Multidimensional Discrete Convolution
In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions ''f'' and ''g'' on an ''n''-dimensional lattice that produces a third function, also of ''n''-dimensions. Multidimensional discrete convolution is the discrete analog of the convolution#Domain of definition, multidimensional convolution of functions on Euclidean space. It is also a special case of convolution#Convolutions on groups, convolution on groups when the group (mathematics), group is the group of ''n''-tuples of integers. Definition Problem statement and basics Similar to the one-dimensional case, an asterisk is used to represent the convolution operation. The number of dimensions in the given operation is reflected in the number of asterisks. For example, an ''M''-dimensional convolution would be written with ''M'' asterisks. The following represents a ''M''-dimensional convolution of discrete signals: y(n_1,n_2,...,n_M)=x(n_1,n_2,...,n_M)* \overset *h ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term ''convolution'' refers to both the resulting function and to the process of computing it. The integral is evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). Graphically, it expresses how the 'shape' of one function is modified by the other. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f*g differs from cross-correlation f \star g only in that either f(x) or g(x) is reflected about the y-axis in convolution; thus i ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Fast Fourier Transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by Matrix decomposition, factorizing the DFT matrix into a product of Sparse matrix, sparse (mostly zero) factors. As a result, it manages to reduce the Computational complexity theory, complexity of computing the DFT from O(n^2), which arises if one simply applies the definition of DFT, to O(n \log n), where is the data size. The difference in speed can be enormous, especially for long data sets where may be in the thousands or millions. ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Kernel (image Processing)
In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image An image or picture is a visual representation. An image can be Two-dimensional space, two-dimensional, such as a drawing, painting, or photograph, or Three-dimensional space, three-dimensional, such as a carving or sculpture. Images may be di .... Or more simply, when each pixel in the output image is a function of the nearby pixels (including itself) in the input image, the kernel is that function. Details The general expression of a convolution is g_ = \omega * f_ = \sum_^a , where g(x,y) is the filtered image, f(x,y) is the original image, \omega is the filter kernel. Every element of the filter kernel is considered by -a \leq i \leq a and -b \leq j \leq b. Depending on the element values, a kernel can cause a wide range of effects: The a ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term ''convolution'' refers to both the resulting function and to the process of computing it. The integral is evaluated for all values of shift, producing the convolution function. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). Graphically, it expresses how the 'shape' of one function is modified by the other. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f*g differs from cross-correlation f \star g only in that either f(x) or g(x) is reflected about the y-axis in convolution; thus i ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Scale-invariant Feature Transform
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local '' features'' in images, invented by David Lowe in 1999. Applications include object recognition, robotic mapping and navigation, image stitching, 3D modeling, gesture recognition, video tracking, individual identification of wildlife and match moving. SIFT keypoints of objects are first extracted from a set of reference images and stored in a database. An object is recognized in a new image by individually comparing each feature from the new image to this database and finding candidate matching features based on Euclidean distance of their feature vectors. From the full set of matches, subsets of keypoints that agree on the object and its location, scale, and orientation in the new image are identified to filter out good matches. The determination of consistent clusters is performed rapidly by using an efficient hash table implementation of the generalised Hough t ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
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]   |
|
Finite Impulse Response
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of ''finite'' duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying). The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero. FIR filters can be discrete-time or continuous-time, and digital or analog. Definition For a causal discrete-time FIR filter of order ''N'', each value of the output sequence is a weighted sum of the most recent input values: :\begin y &= b_0 x + b_1 x -1+ \cdots + b_N x -N\\ &= \sum_^N b_i\cdot x -i \end where: * x /math> is the input signal, * y /math> is the outpu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Wiki Gauss
A wiki ( ) is a form of hypertext publication on the internet which is collaboratively edited and managed by its audience directly through a web browser. A typical wiki contains multiple pages that can either be edited by the public or limited to use within an organization for maintaining its internal knowledge base. Its name derives from the first user-editable website called "WikiWikiWeb," with "wiki" being a Hawaiian word meaning "quick." Wikis are powered by wiki software, also known as wiki engines. Being a form of content management system, these differ from other web-based systems such as blog software or static site generators in that the content is created without any defined owner or leader. Wikis have little inherent structure, allowing one to emerge according to the needs of the users. Wiki engines usually allow content to be written using a lightweight markup language and sometimes edited with the help of a rich-text editor. There are dozens of different wik ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Cartesian Combined
Cartesian means of or relating to the French philosopher RenĂ© Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics *Cartesian closed category, a closed category in category theory *Cartesian coordinate system, modern rectangular coordinate system * Cartesian diagram, a construction in category theory *Cartesian geometry, now more commonly called analytic geometry *Cartesian morphism, formalisation of ''pull-back'' operation in category theory * Cartesian oval, a curve *Cartesian product, a direct product of two sets *Cartesian product of graphs, a binary operation on graphs *Cartesian tree, a binary tree in computer science Philosophy * Cartesian anxiety, a hope that studying the world will give us unchangeable knowledge of ourselves and the world *Cartesian circle, a potential mistake in reasoning *Cartesian doubt, a form of methodical skepticism as a basis for philosophical rigor *Cartesian dualism, the philosophy of the distinction between mind and ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Combined Convo
{{Disambiguation ...
Combined may refer to: * Alpine combined (skiing), the combination of slalom and downhill skiing as a single event ** Super combined (skiing) * Nordic combined (skiing), the combination of cross country skiing and ski jumping as a single event * The Combined (Group), a criminal organization * CombinedX, a Swedish group of IT companies See also * * Combo (other) * Combine (other) * Combination (other) A combination is a mathematical collection of things in a context where their specific order is irrelevant. Combination, combinations, or combo may also refer to: * Combination (chess), a relatively long sequence of chess moves, involving tempora ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Conjoined Blocks
Conjoined twins, popularly referred to as Siamese twins, are twins joined ''Uterus, in utero''. It is a very rare phenomenon, estimated to occur in anywhere between one in 50,000 births to one in 200,000 births, with a somewhat higher incidence in southwest Asia and Africa. Approximately half are stillbirth, stillborn, and an additional one-third die within 24 hours. Most live births are female, with a ratio of 3:1. Two possible explanations of the cause of conjoined twins have been proposed. The one that is generally accepted is ''fission'', in which the fertilized egg splits partially. The other explanation, no longer believed to be accurate, is ''fusion'', in which the fertilized egg completely separates, but stem cells (that search for similar cells) find similar stem cells on the other twin and fuse the twins together. Conjoined twins and some monozygotic, but not conjoined, twins share a single common chorion, placenta, and amniotic sac ''in utero''. Chang and Eng Bunker (1 ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |