This document discusses pixel relationships and neighborhood concepts in digital images. It defines a pixel and pixel connectivity. There are different types of pixel neighborhoods, including 4-neighbor, 8-neighbor, and diagonal neighbors. Connected components are sets of pixels that are connected based on pixel adjacency. Algorithms can label connected components and identify distinct image regions. Various distance measures quantify how close pixels are, such as Euclidean, Manhattan, and chessboard distances. Arithmetic and logical operators can combine pixel values from different images. Neighborhood operations apply functions to pixels based on their values and those of nearby pixels.
The document discusses basic relationships between pixels in digital images. It defines that a pixel has 4 horizontal and vertical neighbors, called 4-neighbors. It also has 4 diagonal neighbors, and together with the 4-neighbors they form the 8-neighbors of a pixel. Adjacency between pixels is defined based on 4, 8 or m-connectivity depending on pixel intensity values. Connectivity and paths between pixels are also described. Regions in an image are defined as connected subsets of pixels, and region boundaries are pixels adjacent to the complement of the region.
This document discusses different types of distance measures. It defines four axioms that a distance function must satisfy: being positive, only equal to 0 if points are identical, symmetric, and satisfying the triangle inequality. There are two major classes of distance measures - Euclidean and non-Euclidean. Euclidean distances are based on the location of points in a space, while non-Euclidean distances are based on other point properties. Examples of different distance measures are provided, including L1, L2, Jaccard, cosine, edit, and Hamming distances.
Distance is a numerical description of how far apart objects are. In mathematics, a distance function or metric describes distance in a generalized way and must satisfy specific rules. There are various ways to define and calculate distance between points, objects, and sets depending on the context, such as Euclidean distance, taxicab distance, or Hausdorff distance. Distance is an important concept in fields like physics, geometry, and graph theory.
Diameter Estimation for Very Large GraphsGianni Amati
A highly efficient and effective algorithm to estimate diameter on very large graphs. In order to efficiently provide good approximations to the size of the neighborhood set of any node, we refer to the MinHash Signatures approach to derive compressed representations of large sparse datasets but preserving similarity. The technique, called MinHash Signature Estimation (MHSE), exploits the similarity between signatures to estimate the size of the neighborhood function.
We compare MHSE with HyperANF, which is considered the state of art approach for the estimation of the effective diameter of a very large graph.
Performing both parametric (t-test) and non-parametric (Wilcoxon) statistical tests on residuals for average distance, effective diameter and number of connected pairs, the p-values show that MHSE is more statistically significant than HyperANF. On the other hand, we show that MHSE is a very simple and easily distributable algorithm.
In addition, by the property of the signatures to preserve similarity between neighborhoods of nodes, the algorithm can be suitably applied to allow to search and estimate the overlapping size of the most similar neighborhood at different distances.
Iaetsd vlsi implementation of gabor filter based image edge detectionIaetsd Iaetsd
This document describes a VLSI implementation of an edge detection technique using Gabor filtering and rough clustering. The proposed technique smoothes images using Gabor filtering and performs edge detection using rough clustering. It was tested on various images and compared to other edge detection methods. The technique achieved noise-free and robust edge detection results. Finally, the technique was implemented in Verilog HDL and tested on a Xilinx FPGA for VLSI implementation.
Otsu thresholding is an effective thresholding method for images with low signal-to-noise ratios and low contrast. It assumes a bimodal histogram with two peaks, foreground and background, and finds a threshold that minimizes intra-class variance. 2D Otsu thresholding uses a joint 2D histogram of pixel values and local neighborhood averages to find an optimal threshold vector, improving segmentation especially for noisy images. The algorithm calculates the 2D histogram, finds probabilities and mean values, and selects the threshold pair that maximizes between-class variance. On a noisy test image, 2D Otsu thresholding produces a clean binary segmentation with the threshold pair (171, 171).
1. Images can be represented as matrices, with each entry containing the intensity of the corresponding pixel. Blurring can be modeled as a linear operation on the image matrix using a blurring matrix A.
2. Convolution is used to calculate the blurred image, with each blurred pixel value being a weighted sum of neighboring pixel values in the original image. This allows the blurring matrix A to be constructed from the point spread function (PSF).
3. For separable blur, where the PSF can be written as an outer product, the large blurring matrix A can be represented more compactly using the Kronecker product of smaller horizontal and vertical blur matrices.
This document discusses pixel relationships and neighborhood concepts in digital images. It defines a pixel and pixel connectivity. There are different types of pixel neighborhoods, including 4-neighbor, 8-neighbor, and diagonal neighbors. Connected components are sets of pixels that are connected based on pixel adjacency. Algorithms can label connected components and identify distinct image regions. Various distance measures quantify how close pixels are, such as Euclidean, Manhattan, and chessboard distances. Arithmetic and logical operators can combine pixel values from different images. Neighborhood operations apply functions to pixels based on their values and those of nearby pixels.
