Related Research Articles
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices which are connected by edges. A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
Pattern recognition is the automated recognition of patterns and regularities in data. It 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. These activities can be viewed as two facets of the same field of application, and they have undergone substantial development over the past few decades.
Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, military automatic target recognition, and compiling and analyzing images and data from satellites. Registration is necessary in order to be able to compare or integrate the data obtained from these different measurements.
In graph theory, an isomorphism of graphsG and H is a bijection between the vertex sets of G and H
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.
Automatic summarization is the process of shortening a set of data computationally, to create a subset that represents the most important or relevant information within the original content. Artificial intelligence algorithms are commonly developed and employed to achieve this, specialized for different types of data.
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. What kind of graph is used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions.
Grammar induction is the process in machine learning of learning a formal grammar from a set of observations, thus constructing a model which accounts for the characteristics of the observed objects. More generally, grammatical inference is that branch of machine learning where the instance space consists of discrete combinatorial objects such as strings, trees and graphs.
In computer science, the Hopcroft–Karp algorithm is an algorithm that takes a bipartite graph as input and produces a maximum-cardinality matching as output — a set of as many edges as possible with the property that no two edges share an endpoint. It runs in time in the worst case, where is set of edges in the graph, is set of vertices of the graph, and it is assumed that . In the case of dense graphs the time bound becomes , and for sparse random graphs it runs in time with high probability.
Syntactic pattern recognition or structural pattern recognition is a form of pattern recognition, in which each object can be represented by a variable-cardinality set of symbolic, nominal features. This allows for representing pattern structures, taking into account more complex interrelationships between attributes than is possible in the case of flat, numerical feature vectors of fixed dimensionality, that are used in statistical classification.
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values.
As applied in the field of computer vision, graph cut optimization can be employed to efficiently solve a wide variety of low-level computer vision problems, such as image smoothing, the stereo correspondence problem, image segmentation, object co-segmentation, and many other computer vision problems that can be formulated in terms of energy minimization. Many of these energy minimization problems can be approximated by solving a maximum flow problem in a graph. Under most formulations of such problems in computer vision, the minimum energy solution corresponds to the maximum a posteriori estimate of a solution. Although many computer vision algorithms involve cutting a graph, the term "graph cuts" is applied specifically to those models which employ a max-flow/min-cut optimization.
The image segmentation problem is concerned with partitioning an image into multiple regions according to some homogeneity criterion. This article is primarily concerned with graph theoretic approaches to image segmentation applying graph partitioning via minimum cut or maximum cut. Segmentation-based object categorization can be viewed as a specific case of spectral clustering applied to image segmentation.
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points. Skew-symmetric graphs are identical to the double covering graphs of bidirected graphs.
Image segmentation strives to partition a digital image into regions of pixels with similar properties, e.g. homogeneity. The higher-level region representation simplifies image analysis tasks such as counting objects or detecting changes, because region attributes can be compared more readily than raw pixels.
In mathematics and computer science, graph edit distance (GED) is a measure of similarity 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 following outline is provided as an overview of and topical guide to machine learning. Machine learning is a subfield of soft computing within computer science that evolved from the study of pattern recognition and computational learning theory in artificial intelligence. In 1959, Arthur Samuel defined machine learning as a "field of study that gives computers the ability to learn without being explicitly programmed". Machine learning explores the study and construction of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from an example training set of input observations in order to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions.
References
- 1 2 3 Endika Bengoetxea, "Inexact Graph Matching Using Estimation of Distribution Algorithms" Archived 2017-01-11 at the Wayback Machine , Ph. D., 2002, Chapter 2:The graph matching problem Archived 2017-05-16 at the Wayback Machine (retrieved June 28, 2017)
- ↑ Endika Bengoetxea, Ph.D., Abstract Archived 2017-01-11 at the Wayback Machine
- ↑ Graph-Based Methods in Computer Vision: Developments and Applications, p. 58
- ↑ Neuhaus, Michel; Bunke, Horst (2007). Bridging the Gap Between Graph Edit Distance and Kernel Machines. World Scientific. p. 16. ISBN 981-270-817-0. Archived from the original on 30 December 2022. Retrieved 30 December 2022.
- 1 2 Horst Bunke, Xiaoyi Jang, "Graph Matching and Similarity", in: Intelligent Systems and Interfaces, pp. 281-304 (2000) doi : 10.1007/978-1-4615-4401-2_10
 | This computer science article is a stub. You can help Wikipedia by expanding it. |