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Edge Detection
Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuities in one-dimensional signals is known as ''step detection'' and the problem of finding signal discontinuities over time is known as ''change detection''. Edge detection is a fundamental tool in image processing, machine vision and computer vision, particularly in the areas of feature detection and feature extraction. Motivations The purpose of detecting sharp changes in image brightness is to capture important events and changes in properties of the world. It can be shown that under rather general assumptions for an image formation model, discontinuities in image brightness are likely to correspond to: * discontinuities in depth, * discontinuities in surface orientation, * changes in material properties and * variations in scene illumi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ron Kimmel
Ron Kimmel ( he, רון קימל, b. 1963) is a professor of Computer Science and Electrical and Computer Engineering (by courtesy) at the Technion Israel Institute of Technology. He holds a D.Sc. degree in electrical engineering (1995) from the Technion, and was a post-doc at UC Berkeley and Berkeley Labs, and a visiting professor at Stanford University. He has worked in various areas of image and shape analysis in computer vision, image processing, and computer graphics. Kimmel's interest in recent years has been non-rigid shape processing and analysis, medical imaging, computational biometry, deep learning, numerical optimization of problems with a geometric flavor, and applications of metric and differential geometry. Kimmel is an author of two books, an editor of one, and an author of numerous articles. He is the founder of the Geometric Image Processing La and a founder and advisor of several successful image processing and analysis companies. Kimmel's contributions includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marr–Hildreth Algorithm
In computer vision, the Marr–Hildreth algorithm is a method of detecting edges in digital images, that is, continuous curves where there are strong and rapid variations in image brightness. The Marr–Hildreth edge detection method is simple and operates by convolving the image with the Laplacian of the Gaussian function, or, as a fast approximation by difference of Gaussians. Then, zero crossings are detected in the filtered result to obtain the edges. The Laplacian-of-Gaussian image operator is sometimes also referred to as the Mexican hat wavelet due to its visual shape when turned upside-down. David Marr and Ellen C. Hildreth are two of the inventors. Limitations The Marr–Hildreth operator suffers from two main limitations. It generates responses that do not correspond to edges, so-called "false edges", and the localization error may be severe at curved edges. Today, there are much better edge detection methods, such as the Canny edge detector based on the search for loca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haralick
Robert M. Haralick (born 1943) is Distinguished Professor in Computer Science at Graduate Center of the City University of New York (CUNY). Haralick is one of the leading figures in computer vision, pattern recognition, and image analysis. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and a Fellow and past president of the International Association for Pattern Recognition. Prof. Haralick is the ''King-Sun Fu Prize winner of 2016'', "for contributions in image analysis, including remote sensing, texture analysis, mathematical morphology, consistent labeling, and system performance evaluation". Biography Haralick received a B.A. degree in mathematics from the University of Kansas in 1964, a B.S. degree in electrical engineering in 1966, and a M.S. degree in electrical engineering in 1967. In 1969, after completing his Ph.D. at the University of Kansas, he joined the faculty of the electrical engineering department, serving as professor from 1975 to 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Canny
John F. Canny (born in 1958) is an Australian computer scientist, and '' Paul E Jacobs and Stacy Jacobs Distinguished Professor of Engineering'' in the Computer Science Department of the University of California, Berkeley. He has made significant contributions in various areas of computer science and mathematics, including artificial intelligence, robotics, computer graphics, human-computer interaction, computer security, computational algebra, and computational geometry. Biography John Canny received his B.Sc. in Computer Science and Theoretical Physics from the University of Adelaide in South Australia, 1979, a B.E. (Hons) in Electrical Engineering, University of Adelaide, 1980, a M.S. and Ph.D. from the Massachusetts Institute of Technology, 1983 and 1987, respectively. In 1987, he joined the faculty of Electrical Engineering and Computer Sciences at UC Berkeley. In 1987, he received the Machtey Award and the ACM Doctoral Dissertation Award. In 1999, he was the co-chair of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noise Reduction
Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio. All signal processing devices, both analog and digital, have traits that make them susceptible to noise. Noise can be random with an even frequency distribution (white noise), or frequency-dependent noise introduced by a device's mechanism or signal processing algorithms. In electronic systems, a major type of noise is ''hiss'' created by random electron motion due to thermal agitation. These agitated electrons rapidly add and subtract from the output signal and thus create detectable noise. In the case of photographic film and magnetic tape, noise (both visible and audible) is introduced due to the grain structure of the medium. In photograp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Smoothing
In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss). It is a widely used effect in graphics software, typically to reduce image noise and reduce detail. The visual effect of this blurring technique is a smooth blur resembling that of viewing the image through a translucent screen, distinctly different from the bokeh effect produced by an out-of-focus lens or the shadow of an object under usual illumination. Gaussian smoothing is also used as a pre-processing stage in computer vision algorithms in order to enhance image structures at different scales—see scale space representation and scale space implementation. Mathematics Mathematically, applying a Gaussian blur to an image is the same as convolving the image with a Gaussian function. This is also known as a two-dimensional Weierstrass transform. By contrast, convolving by a circle ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplacian
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the nabla operator), or \Delta. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian of a function at a point measures by how much the average value of over small spheres or balls centered at deviates from . The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics: the Laplacian of the gravitational potential due to a given mass density distribution is a constant multiple of that densit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second-order Derivative Expression
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the deriva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Derivative Expression
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the derivati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero Crossing
A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function. It is a commonly used term in electronics, mathematics, acoustics, and image processing. In electronics In alternating current, the zero-crossing is the instantaneous point at which there is no voltage present. In a sine wave or other simple waveform, this normally occurs twice during each cycle. It is a device for detecting the point where the voltage crosses zero in either direction. The zero-crossing is important for systems that send digital data over AC circuits, such as modems, X10 home automation control systems, and Digital Command Control type systems for Lionel and other AC model trains. Counting zero-crossings is also a method used in speech processing to estimate the fundamental frequency of speech. In a system where an amplifier with digitally controlled gain is appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