The document discusses basic relationships between pixels in digital images. It defines that a pixel has 4 horizontal and vertical neighbors, called 4-neighbors. It also has 4 diagonal neighbors, and together with the 4-neighbors they form the 8-neighbors of a pixel. Adjacency between pixels is defined based on 4, 8 or m-connectivity depending on pixel intensity values. Connectivity and paths between pixels are also described. Regions in an image are defined as connected subsets of pixels, and region boundaries are pixels adjacent to the complement of the region.
This document discusses different types of distance measures. It defines four axioms that a distance function must satisfy: being positive, only equal to 0 if points are identical, symmetric, and satisfying the triangle inequality. There are two major classes of distance measures - Euclidean and non-Euclidean. Euclidean distances are based on the location of points in a space, while non-Euclidean distances are based on other point properties. Examples of different distance measures are provided, including L1, L2, Jaccard, cosine, edit, and Hamming distances.
Distance is a numerical description of how far apart objects are. In mathematics, a distance function or metric describes distance in a generalized way and must satisfy specific rules. There are various ways to define and calculate distance between points, objects, and sets depending on the context, such as Euclidean distance, taxicab distance, or Hausdorff distance. Distance is an important concept in fields like physics, geometry, and graph theory.
Diameter Estimation for Very Large GraphsGianni Amati
A highly efficient and effective algorithm to estimate diameter on very large graphs. In order to efficiently provide good approximations to the size of the neighborhood set of any node, we refer to the MinHash Signatures approach to derive compressed representations of large sparse datasets but preserving similarity. The technique, called MinHash Signature Estimation (MHSE), exploits the similarity between signatures to estimate the size of the neighborhood function.
We compare MHSE with HyperANF, which is considered the state of art approach for the estimation of the effective diameter of a very large graph.
Performing both parametric (t-test) and non-parametric (Wilcoxon) statistical tests on residuals for average distance, effective diameter and number of connected pairs, the p-values show that MHSE is more statistically significant than HyperANF. On the other hand, we show that MHSE is a very simple and easily distributable algorithm.
In addition, by the property of the signatures to preserve similarity between neighborhoods of nodes, the algorithm can be suitably applied to allow to search and estimate the overlapping size of the most similar neighborhood at different distances.
Iaetsd vlsi implementation of gabor filter based image edge detectionIaetsd Iaetsd
This document describes a VLSI implementation of an edge detection technique using Gabor filtering and rough clustering. The proposed technique smoothes images using Gabor filtering and performs edge detection using rough clustering. It was tested on various images and compared to other edge detection methods. The technique achieved noise-free and robust edge detection results. Finally, the technique was implemented in Verilog HDL and tested on a Xilinx FPGA for VLSI implementation.
Otsu thresholding is an effective thresholding method for images with low signal-to-noise ratios and low contrast. It assumes a bimodal histogram with two peaks, foreground and background, and finds a threshold that minimizes intra-class variance. 2D Otsu thresholding uses a joint 2D histogram of pixel values and local neighborhood averages to find an optimal threshold vector, improving segmentation especially for noisy images. The algorithm calculates the 2D histogram, finds probabilities and mean values, and selects the threshold pair that maximizes between-class variance. On a noisy test image, 2D Otsu thresholding produces a clean binary segmentation with the threshold pair (171, 171).
1. Images can be represented as matrices, with each entry containing the intensity of the corresponding pixel. Blurring can be modeled as a linear operation on the image matrix using a blurring matrix A.
2. Convolution is used to calculate the blurred image, with each blurred pixel value being a weighted sum of neighboring pixel values in the original image. This allows the blurring matrix A to be constructed from the point spread function (PSF).
3. For separable blur, where the PSF can be written as an outer product, the large blurring matrix A can be represented more compactly using the Kronecker product of smaller horizontal and vertical blur matrices.
This document provides an overview of image deblurring techniques. It discusses how digital images can be represented as matrices, with each pixel corresponding to an entry in the matrix. A linear model is presented for how a sharp, ideal image (X) becomes blurred (B) through a blurring matrix (A) such that Ax=b. Point spread functions are introduced to describe how a point source becomes blurred and these are used to construct the columns of the blurring matrix A. The document concludes with a simple example of applying these concepts to a small test image.
This document discusses image restoration techniques. It defines image restoration as the process of taking a degraded image and estimating the original clean image. Common types of degradation include motion blur and noise. The document outlines the image formation process and degradation model both in continuous and discrete domains. It describes how degradation can be modeled as a convolution of the original image with a point spread function representing the blurring plus additive noise. The properties of linearity, homogeneity, and position invariance of degradation operators are also covered. Frequency domain techniques and references on image restoration are mentioned.
Optimization algorithms for solving computer vision problemsKrzysztof Wegner
The document discusses optimization algorithms for solving computer vision problems. It describes how computer vision problems can be formulated as energy minimization problems over pixel labels. Specific examples of segmentation and depth estimation are provided. Graph cuts is presented as an efficient algorithm for minimizing energies that can be expressed as sums of unary and pairwise terms. The algorithm works by finding the minimum s-t cut in a graph constructed from the energy terms.
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.
