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.
ARABIC HANDWRITTEN CHARACTER RECOGNITION USING STRUCTURAL SHAPE DECOMPOSITIONsipij
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.
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.
MC0083 – Object Oriented Analysis &. Design using UML - Master of Computer Sc...Aravind NC
The document discusses several object-oriented concepts and methodologies. It defines objects as instances of classes that can perform related activities. Encapsulation is achieved through classes that expose public methods while hiding internal details. Polymorphism allows the same operations to be performed on different types of objects. It also explains the Object Modeling Technique (OMT) methodology, including its object model, dynamic model, and functional model. The Booch methodology is also briefly described.
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.
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.
The document proposes a one-dimensional signature representation method for recognizing three-dimensional convex objects that is invariant to position, orientation, and scale. The method involves translating an input 3D object to the centroid, rotating to align the principal axis, converting to spherical coordinates, taking the 2D Fourier transform magnitude spectrum, and averaging into a 1D signature vector. Experimental results using simple synthesized 3D convex objects show the signature distances between objects of different shapes are larger than distances between similar objects with different positions, orientations, or scales, demonstrating the proposed signature's discriminative and invariant properties.
ARABIC HANDWRITTEN CHARACTER RECOGNITION USING STRUCTURAL SHAPE DECOMPOSITIONsipij
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.
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.
MC0083 – Object Oriented Analysis &. Design using UML - Master of Computer Sc...Aravind NC
The document discusses several object-oriented concepts and methodologies. It defines objects as instances of classes that can perform related activities. Encapsulation is achieved through classes that expose public methods while hiding internal details. Polymorphism allows the same operations to be performed on different types of objects. It also explains the Object Modeling Technique (OMT) methodology, including its object model, dynamic model, and functional model. The Booch methodology is also briefly described.
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.
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.
The document proposes a one-dimensional signature representation method for recognizing three-dimensional convex objects that is invariant to position, orientation, and scale. The method involves translating an input 3D object to the centroid, rotating to align the principal axis, converting to spherical coordinates, taking the 2D Fourier transform magnitude spectrum, and averaging into a 1D signature vector. Experimental results using simple synthesized 3D convex objects show the signature distances between objects of different shapes are larger than distances between similar objects with different positions, orientations, or scales, demonstrating the proposed signature's discriminative and invariant properties.
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.
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
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.
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.
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.
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.
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.
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.
Semi-Supervised Discriminant Analysis Based On Data Structureiosrjce
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
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.
Template matching is a technique used in computer vision to find sub-images in a target image that match a template image. It involves moving the template over the target image and calculating a measure of similarity at each position. This is computationally expensive. Template matching can be done at the pixel level or on higher-level features and regions. Various measures are used to quantify the similarity or dissimilarity between images during the matching process. Template matching has applications in areas like object detection but faces challenges with noise, occlusions, and variations in scale and rotation.
The document compares using Euclidean distance versus Mahalanobis distance for supervised self-organizing maps in a rail defect classification application. It finds that using Mahalanobis distance, which accounts for variance differences across input dimensions, leads to better classification results, especially when using a partitioning approach that separates the multi-class problem into binary sub-problems. Specifically, the Mahalanobis distance improved classification rates from 92.8% to 94.1% for a global classifier, and from 90% to 95% for a partitioning classifier.
A NOVEL FEATURE SET FOR RECOGNITION OF SIMILAR SHAPED HANDWRITTEN HINDI CHARA...cscpconf
This document describes a study that uses machine learning algorithms to recognize similar shaped handwritten Hindi characters. It extracts 85 features from each character image based on geometry. Four machine learning algorithms (Bayesian Network, RBFN, MLP, C4.5 Decision Tree) are trained on datasets containing samples of a target character pair and evaluated based on precision, misclassification rate, and model build time. Feature selection techniques are also used to reduce the feature set dimensionality before classification. Experimental results show that different algorithms perform best depending on the feature set and number of samples used for training.
Eugen Zaharescu-STATEMENT OF RESEARCH INTERESTEugen Zaharescu
- The document is a research statement from Dr. Eugen ZAHARESCU that outlines his interests in mathematical morphology, image analysis, and ontology generation.
- His research has included extending mathematical morphology theory to multivariate images and exploring morphological operators in logarithmic image processing.
- More recently, he has developed algorithms and tools for machine learning, computer vision, and image understanding by applying mathematical concepts from morphology.
FIDUCIAL POINTS DETECTION USING SVM LINEAR CLASSIFIERScsandit
Currently, there is a growing interest from the scientific and/or industrial community in respect
to methods that offer solutions to the problem of fiducial points detection in human faces. Some
methods use the SVM for classification, but we observed that some formulations of optimization
problems were not discussed. In this article, we propose to investigate the performance of
mathematical formulation C-SVC when applied in fiducial point detection system. Futhermore,
we explore new parameters for training the proposed system. The performance of the proposed
system is evaluated in a fiducial points detection problem. The results demonstrate that the
method is competitive.
AUTOMATIC TRAINING DATA SYNTHESIS FOR HANDWRITING RECOGNITION USING THE STRUC...ijaia
The paper presents a novel technique called “Structural Crossing-Over” to synthesize qualified data for training machine learning-based handwriting recognition. The proposed technique can provide a greater variety of patterns of training data than the existing approaches such as elastic distortion and tangentbased affine transformation. A couple of training characters are chosen, then they are analyzed by their similar and different structures, and finally are crossed over to generate the new characters. The experiments are set to compare the performances of tangent-based affine transformation and the proposed approach in terms of the variety of generated characters and percent of recognition errors. The standard
MNIST corpus including 60,000 training characters and 10,000 test characters is employed in the
experiments. The proposed technique uses 1,000 characters to synthesize 60,000 characters, and then uses
these data to train and test the benchmark handwriting recognition system that exploits Histogram of
Gradient: HOG as features and Support Vector Machine: SVM as recognizer. The experimental result
yields 8.06% of errors. It significantly outperforms the tangent-based affine transformation and the
original MNIST training data, which are 11.74% and 16.55%, respectively.
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.
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.
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.
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
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.
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
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.
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.
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.
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.
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.
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.
Semi-Supervised Discriminant Analysis Based On Data Structureiosrjce
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
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.
Template matching is a technique used in computer vision to find sub-images in a target image that match a template image. It involves moving the template over the target image and calculating a measure of similarity at each position. This is computationally expensive. Template matching can be done at the pixel level or on higher-level features and regions. Various measures are used to quantify the similarity or dissimilarity between images during the matching process. Template matching has applications in areas like object detection but faces challenges with noise, occlusions, and variations in scale and rotation.
The document compares using Euclidean distance versus Mahalanobis distance for supervised self-organizing maps in a rail defect classification application. It finds that using Mahalanobis distance, which accounts for variance differences across input dimensions, leads to better classification results, especially when using a partitioning approach that separates the multi-class problem into binary sub-problems. Specifically, the Mahalanobis distance improved classification rates from 92.8% to 94.1% for a global classifier, and from 90% to 95% for a partitioning classifier.
A NOVEL FEATURE SET FOR RECOGNITION OF SIMILAR SHAPED HANDWRITTEN HINDI CHARA...cscpconf
This document describes a study that uses machine learning algorithms to recognize similar shaped handwritten Hindi characters. It extracts 85 features from each character image based on geometry. Four machine learning algorithms (Bayesian Network, RBFN, MLP, C4.5 Decision Tree) are trained on datasets containing samples of a target character pair and evaluated based on precision, misclassification rate, and model build time. Feature selection techniques are also used to reduce the feature set dimensionality before classification. Experimental results show that different algorithms perform best depending on the feature set and number of samples used for training.
Eugen Zaharescu-STATEMENT OF RESEARCH INTERESTEugen Zaharescu
- The document is a research statement from Dr. Eugen ZAHARESCU that outlines his interests in mathematical morphology, image analysis, and ontology generation.
- His research has included extending mathematical morphology theory to multivariate images and exploring morphological operators in logarithmic image processing.
- More recently, he has developed algorithms and tools for machine learning, computer vision, and image understanding by applying mathematical concepts from morphology.
FIDUCIAL POINTS DETECTION USING SVM LINEAR CLASSIFIERScsandit
Currently, there is a growing interest from the scientific and/or industrial community in respect
to methods that offer solutions to the problem of fiducial points detection in human faces. Some
methods use the SVM for classification, but we observed that some formulations of optimization
problems were not discussed. In this article, we propose to investigate the performance of
mathematical formulation C-SVC when applied in fiducial point detection system. Futhermore,
we explore new parameters for training the proposed system. The performance of the proposed
system is evaluated in a fiducial points detection problem. The results demonstrate that the
method is competitive.
AUTOMATIC TRAINING DATA SYNTHESIS FOR HANDWRITING RECOGNITION USING THE STRUC...ijaia
The paper presents a novel technique called “Structural Crossing-Over” to synthesize qualified data for training machine learning-based handwriting recognition. The proposed technique can provide a greater variety of patterns of training data than the existing approaches such as elastic distortion and tangentbased affine transformation. A couple of training characters are chosen, then they are analyzed by their similar and different structures, and finally are crossed over to generate the new characters. The experiments are set to compare the performances of tangent-based affine transformation and the proposed approach in terms of the variety of generated characters and percent of recognition errors. The standard
MNIST corpus including 60,000 training characters and 10,000 test characters is employed in the
experiments. The proposed technique uses 1,000 characters to synthesize 60,000 characters, and then uses
these data to train and test the benchmark handwriting recognition system that exploits Histogram of
Gradient: HOG as features and Support Vector Machine: SVM as recognizer. The experimental result
yields 8.06% of errors. It significantly outperforms the tangent-based affine transformation and the
original MNIST training data, which are 11.74% and 16.55%, respectively.
