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Mexican Hat Wavelet
In mathematics and numerical analysis, the Ricker wavelet :\psi(t) = \frac \left(1 - \left(\frac\right)^2 \right) e^ is the negative normalized second derivative of a Gaussian function, i.e., up to scale and normalization, the second Hermite function. It is a special case of the family of continuous wavelets (wavelets used in a continuous wavelet transform) known as Hermitian wavelets. The Ricker wavelet is frequently employed to model seismic data, and as a broad spectrum source term in computational electrodynamics. It is usually only referred to as the Mexican hat wavelet in the Americas, due to taking the shape of a sombrero when used as a 2D image processing kernel. It is also known as the Marr wavelet for David Marr. : \psi(x,y) = \frac\left(1-\frac \left(\frac\right)\right) e^ The multidimensional generalization of this wavelet is called the Laplacian of Gaussian function. In practice, this wavelet is sometimes approximated by the difference of Gaussians (DoG) function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Marr (neuroscientist)
David Courtenay Marr (19 January 1945 – 17 November 1980) from the ''International Encyclopaedia of Social and Behavioral Sciences'', by Shimon Edelman and Lucia M. Vaina; published 2001-01-08; archived at ; retrieved 2021-07-21 was a British and physiologist. Marr integrated results from , |
B-spline
In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. B-splines can be used for curve-fitting and numerical differentiation of experimental data. In computer-aided design and computer graphics, spline functions are constructed as linear combinations of B-splines with a set of control points. Introduction The term "B-spline" was coined by Isaac Jacob Schoenberg and is short for basis spline. A spline function of order n is a piecewise polynomial function of degree n - 1 in a variable x. The places where the pieces meet are known as knots. The key property of spline functions is that they and their derivatives may be continuous, depending on the multiplicities of the k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference Of Gaussians
In imaging science, difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one Gaussian blurred version of an original image from another, less blurred version of the original. In the simple case of grayscale images, the blurred images are obtained by convolving the original grayscale images with Gaussian kernels having differing width (standard deviations). Blurring an image using a Gaussian kernel suppresses only high-frequency spatial information. Subtracting one image from the other preserves spatial information that lies between the range of frequencies that are preserved in the two blurred images. Thus, the DoG is a spatial band-pass filter that attenuates frequencies in the original grayscale image that are far from the band center. \sigma_1. In one dimension, \Gamma is defined as: :\Gamma_(x) = I*\frac \, e^-I*\frac \, e^. and for the centered two-dimensional case: :\Gamma_(x,y) = I*\frac e^ - I*\frac e^ which is formally eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Space
Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures.Ijima, T. "Basic theory on normalization of pattern (in case of typical one-dimensional pattern)". Bull. Electrotech. Lab. 26, 368– 388, 1962. (in Japanese) The parameter t in this family is referred to as the ''scale parameter'', with the interpretation that image structures of spatial size smaller than about \sqrt have largely been smoothed away in the scale-space level at scale t. The main type of scale space is the ''linear (Gaussian) scale space'', which has wide applicability as well as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Vision
Computer vision is an interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the human visual system can do. 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 forms of decisions. Understanding in this context means the transformation of visual images (the input of 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blob Detection
In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution. Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i) '' differential methods'', which are based on derivatives of the function with respect to position, and (ii) ''methods based on local extrema'', which are based on finding the local maxima and minima of the function. With the more recent terminology used in the field, these detectors can also be referred to as ''interest point operators'', or alternatively interest region operators (see also interest point detectio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference Of Gaussians
In imaging science, difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one Gaussian blurred version of an original image from another, less blurred version of the original. In the simple case of grayscale images, the blurred images are obtained by convolving the original grayscale images with Gaussian kernels having differing width (standard deviations). Blurring an image using a Gaussian kernel suppresses only high-frequency spatial information. Subtracting one image from the other preserves spatial information that lies between the range of frequencies that are preserved in the two blurred images. Thus, the DoG is a spatial band-pass filter that attenuates frequencies in the original grayscale image that are far from the band center. \sigma_1. In one dimension, \Gamma is defined as: :\Gamma_(x) = I*\frac \, e^-I*\frac \, e^. and for the centered two-dimensional case: :\Gamma_(x,y) = I*\frac e^ - I*\frac e^ which is formally eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplacian Of Gaussian
In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution. Given some property of interest expressed as a function of position on the image, there are two main classes of blob detectors: (i) '' differential methods'', which are based on derivatives of the function with respect to position, and (ii) ''methods based on local extrema'', which are based on finding the local maxima and minima of the function. With the more recent terminology used in the field, these detectors can also be referred to as ''interest point operators'', or alternatively interest region operators (see also interest point detecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sombrero
A sombrero (Spanish , ) is a type of wide-brimmed Mexican men's hat used to shield the face and eyes from the sun. It usually has a high pointed crown, an extra-wide brim (broad enough to cast a shadow over the head, neck and shoulders of the wearer) that is slightly upturned at the edge, and a chin strap to hold it in place. In Mexico, this hat type is known as a ("charro hat", referring to the traditional Mexican horsemen). In Spanish, any wide-brimmed hat may be considered a sombrero. Design Sombreros, like cowboy hats, were designed in response to the demands of the physical environment. The concept of a broad-brimmed hat worn by a rider on horseback can be seen as far back as the Mongolian horsemen of the 13th century. In hot, sunny climates hats often have evolved wide brims. The exact origin of the Mexican sombrero is unknown, but it is usually accepted that the hat originated with Mestizo cowboys in Central Mexico. Although ''sombrero'' is usually taken to refer t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
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] |
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