The document discusses various techniques for clustering and dimensionality reduction of web documents. It introduces machine learning clustering methods like k-means clustering and discusses challenges like handling different cluster sizes and shapes. It also covers dimensionality reduction methods like principal component analysis (PCA) and locality-sensitive hashing that can be used to cluster high dimensional web document datasets by reducing their dimensionality.
THE WEAK SOLUTION OF BLACK-SCHOLE’S OPTION PRICING MODEL WITH TRANSACTION COSTmathsjournal
This paper considers the equation of the type
− + + = , ( , ) ∈ ℝ × (0, );
which is the Black-Scholes option pricing model that includes the presence of transaction cost. The
existence, uniqueness and continuous dependence of the weak solution of the Black-Scholes model with
transaction cost are established.The continuity of weak solution of the parameters was discussed and
similar solution as in literature obtained.
Jack Bresenham developed an efficient algorithm for drawing lines on a raster display. The Bresenham's line algorithm uses only integer arithmetic to determine the next pixel to plot, allowing fast computation. It works by calculating a decision parameter to choose either the upper or lower pixel as it moves from the starting to ending point of the line. The algorithm guarantees connected lines and plots each point exactly once for accurate rendering compared to other methods.
The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found
applications in optimization, navigation, network theory, image processing, pattern recognition etc.
Several other authors have studied metric dimension of various standard graphs. In this paper we
introduce a real valued function called generalized metric G X × X × X ® R+ d : where X = r(v /W) =
{(d(v,v1),d(v,v2 ),...,d(v,v ) / v V (G))} k Î , denoted d G and is used to study metric dimension of graphs. It
has been proved that metric dimension of any connected finite simple graph remains constant if d G
numbers of pendant edges are added to the non-basis vertices.
The document discusses various techniques for clustering data, including hierarchical clustering, k-means algorithms, and distance measures. It provides examples of how different types of data like documents, customer purchases, DNA sequences can be represented as vectors and clustered. Key clustering approaches described are hierarchical agglomerative clustering using different linkage criteria, k-means clustering and its variant BFR for large datasets.
- The lecture covered graphics math topics including homogeneous coordinates and projective transformations.
- Homework 2 was due and an in-class quiz was given. Details on Project 1 were announced.
- The final exam date was moved and last class will be a review session. Daily quiz solutions will be provided.
- Office hours and last lecture topics were reviewed to introduce the current lecture on further graphics math concepts.
The document summarizes key concepts from Chapter 8 of the textbook "Fundamentals of Multimedia" on lossy compression algorithms. It introduces lossy compression and discusses distortion measures, rate-distortion theory, quantization techniques including uniform, non-uniform, and vector quantization. It also covers transform coding techniques such as the discrete cosine transform and its use in image compression standards to remove spatial redundancies by transforming pixel values into frequency coefficients.
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
This document discusses antiderivatives and indefinite integrals. It begins by introducing the concept of an antiderivative, which is a function whose derivative is a known function. It then defines the indefinite integral as representing the set of all antiderivatives. Several properties of antiderivatives and indefinite integrals are presented, including: the constant of integration; basic integration rules like power, exponential, and logarithmic rules; and notation used to represent indefinite integrals. Examples are provided to illustrate key concepts and properties.
The document summarizes hierarchical clustering techniques. It discusses two main types of hierarchical clustering - agglomerative and divisive. It presents an example dendrogram to illustrate hierarchical clustering. It also summarizes a research paper on a new algorithm called CLUBS that performs faster and more accurate hierarchical clustering compared to existing algorithms. The document concludes by discussing experiments applying hierarchical clustering on two biomedical datasets containing gene expression data to group patients and cell samples.
The document provides an overview of image processing, including its components, representations of images using matrices, types of images like color, grayscale and binary, concepts of neighborhoods, preprocessing techniques like median filtering and edge detection, segmentation using thresholding and connected components, and morphology operations like erosion, dilation, opening and closing.
Bellman Ford Routing Algorithm-Computer NetworksSimranJain63
The Bellman-Ford routing algorithm computes the shortest paths from a single source vertex to all other vertices in a weighted digraph. It is also known as the distance vector algorithm. The algorithm uses the principle of relaxation to iteratively update the cost of the shortest paths by relaxing edges until it either finds the shortest paths or detects a negative cost cycle. It runs in O(|V||E|) time in the worst case. Each node maintains a distance vector with the estimated cost to all other nodes and shares this information with neighbors to iteratively update the costs until reaching an optimal solution.
This document contains lecture notes on calculus of functions of several variables. It covers topics including vectors and vector spaces, geometry, vectors and the dot product, cross product, lines and planes in space, functions, vector valued functions, parameterized surfaces, parameterized curves, arc length and curvature. The notes provide definitions, examples, and exercises for each topic.
The document summarizes the Levenshtein distance algorithm and tree edit distance algorithm. It discusses how Levenshtein distance finds the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It then explains how tree edit distance extends this to find the minimum cost sequence of node edit operations (insert, delete, relabel) to transform one tree into another using Tai mappings and the Zhang-Shasha algorithm.
