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Boundary Tracing
Boundary tracing, also known as contour tracing, of a binary digital region can be thought of as a segmentation technique that identifies the boundary pixels of the digital region. Boundary tracing is an important first step in the analysis of that region. Boundary is a topological notion. However, a digital image is no topological space. Therefore, it is impossible to define the notion of a boundary in a digital image mathematically exactly. Most publications about tracing the boundary of a subset S of a digital image I describe algorithms which find a set of pixels belonging to S and having in their direct neighborhood pixels belonging both to S and to its complement I - S. According to this definition the boundary of a subset S is different from the boundary of the complement I – S which is a topological paradox. To define the boundary correctly it is necessary to introduce a topological space corresponding to the given digital image. Such space can be a two-dimensional abst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Image
A digital image is an image composed of picture elements, also known as ''pixels'', each with ''finite'', '' discrete quantities'' of numeric representation for its intensity or gray level that is an output from its two-dimensional functions fed as input by its spatial coordinates denoted with ''x'', ''y'' on the x-axis and y-axis, respectively. Depending on whether the image resolution is fixed, it may be of vector or raster type. Raster Raster images have a finite set of digital values, called ''picture elements'' or pixels. The digital image contains a fixed number of rows and columns of pixels. Pixels are the smallest individual element in an image, holding antiquated values that represent the brightness of a given color at any specific point. Typically, the pixels are stored in computer memory as a raster image or raster map, a two-dimensional array of small integers. These values are often transmitted or stored in a compressed form. Raster images can be created b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ( 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 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 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 contours extracted from the image (see edge detection). Each of the pixels in a region are similar with respect to some characteristic or computed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Analysis
Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading bar coded tags or as sophisticated as identifying a person from their face. Computers are indispensable for the analysis of large amounts of data, for tasks that require complex computation, or for the extraction of quantitative information. On the other hand, the human visual cortex is an excellent image analysis apparatus, especially for extracting higher-level information, and for many applications — including medicine, security, and remote sensing — human analysts still cannot be replaced by computers. For this reason, many important image analysis tools such as edge detectors and neural networks are inspired by human visual perception models. Digital Digital Image Analysis or Computer Image Analysis is when a computer or electrical device au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Antonovich Kovalevsky
Vladimir Antonovich Kovalevsky (born 1927) is a physicist. His research interests include digital geometry, digital topology, computer vision, image processing and pattern recognition. Scientific activity Vladimir A. Kovalevsky received his diploma in physics from Kharkiv University (Ukraine) in 1950, his first doctoral degree in technical sciences from the Central Institute of Metrology (Leningrad) in 1957 and his second doctoral degree in computer science from the Institute of Cybernetics of the Academy of Sciences of the Ukraine ( Kiev) in 1968. From 1961 to 1983 he served as Head of Department of Pattern Recognition at that Institute. In 1983 he moved to the GDR. He worked as teaching professor or as scientific collaborator on universities in Germany (Zentralinstitut für Kybernetik at the ADW, Berlin University of Applied Sciences and Technology, University of Rostock, Technische Universität Dresden), USA (University of Pennsylvania, Drexel University), Mexico ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moore Neighborhood
In cellular automata, the Moore neighborhood is defined on a two-dimensional square lattice and is composed of a central cell and the eight cells that surround it. Name The neighborhood is named after Edward F. Moore, a pioneer of cellular automata theory. Importance It is one of the two most commonly used neighborhood types, the other one being the von Neumann neighborhood, which excludes the corner cells. The well known Conway's Game of Life, for example, uses the Moore neighborhood. It is similar to the notion of 8-connected pixels in computer graphics. The Moore neighbourhood of a cell is the cell itself and the cells at a Chebyshev distance of 1. The concept can be extended to higher dimensions, for example forming a 26-cell cubic neighborhood for a cellular automaton in three dimensions, as used by 3D Life. In dimension ''d,'' where 0 \le d, d \in \mathbb, the size of the neighborhood is 3''d'' − 1. In two dimensions, the number of cells in an ''ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pathfinding
Pathfinding or pathing is the plotting, by a computer application, of the shortest route between two points. It is a more practical variant on solving mazes. This field of research is based heavily on Dijkstra's algorithm for finding the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph theory, which examines how to identify the path that best meets some criteria (shortest, cheapest, fastest, etc) between two points in a large network. Algorithms At its core, a pathfinding method searches a graph by starting at one vertex and exploring adjacent nodes until the destination node is reached, generally with the intent of finding the cheapest route. Although graph searching methods such as a breadth-first search would find a route if given enough time, other methods, which "explore" the graph, would tend to reach the destination sooner. An analogy would be a person walking across a room; rather than examining every pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curve Sketching
In geometry, curve sketching (or curve tracing) are techniques for producing a rough idea of overall shape of a plane curve given its equation, without computing the large numbers of points required for a detailed plot. It is an application of the theory of curves to find their main features. Basic techniques The following are usually easy to carry out and give important clues as to the shape of a curve: *Determine the ''x'' and ''y'' intercepts of the curve. The ''x'' intercepts are found by setting ''y'' equal to 0 in the equation of the curve and solving for ''x''. Similarly, the ''y'' intercepts are found by setting ''x'' equal to 0 in the equation of the curve and solving for ''y''. *Determine the symmetry of the curve. If the exponent of ''x'' is always even in the equation of the curve then the ''y''-axis is an axis of symmetry for the curve. Similarly, if the exponent of ''y'' is always even in the equation of the curve then the ''x''-axis is an axis of symmetry for the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chain Code
A chain code is a lossless compression based image segmentation method for binary images based upon tracing image contours. The basic principle of chain coding, like other contour codings, is to separately encode each connected component, or "blob", in the image. For each such region, a point on the boundary is selected and its coordinates are transmitted. The encoder then moves along the boundary of the region and, at each step, transmits a symbol representing the direction of this movement. This continues until the encoder returns to the starting position, at which point the blob has been completely described, and encoding continues with the next blob in the image. This encoding method is particularly effective for images consisting of a reasonably small number of large connected components. Variations Some popular chain codes include: * the Freeman Chain Code of Eight Directions (FCCE) * Directional Freeman Chain Code of Eight Directions (DFCCE) * Vertex Chain Code (VCC) * T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pixel Connectivity
In image processing, pixel connectivity is the way in which pixels in 2-dimensional (or hypervoxels in n-dimensional) images relate to their neighbors. Formulation In order to specify a set of connectivities, the dimension N and the width of the neighborhood n , must be specified. The dimension of a neighborhood is valid for any dimension n\geq1 . A common width is 3, which means along each dimension, the central cell will be adjacent to 1 cell on either side for all dimensions. Let M_N^n represent a N-dimensional hypercubic neighborhood with size on each dimension of n=2k+1, k\in\mathbb Let \vec represent a discrete vector in the first orthant from the center structuring element to a point on the boundary of M_N^n. This implies that each element q_i \in \ ,\forall i \in \ and that at least one component q_i = k Let S_N^d represent a N-dimensional hypersphere with radius of d=\left \Vert \vec \right \Vert. Define the amount of elements on the hypersphere S_N^d with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization Problem
In mathematics, computer science and economics, 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. Continuous optimization problem The '' standard form'' of a continuous optimization problem is \begin &\underset& & f(x) \\ &\operatorname & &g_i(x) \leq 0, \quad i = 1,\dots,m \\ &&&h_j(x) = 0, \quad j = 1, \dots,p \end where * is the objective function to be minimized over the -variable vector , * are called ine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
