows the correct and incorrect label assignments for each shape-class as a
function per iteration number. The stroke-class label replacement hypothesis converges in a fewer
iterations.
Table 2: Stroke-Shape class label replacement error as a function per iteration number
7. CONCLUSION
In This Paper, we have described a hierarchical probabilistic framework for shape recognition via
stroke decomposition. The structural component of the method is represented using symbolic
dictionaries, while geometric component is represented using Point Distribution Models.
Experiments on Arabic character recognition reveal that the method offers advantages over a global
PDM.
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