This document provides an overview of image deblurring techniques. It discusses how digital images can be represented as matrices, with each pixel corresponding to an entry in the matrix. A linear model is presented for how a sharp, ideal image (X) becomes blurred (B) through a blurring matrix (A) such that Ax=b. Point spread functions are introduced to describe how a point source becomes blurred and these are used to construct the columns of the blurring matrix A. The document concludes with a simple example of applying these concepts to a small test image.
This document discusses image restoration techniques. It defines image restoration as the process of taking a degraded image and estimating the original clean image. Common types of degradation include motion blur and noise. The document outlines the image formation process and degradation model both in continuous and discrete domains. It describes how degradation can be modeled as a convolution of the original image with a point spread function representing the blurring plus additive noise. The properties of linearity, homogeneity, and position invariance of degradation operators are also covered. Frequency domain techniques and references on image restoration are mentioned.
Optimization algorithms for solving computer vision problemsKrzysztof Wegner
The document discusses optimization algorithms for solving computer vision problems. It describes how computer vision problems can be formulated as energy minimization problems over pixel labels. Specific examples of segmentation and depth estimation are provided. Graph cuts is presented as an efficient algorithm for minimizing energies that can be expressed as sums of unary and pairwise terms. The algorithm works by finding the minimum s-t cut in a graph constructed from the energy terms.
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.
The document discusses various techniques for clustering and dimensionality reduction of web documents. It introduces machine learning clustering methods like k-means clustering and discusses challenges like handling different cluster sizes and shapes. It also covers dimensionality reduction methods like principal component analysis (PCA) and locality-sensitive hashing that can be used to cluster high dimensional web document datasets by reducing their dimensionality.
THE WEAK SOLUTION OF BLACK-SCHOLE’S OPTION PRICING MODEL WITH TRANSACTION COSTmathsjournal
This paper considers the equation of the type
− + + = , ( , ) ∈ ℝ × (0, );
which is the Black-Scholes option pricing model that includes the presence of transaction cost. The
existence, uniqueness and continuous dependence of the weak solution of the Black-Scholes model with
transaction cost are established.The continuity of weak solution of the parameters was discussed and
similar solution as in literature obtained.
Jack Bresenham developed an efficient algorithm for drawing lines on a raster display. The Bresenham's line algorithm uses only integer arithmetic to determine the next pixel to plot, allowing fast computation. It works by calculating a decision parameter to choose either the upper or lower pixel as it moves from the starting to ending point of the line. The algorithm guarantees connected lines and plots each point exactly once for accurate rendering compared to other methods.
The idea of metric dimension in graph theory was introduced by P J Slater in [2]. It has been found
applications in optimization, navigation, network theory, image processing, pattern recognition etc.
Several other authors have studied metric dimension of various standard graphs. In this paper we
introduce a real valued function called generalized metric G X × X × X ® R+ d : where X = r(v /W) =
{(d(v,v1),d(v,v2 ),...,d(v,v ) / v V (G))} k Î , denoted d G and is used to study metric dimension of graphs. It
has been proved that metric dimension of any connected finite simple graph remains constant if d G
numbers of pendant edges are added to the non-basis vertices.
The document discusses various techniques for clustering data, including hierarchical clustering, k-means algorithms, and distance measures. It provides examples of how different types of data like documents, customer purchases, DNA sequences can be represented as vectors and clustered. Key clustering approaches described are hierarchical agglomerative clustering using different linkage criteria, k-means clustering and its variant BFR for large datasets.
- The lecture covered graphics math topics including homogeneous coordinates and projective transformations.
- Homework 2 was due and an in-class quiz was given. Details on Project 1 were announced.
- The final exam date was moved and last class will be a review session. Daily quiz solutions will be provided.
- Office hours and last lecture topics were reviewed to introduce the current lecture on further graphics math concepts.
The document summarizes key concepts from Chapter 8 of the textbook "Fundamentals of Multimedia" on lossy compression algorithms. It introduces lossy compression and discusses distortion measures, rate-distortion theory, quantization techniques including uniform, non-uniform, and vector quantization. It also covers transform coding techniques such as the discrete cosine transform and its use in image compression standards to remove spatial redundancies by transforming pixel values into frequency coefficients.
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
This document discusses antiderivatives and indefinite integrals. It begins by introducing the concept of an antiderivative, which is a function whose derivative is a known function. It then defines the indefinite integral as representing the set of all antiderivatives. Several properties of antiderivatives and indefinite integrals are presented, including: the constant of integration; basic integration rules like power, exponential, and logarithmic rules; and notation used to represent indefinite integrals. Examples are provided to illustrate key concepts and properties.
The document summarizes hierarchical clustering techniques. It discusses two main types of hierarchical clustering - agglomerative and divisive. It presents an example dendrogram to illustrate hierarchical clustering. It also summarizes a research paper on a new algorithm called CLUBS that performs faster and more accurate hierarchical clustering compared to existing algorithms. The document concludes by discussing experiments applying hierarchical clustering on two biomedical datasets containing gene expression data to group patients and cell samples.
The document provides an overview of image processing, including its components, representations of images using matrices, types of images like color, grayscale and binary, concepts of neighborhoods, preprocessing techniques like median filtering and edge detection, segmentation using thresholding and connected components, and morphology operations like erosion, dilation, opening and closing.
Bellman Ford Routing Algorithm-Computer NetworksSimranJain63
The Bellman-Ford routing algorithm computes the shortest paths from a single source vertex to all other vertices in a weighted digraph. It is also known as the distance vector algorithm. The algorithm uses the principle of relaxation to iteratively update the cost of the shortest paths by relaxing edges until it either finds the shortest paths or detects a negative cost cycle. It runs in O(|V||E|) time in the worst case. Each node maintains a distance vector with the estimated cost to all other nodes and shares this information with neighbors to iteratively update the costs until reaching an optimal solution.
This document contains lecture notes on calculus of functions of several variables. It covers topics including vectors and vector spaces, geometry, vectors and the dot product, cross product, lines and planes in space, functions, vector valued functions, parameterized surfaces, parameterized curves, arc length and curvature. The notes provide definitions, examples, and exercises for each topic.
The document summarizes the Levenshtein distance algorithm and tree edit distance algorithm. It discusses how Levenshtein distance finds the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It then explains how tree edit distance extends this to find the minimum cost sequence of node edit operations (insert, delete, relabel) to transform one tree into another using Tai mappings and the Zhang-Shasha algorithm.
The document discusses randomized graph algorithms and techniques for analyzing them. It describes a linear time algorithm for finding minimum spanning trees (MST) that samples edges and uses Boruvka's algorithm and edge filtering. It also discusses Karger's algorithm for approximating the global minimum cut in near-linear time using edge contractions. Finally, it presents an approach for 3-approximate distance oracles that preprocesses a graph to build a data structure for answering approximate shortest path queries in constant time using landmark vertices and storing local and global distance information.
The document discusses drawing 2D primitives such as lines, circles, and polygons in a raster graphics system. It covers:
- Representations of lines, circles, and polygons using implicit, explicit, and parametric formulas
- Scan conversion algorithms to draw these primitives by mapping them to pixels, including basic and midpoint line algorithms, a circle midpoint algorithm, and flood fill and scan conversion approaches for polygon fill
- Components of an interactive graphics system including the application model, program, and graphics system that interfaces with display hardware like CRT and FED displays
A Szemeredi-type theorem for subsets of the unit cubeVjekoslavKovac1
This document summarizes a talk on gaps between arithmetic progressions in subsets of the unit cube. It presents three key propositions:
1) For subsets A of positive measure, structured progressions contribute a lower bound depending on the measure of A and the best known bounds for Szemerédi's theorem.
2) Estimating errors by pigeonholing scales, the difference between smooth and sharp progressions over various scales is bounded above by a sublinear function of scales.
3) For sufficiently nice subsets, the difference between measure and smoothed measure is arbitrarily small by choosing a small smoothing parameter.
Combining these propositions shows that for sufficiently nice subsets, gaps between progressions contain an interval
This document provides notes on determining various properties of planes in 3D space, including:
1) The perpendicular distance from a point to a plane using either vector or Cartesian methods.
2) The angle between a plane and line by taking the arcsine of the dot product of their normal vectors.
3) The angle between two planes by taking the arccosine of the dot product of their normal vectors.
Worked examples are provided for calculating distances, angles, and deriving relevant formulas. Revision questions at the end reinforce the content through calculation practice.
This document discusses dynamic programming and algorithms for solving all-pair shortest path problems. It begins by defining dynamic programming as avoiding recalculating solutions by storing results in a table. It then describes Floyd's algorithm for finding shortest paths between all pairs of nodes in a graph. The algorithm iterates through nodes, calculating shortest paths that pass through each intermediate node. It takes O(n3) time for a graph with n nodes. Finally, it discusses the multistage graph problem and provides forward and backward algorithms to find the minimum cost path from source to destination in a multistage graph in O(V+E) time, where V and E are the numbers of vertices and edges.
This document discusses dynamic programming and algorithms for solving all-pair shortest path problems. It begins by explaining dynamic programming as an optimization technique that works bottom-up by solving subproblems once and storing their solutions, rather than recomputing them. It then presents Floyd's algorithm for finding shortest paths between all pairs of nodes in a graph. The algorithm iterates through nodes, updating the shortest path lengths between all pairs that include that node by exploring paths through it. Finally, it discusses solving multistage graph problems using forward and backward methods that work through the graph stages in different orders.
DISTANCE TWO LABELING FOR MULTI-STOREY GRAPHSgraphhoc
An L (2, 1)-labeling of a graph G (also called distance two labeling) is a function f from the vertex set V (G) to the non negative integers {0,1,…, k }such that |f(x)-f(y)| ≥2 if d(x, y) =1 and | f(x)- f(y)| ≥1 if d(x, y) =2. The L (2, 1)-labeling number λ (G) or span of G is the smallest k such that there is a f with
max {f (v) : vє V(G)}= k. In this paper we introduce a new type of graph called multi-storey graph. The distance two labeling of multi-storey of path, cycle, Star graph, Grid, Planar graph with maximal edges and its span value is determined. Further maximum upper bound span value for Multi-storey of simple
graph are discussed.
