convolution


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Related to convolution: Fourier transform, Convolution theorem

convolution

Anatomy any of the numerous convex folds or ridges of the surface of the brain

convolution

(kon-vŏ-loo -shŏn) A mathematical operation that is performed on two functions and expresses how the shape of one is ‘smeared’ by the other. Mathematically, the convolution of the functions f(x) and g(x) is given by
(u )g(x u )du

It finds wide application in physics; it describes, for example, how the transfer function of an instrument affects the response to an input signal. See also autocorrelation function; radio-source structure.

Convolution

 

The convolution of the two functions f1(x) and f2(x) is the function

The convolution of f1(x) and f2(x) is sometimes denoted by f1 * f2

If f1 and f2 are the probability density functions of two independent random variables X and Y, then f1 * f2 is the probability density function of the random variable X + Y. If Fk(x) is the Fourier transform of the function fk(x), that is,

then F1(x) F2(x) is the Fourier transform of the function f1 * f2. This property of convolutions has important applications in probability theory. The convolution of two functions exhibits an analogous property with respect to the Laplace transform; this fact underlies broad applications of convolutions in operational calculus.

The operation of convolution of functions is commutative and associative—that is, f1 * f2 = f2 * f1 and f1 * (f2 * f3) = (f1 * f2) * f3. For this reason, the convolution of two functions can be regarded as a type of multiplication. Consequently, the theory of normed rings can be applied to the study of convolutions of functions.

convolution

[‚kän·və′lü·shən]
(anatomy)
A fold, twist, or coil of any organ, especially any one of the prominent convex parts of the brain, separated from each other by depressions or sulci.
(geology)
The process of developing convolute bedding.
A structure resulting from a convolution process, such as a small-scale but intricate fold.
(mathematics)
The convolution of the functions ƒ and g is the function F, defined by
(statistics)
A method for finding the distribution of the sum of two or more random variables; computed by direct integration or summation as contrasted with, for example, the method of characteristic functions.
References in periodicals archive ?
A squeeze layer is comprised of 1x1 convolution filters to help to limit the number of input channels.
A convolution operation is achieved by sliding a kernel over the input and computing the dot product between the input and the filter.
[X.sub.ij], is a convolution of functions [X.sub.i] and [X.sub.j]
The generator architecture consists of two parallel convolution subnetworks that have different kernel sizes, specifically, one subnetwork with large kernel size that captures more spatial information of the raw image, and the other subnetwork with relatively small kernel size which aims to acquire more local rain streaks knowledge.
MKNet-C has one more convolution block on the basis of MKNet-B and adds 1*1 convolution layer to each convolution block to increase the fully connected layer fc2.
In order to rationally use all of the information of the signal and extract a more suitable feature, this article adopts the extraction method of extracting self-adaptively the advanced features of signal through multilayer convolution by taking the original sound signal after overlapping framing directly as the input feature figure of convolutional networks.
Jia et al., "Going deeper with convolutions," in The Conference on Computer Vision and Pattern Recognition, pp.
Each convolution layer possessing the ReLU function is followed by a max pooling layer having a certain pooling size.
Dilated convolution is a generalization of Kronecker-factored convolutional filters [6] which expand exponentially receptive fields without losing resolution by disposing of some pooling layers.
In this paper, the convolution products arising in the stress and displacement calculation as a result of superposition of effects of fundamental solutions are evaluated in the frequency domain with improved computational efficiency and high precision.
Compared with traditional machine learning, its most prominent feature is a multilayer network structure, with an increased convolution and a down-sampling layer.
RCNN [4] uses selective search [23] to produce about 2000 RoLs for each picture and then extracts and classifies the convolution features of the 2000 RoLs, respectively.