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.
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.
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.
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
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.
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.
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.
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
1) The document proposes a penalized likelihood method using a penalty function like SCAD to perform simultaneous variable selection and parameter estimation in structural equation models (SEMs).
2) The method considers a general SEM where latent variables are linearly regressed on themselves with a coefficient matrix, avoiding the need to specify outcome and explanatory latent variables. Selecting nonzero coefficients in the matrix identifies the structure of the latent variable model.
3) Under regularity conditions, the consistency and oracle properties of the proposed penalized maximum likelihood estimators are established. An expectation-conditional maximization algorithm is developed for computation.
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
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.
The document proposes a new method for pose-consistent segmentation of 3D shapes based on a quantum mechanical feature descriptor called the Wave Kernel Signature (WKS). The method groups points on a shape's surface where quantum particles at different energy levels have similar probabilities of being measured. It learns clusters of points from multiple poses during training then segments new poses by assigning points to the most likely cluster. Experimental results show the segments agree with human intuition and labels are consistently transferred across poses, demonstrating the method is robust to noise and useful for shape retrieval.
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.
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.
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.
The Positive Effects of Fuzzy C-Means Clustering on Supervised Learning Class...CSCJournals
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.
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.
Symbol Based Modulation Classification using Combination of Fuzzy Clustering ...CSCJournals
Most of approaches for recognition and classification of modulation have been founded on modulated signal’s components. In this paper, we develop an algorithm using fuzzy clustering and consequently hierarchical clustering algorithms considering the constellation of the received signal to identify the modulation types of the communication signals automatically. The simulation that has been conducted shows high capability of this method for recognition of modulation levels in the presence of noise and also, this method is applicable to digital modulations of arbitrary size and dimensionality. In addition this classification finds the decision boundary of the signal which is critical information for bit detection.
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.
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2. 40 Computer Science & Information Technology (CS & IT)
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.
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
ρρ
which consists of a set of p
ordered but unlabelled landmark points with 2D co-ordinate vectors 1w
ρ
, ...., pw
ρ
. The shape is
assumed to be segmented into a set of K non-overlapping strokes. Each stroke consists of a set
3. Computer Science & Information Technology (CS & IT) 41
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
ρρ
∑∈
1
= (1)
The geometry of stroke arrangement is captured by the set of mean position vectors
},....{= 1 KccC
ρρ
.
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
ρρ
. 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
ρρρ
. 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)
4. 42 Computer Science & Information Technology (CS & IT)
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.
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 .
We have recently described how a mixture of point-distribution models may be fitted to samples
of shapes. The method is based on the EM algorithm and can be used to learn point distribution
models for both the stroke and shape classes in an unsupervised manner. We have used this
method to learn the mean shapes and the modal matrices for the strokes. More details of the
method are found in [7].
3. 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 (5)
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
5. Computer Science & Information Technology (CS & IT) 43
),,|(maxarg= λλ
λ
γ Φ
Ω∈
k
s
k zlPl (6)
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 (7)
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
(8)
The optimal set of stroke-centre alignment parameters satisfies the condition
),|(ln)},,|(){|(maxarg=*
ωωωλωλ
ω
ωω γλ ΓΦΦΛΓ ∏Γ
XpzPLP
kk
kk
k
(9)
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
(10)
6. 44 Computer Science & Information Technology (CS & IT)
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 .
)|),((),,|(maxarg= ωλ
λ
λγλ ΛΦ
Ω∈
kLPzPl k
lk
s
k (11)
Finally, the maximum likelihood parameters for the strokes are refined
)),,|(maxarg= *
ω
γ
γγ ΓΦ
klkk zp
ρ
(12)
These labels are passed to the shape-layer and the process is iterated to convergence.
4. MODELS
In this section we describe the probability distributions used to model the point-distribution
alignment process and the symbol assignment process.
4.1 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
ρ
are derived from the model points through a
Gaussian error process. According to our Gaussian model of the alignment errors,
)]()(12[exp12=),|( 2
λωωλωωλλ γγσπσγ Φ−−Φ−−−Φ YzYzzp k
T
kk
ρρρ
(13)
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 − ρ
(14)
A similar procedure may be applied to estimate the parameters of the stroke centre point
distribution model.
4.2 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 (15)
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 (16)
7. Computer Science & Information Technology (CS & IT) 45
where
K
p pK )(1= − and
p
p
kp
−1
ln= (17)
are constants determined by the label-error probability p .
5. 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
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 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 )
8. 46 Computer Science & Information Technology (CS & IT)
Figure 2 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 1. Alignment convergence rate as a function per iteration number
Figure 2. 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 3 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 function of point position error. Stroke decomposition methods shows a
better performance when points are moved randomly away of their original location.
Figure 4. Recognition rate with respect to random point position
9. Computer Science & Information Technology (CS & IT) 47
6. 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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