The document provides information on various integration techniques including the midpoint rule, trapezoidal rule, Simpson's rule, integration by parts, trigonometric substitutions, and applications of integrals such as finding the area between curves, arc length, surface area of revolution, and volume of revolution. It also covers integrals of common functions, properties of integrals, and techniques for parametric and polar coordinates.
Problem Solving by Computer Finite Element MethodPeter Herbert
This document discusses using finite element methods and the cotangent Laplacian to solve partial differential equations numerically. It begins by explaining how to generate simplicial meshes by dividing a region into basic pieces. It then introduces the cotangent Laplacian, which approximates the Laplacian operator, and how it is calculated based on angles in triangles. Finally, it demonstrates applying the cotangent Laplacian to solve sample Dirichlet and Neumann boundary value problems and compares the approximate solutions to exact solutions, showing convergence as the mesh is refined.
The document describes algorithms for scan converting lines and circles in raster graphics.
For line drawing, it discusses direct solutions, the digital difference analyzer (DDA) algorithm, and the midpoint line algorithm. The midpoint line algorithm uses incremental calculations and the sign of a decision variable to determine whether to select the east or northeast pixel at each step.
For circle drawing, it describes using the implicit equation and symmetry to scan convert circles centered at the origin. It then presents the midpoint circle algorithm, which similarly uses a decision variable and incremental updates to select between the east and southeast pixels at each step.
This document discusses using the Wasserstein distance for inference in generative models. It begins with an overview of approximate Bayesian computation (ABC) and how distances between samples are used. It then introduces the Wasserstein distance as an alternative distance that can have lower variance than the Euclidean distance. Computational aspects and asymptotics of using the Wasserstein distance are discussed. The document also covers how transport distances can handle time series data.
안녕하세요 딥러닝 논문읽기 모임 입니다! 오늘 소개할 논문은 3D관련 업무를 진행 하시는/ 희망하시는 분들의 필수 논문인 VoxelNET 입니다.
발표자료:https://www.slideshare.net/taeseonryu/mcsemultimodal-contrastive-learning-of-sentence-embeddings
안녕하세요! 딥러닝 논문읽기 모임입니다.
오늘은 자율 주행, 가정용 로봇, 증강/가상 현실과 같은 다양한 응용 분야에서 중요한 문제인 3D 포인트 클라우드에서의 객체 탐지에 대한 획기적인 진전을 소개하고자 합니다. 이를 위해 'VoxelNet'이라는 새로운 3D 탐지 네트워크에 대해 알아보겠습니다.
1. 기존 방법의 한계
기존의 많은 노력은 수동으로 만들어진 특징 표현, 예를 들어 새의 눈 시점 투영 등에 집중해 왔습니다. 하지만 이러한 방법들은 LiDAR 포인트 클라우드와 영역 제안 네트워크(RPN) 사이의 연결을 효과적으로 수행하기 어렵습니다.
2. VoxelNet의 혁신적 접근법
VoxelNet은 3D 포인트 클라우드를 위한 수동 특징 공학의 필요성을 없애고, 특징 추출과 바운딩 박스 예측을 단일 단계, end-to-end 학습 가능한 깊은 네트워크로 통합합니다. VoxelNet은 포인트 클라우드를 균일하게 배치된 3D 복셀로 나누고, 새롭게 도입된 복셀 특징 인코딩(VFE) 레이어를 통해 각 복셀 내의 포인트 그룹을 통합된 특징 표현으로 변환합니다.
3. 효과적인 기하학적 표현 학습
이 방식을 통해 포인트 클라우드는 서술적인 체적 표현으로 인코딩되며, 이는 RPN에 연결되어 탐지를 생성합니다. VoxelNet은 다양한 기하학적 구조를 가진 객체의 효과적인 구별 가능한 표현을 학습합니다.
4. 성능 평가
KITTI 자동차 탐지 벤치마크에서의 실험 결과, VoxelNet은 기존의 LiDAR 기반 3D 탐지 방법들을 큰 차이로 능가했습니다. 또한, LiDAR만을 기반으로 한 보행자와 자전거 탐지에서도 희망적인 결과를 보였습니다.
VoxelNet의 도입은 3D 포인트 클라우드에서의 객체 탐지를 혁신적으로 개선하고 있으며, 이 분야에서의 미래 발전에 중요한 영향을 미칠 것으로 기대됩니다.
오늘 논문 리뷰를 위해 이미지처리 허정원님이 자세한 리뷰를 도와주셨습니다 많은 관심 미리 감사드립니다!
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Introduction of metric dimension of circular graphs is connected graph , The distance and diameter , Resolving sets and location number then Examples . Application in facility location problems . is has motivation (Applications in Chemistry and Networks systems). Definitions of Certain Regular Graphs. Main Results for three graphs (Prism , Antiprism and generalized Petersen graphs .
Dijkstra's algorithm finds the shortest path between a starting vertex and all other vertices in a graph with non-negative edge weights. It works by maintaining a table of distances and predecessors and iteratively updating the distance to neighbors if a shorter path is found. The algorithm picks the vertex with the minimum distance, marks it as known, and updates the distances and predecessors of its neighbors. This continues until all vertices are marked as known.
Land of Pyramids, Petra, and Prayers - Egypt, Jordan, and Israel Tourppd1961
This is the presentation of photos and history of Land of Pyramids, Petra, and Prayers from our Egypt, Jordan, and Israel Tour during February, 2020. This was prepared and presented to the family and friends on 19th July, 2020.
This document discusses object-oriented programming in C++. It covers several topics related to OOP in C++ including classes, constructors, destructors, inheritance, polymorphism, and templates. The document consists of lecture slides that define key concepts and provide examples to illustrate how various OOP features work in C++.
The document discusses digital geometry and provides an overview of the topic. It begins with a brief history of geometry and discusses how the field of digital geometry emerged with the advent of computers and digital images. It then covers some key concepts in digital geometry including tessellations, connectivity in 2D and 3D, and the Jordan curve theorem. The document aims to provide an introduction to digital geometry and its fundamental topics.
This presentation was made in PRISM workshop on Technology Innovations and Trends in IT in the second decade of 21st century. The agenda is from IEEE Computer Society.
This presentation as made as a tutorial at NCVPRIPG (http://www.iitj.ac.in/ncvpripg/) at IIT Jodhpur on 18-Dec-2013.
Kinect is a multimedia sensor from Microsoft. It is shipped as the touch-free console for Xbox 360 video gaming platform. Kinect comprises an RGB Camera, a Depth Sensor (IR Emitter and Camera) and a Microphone Array. It produces a multi-stream video containing RGB, depth, skeleton, and audio streams.
Compared to common depth cameras (laser or Time-of-Flight), the cost of a Kinect is quite low as it uses a novel structured light diffraction and triangulation technology to estimate the depth. In addition, Kinect is equipped with special software to detect human figures and to produce its 20-joints skeletons.
Though Kinect was built for touch-free gaming, its cost effectiveness and human tracking features have proved useful in many indoor applications beyond gaming like robot navigation, surveillance, medical assistance and animation.
The new standard for C++ language has been signed in 2011. This new (extended) language, called C++11, has a number of new semantics (in terms of language constructs) and a number of new standard library support. The major language extensions are discussed in this presentation. The library will be taken up in a later presentation.
The document discusses function call optimization in C++. It provides examples of constructor, base class constructor, and get/set method calls in both debug and release builds. In release builds, the compiler fully optimizes constructor calls and inlines non-virtual functions like get/set methods to improve performance. Only virtual functions cannot be optimized as their call sequence depends on runtime type.
The document discusses different ways to define integer constants in C, including using integer literals, the #define preprocessor directive, enums, and the const qualifier. It provides a table comparing how each option is handled by the C preprocessor, compiler, and debugger. Code examples are given to illustrate the behavior. The key points are that integer literals are replaced directly, #define symbols are replaced textually, enums and const ints create symbols but const ints allow address operations in both the compiler and debugger.
The document discusses the key components of the Standard Template Library (STL) in C++, including containers, iterators, and algorithms. It explains that STL containers manage collections of objects, iterators allow traversing container elements, and algorithms perform operations on elements using iterators. The main STL containers like vector, list, deque, set, and map are introduced along with their basic functionality. Iterators provide a common interface for traversing container elements. Algorithms operate on elements through iterators but are independent of container implementations.
The document discusses object lifetime in C/C++. It covers the fundamentals of object lifetime including construction, use, and destruction. It also describes the different types of objects - static objects which are compiler-managed and have lifetime from program startup to termination, automatic objects which are stack-based and destroyed when they go out of scope, and dynamic objects which are user-managed and allocated on the free store.
This document provides guidance on effective technical documentation. It discusses planning documentation by determining the objective, intended audience, necessary content and approximate length. It also covers tips for clear writing style such as using active voice and avoiding contractions. The goals of technical documentation are clarity, comprehensiveness, conciseness and correctness.
The document discusses VLSI education and development in India, including:
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2. Surveys by VSI that found a growing gap between projected VLSI manpower needs and current outputs from Indian universities.
3. A workshop discussing goals of university-industry collaboration and feedback that graduating students lack industry readiness in areas like design skills and experience with industrial tools.
The document provides an overview of reconfigurable computing architectures. It discusses several leading companies in the field including Elixent, QuickSilver, Pact Corp, and Systolix. It then summarizes key reconfigurable computing architectures including D-Fabrix array, Adaptive Computing Machine (ACM), eXtreme Processing Platform (XPP), and PulseDSPTM. The ACM is based on QuickSilver's Self-Reconfigurable Gate Array (SRGA) architecture, which allows fast context switching and random access of the configuration memory.
