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Graph Matching
Graph matching is the problem of finding a similarity between graphs.Endika Bengoetxea"Inexact Graph Matching Using Estimation of Distribution Algorithms", Ph. D., 2002Chapter 2:The graph matching problem (retrieved June 28, 2017) Graphs are commonly used to encode structural information in many fields, including computer vision and pattern recognition, and graph matching is an important tool in these areas.Endika Bengoetxea, Ph.D.Abstract In these areas it is commonly assumed that the comparison is between the ''data graph'' and the ''model graph''. The case of exact graph matching is known as the graph isomorphism problem. The problem of exact matching of a graph to a part of another graph is called subgraph isomorphism problem. Inexact graph matching refers to matching problems when exact matching is impossible, e.g., when the number of vertices in the two graphs are different. In this case it is required to find the best possible match. For example, in image recognition app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Graph (discrete Mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a Set (mathematics), set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing mon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Computer Vision
Computer vision tasks include methods for image sensor, acquiring, Image processing, processing, Image analysis, analyzing, and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the form of decisions. "Understanding" in this context signifies the transformation of visual images (the input to the retina) into descriptions of the world that make sense to thought processes and can elicit appropriate action. This image understanding can be seen as the disentangling of symbolic information from image data using models constructed with the aid of geometry, physics, statistics, and learning theory. The scientific discipline of computer vision is concerned with the theory behind artificial systems that extract information from images. Image data can take many forms, such as video sequences, views from multiple cameras, multi-dimensional data from a 3D scanning, 3D scanner, 3D point clouds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Pattern Recognition
Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess PR capabilities but their primary function is to distinguish and create emergent patterns. PR has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power. Pattern recognition systems are commonly trained from labeled "training" data. When no labeled data are available, other algorithms can be used to discover previously unknown patterns. KDD and data mining have a larger focus on unsupervised methods and str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Graph Isomorphism Problem
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. The problem is not known to be solvable in polynomial time nor to be NP-complete, and therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism problem is in the low hierarchy of class NP, which implies that it is not NP-complete unless the polynomial time hierarchy collapses to its second level. At the same time, isomorphism for many special classes of graphs can be solved in polynomial time, and in practice graph isomorphism can often be solved efficiently. This problem is a special case of the subgraph isomorphism problem, which asks whether a given graph ''G'' contains a subgraph that is isomorphic to another given graph ''H''; this problem is known to be NP-complete. It is also known to be a special case of the non-abelian hidden subgroup problem over the symmetric group. In the area of image r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Subgraph Isomorphism Problem
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H. Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other cases of subgraph isomorphism may be solved in polynomial time. Sometimes the name subgraph matching is also used for the same problem. This name puts emphasis on finding such a subgraph as opposed to the bare decision problem. Decision problem and computational complexity To prove subgraph isomorphism is NP-complete, it must be formulated as a decision problem. The input to the decision problem is a pair of graphs G and ''H''. The answer to the problem is positive if ''H'' is isomorphic to a subgraph of ''G'', and negative otherwise. Formal question: Let G=(V,E), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Image Recognition
Computer vision tasks include methods for acquiring, processing, analyzing, and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the form of decisions. "Understanding" in this context signifies the transformation of visual images (the input to the retina) into descriptions of the world that make sense to thought processes and can elicit appropriate action. This image understanding can be seen as the disentangling of symbolic information from image data using models constructed with the aid of geometry, physics, statistics, and learning theory. The scientific discipline of computer vision is concerned with the theory behind artificial systems that extract information from images. Image data can take many forms, such as video sequences, views from multiple cameras, multi-dimensional data from a 3D scanner, 3D point clouds from LiDaR sensors, or medical scanning devices. The t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Image Segmentation
In digital image processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions or image objects (Set (mathematics), sets of pixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze.Linda Shapiro, Linda G. Shapiro and George C. Stockman (2001): "Computer Vision", pp 279–325, New Jersey, Prentice-Hall, Image segmentation is typically used to locate objects and Boundary tracing, boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics. The result of image segmentation is a set of segments that collectively cover the entire image, or a set of Contour line, contours extracted from the image (see edge detection). Each of the pixels in a region ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Image Processing
An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a projection on a surface, activation of electronic signals, or digital displays; they can also be reproduced through mechanical means, such as photography, printmaking, or photocopying. Images can also be animated through digital or physical processes. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term ''image'' (or ''optical image'') refers specifically to the reproduction of an object formed by light waves coming from the object. A ''volatile image'' exists or is perceived only for a short period. This may be a reflection of an object by a mirror, a projection of a camera obscura, or a scene displayed on a cathode-ray tube. A ''fixed image'', also called a hard copy, is one that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Attributed Graph
In computer science, an attributed graph grammar is a class of graph grammar that associates vertices with a set of attributes and rewrites with functions on attributes. In the algebraic approach to graph grammars, they are usually formulated using the double-pushout approach or the single-pushout approach. Implementation AGG, a rule-based visual language that directly expresses attributed graph grammars using the single-pushout approach has been developed at TU Berlin for many years. See also * Graph rewriting * Attribute grammar An attribute grammar is a formal way to supplement a formal grammar with semantic information processing. Semantic information is stored in attributes associated with terminal and nonterminal symbols of the grammar. The values of attributes are t ... Notes References *. *Ehrig, Heckel, Korff, Lowe, Ribeiro, Wagner and Corradini, 1997. Algebraic Approaches to Graph Transformation - Part II: Single Pushout Approach and Comparison with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Optimization Problem
In mathematics, engineering, computer science and economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ..., an optimization problem is the problem of finding the ''best'' solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: * An optimization problem with discrete variables is known as a '' discrete optimization'', in which an object such as an integer, permutation or graph must be found from a countable set. * A problem with continuous variables is known as a '' continuous optimization'', in which an optimal value from a continuous function must be found. They can include constrained problems and multimodal problems. Search space In the context of an optim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Graph Edit Distance
In mathematics and computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first formalized mathematically by Alberto Sanfeliu and King-Sun Fu in 1983. A major application of graph edit distance is in inexact graph matching, such as error-tolerant pattern recognition in machine learning. The graph edit distance between two graphs is related to the string edit distance between strings. With the interpretation of strings as connected, directed acyclic graphs of maximum degree one, classical definitions of edit distance such as Levenshtein distance, Hamming distance and Jaro–Winkler distance may be interpreted as graph edit distances between suitably constrained graphs. Likewise, graph edit distance is also a generalization of tree edit distance between rooted trees. Formal definitions and properties The mathematical definition of graph edit distance is dependent upon the defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Similarity Measure
In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions. Use of different similarity measure formulas Different types of similarity measures exist for various types of objects, depending on the objects being compared. For each type of object there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