The document discusses three potential factors that influence women's participation in the workforce: educational systems, technical inclination, and social environment. It explores whether educational systems are a culprit or savior, and whether women have weaker technical skills or are differently abled. Finally, it examines how social environments can be a culprit, through issues like declining sex ratios, workplace discrimination, and domestic discrimination against women with two full-time jobs.
Handling Exceptions In C & C++ [Part B] Ver 2ppd1961
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The document discusses exception handling in C and C++. It covers exception fundamentals, and techniques for handling exceptions in C such as return values, global variables, goto statements, signals, and termination functions. It also discusses exception handling features introduced in C++ such as try/catch blocks and exception specifications.
The document discusses various models for offshore technology services in the electronics industry. It defines key terms like outsourcing, insourcing, onsite, offsite, and offshore. It describes different software delivery models including the onsite, offsite, offshore, and global delivery models. It discusses factors that determine if work can be done offshore, or is "offshoreable", as well as advantages and disadvantages of outsourcing. It outlines different types of offshore outsourcing like ITO, BPO, and software R&D. Finally, it provides a brief overview of software outsourcing in the electronics industry.
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Navigating the world of forex trading can be challenging, especially for beginners. To help you make an informed decision, we have comprehensively compared the best forex brokers in India for 2024. This article, reviewed by Top Forex Brokers Review, will cover featured award winners, the best forex brokers, featured offers, the best copy trading platforms, the best forex brokers for beginners, the best MetaTrader brokers, and recently updated reviews. We will focus on FP Markets, Black Bull, EightCap, IC Markets, and Octa.
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In this article, we will dive into the extraordinary life of Ellen Burstyn, where the curtains rise on a story that's far more attractive than any script.
IMPACT Silver is a pure silver zinc producer with over $260 million in revenue since 2008 and a large 100% owned 210km Mexico land package - 2024 catalysts includes new 14% grade zinc Plomosas mine and 20,000m of fully funded exploration drilling.
How are Lilac French Bulldogs Beauty Charming the World and Capturing Hearts....Lacey Max
“After being the most listed dog breed in the United States for 31
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Best practices for project execution and deliveryCLIVE MINCHIN
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Dive into this presentation and learn about the ways in which you can buy an engagement ring. This guide will help you choose the perfect engagement rings for women.
Garments ERP Software in Bangladesh _ Pridesys IT Ltd.pdfPridesys IT Ltd.
Pridesys Garments ERP is one of the leading ERP solution provider, especially for Garments industries which is integrated with
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Zodiac Signs and Food Preferences_ What Your Sign Says About Your Tastemy Pandit
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The Most Inspiring Entrepreneurs to Follow in 2024.pdfthesiliconleaders
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𝐔𝐧𝐯𝐞𝐢𝐥 𝐭𝐡𝐞 𝐅𝐮𝐭𝐮𝐫𝐞 𝐨𝐟 𝐄𝐧𝐞𝐫𝐠𝐲 𝐄𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐜𝐲 𝐰𝐢𝐭𝐡 𝐍𝐄𝐖𝐍𝐓𝐈𝐃𝐄’𝐬 𝐋𝐚𝐭𝐞𝐬𝐭 𝐎𝐟𝐟𝐞𝐫𝐢𝐧𝐠𝐬
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The APCO Geopolitical Radar - Q3 2024 The Global Operating Environment for Bu...APCO
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Digital Distance Geometry
1. Digital Distance Geometry – Applications to Image Analysis Dr. P. P. Das [email_address] , [email_address] Interra Systems, Inc. www.interrasystems.com ICVGIP ’04. Science City. 18-Dec-04
56. Chamfering for computing Distance Transform o a b a Forward Scanning From Left to Right and Top to Bottom Backward Scanning From Right to Left and Bottom to Top b Distance at o = min (Distance value at Neighboring pixel + local distance between them) 1. Initialize all distance values to a Maximum Value. 2. At every point o compute the distance value from its visited neighbors as follows: Extend this concept with larger neighborhood and dimension. o a b a b
72. Computation of minimal set of maximal disks 1. Compute Local Maximum Blocks from the distance transformed image. Form a relational table expressing the relationships between boundary pixels and individual disks. The problem is mapped to the covering of the list of boundary pixels with the optimal set of maximal blocks. 2 . 3. Nilson-Danielsson’96
76. Thinning from Distance Transform Compute the set of Maximal Blocks. Use them as anchor points while iteratively deleting boundary points preserving the topology. Vincent ’91, Ragnemalm ’93, Svensson-Borgefors-Nystrom ’99
83. Decomposition of 3D Objects Identification of seed of a component from inner layers of Distance Transformed Image. Seed-fusion by expansion and shrinking Region growing by reversed DT. Surface smoothing and merging. Svensson-Saniti di Baja’02
90. O(1) neighbors O(2) neighbors O(3) neighbors O(1) neighbors O(2) neighbors 2D 3D M-neighbors o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o