Convolution Operator
A Convolution Operator is a mathematical operation on two math functions f and g, producing a third function that is a modified version of one of the original functions.
- AKA: Convolutional Function, Convolutional Neural Network Feature Detector.
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- Example(s):
- a Convolutional Kernel, such as a convolutional kernel matrix.
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- Counter-Example(s):
- See: Deconvolution, Mathematics, Functional Analysis, Operation (Mathematics), Function (Mathematics), Translation (Geometry), Cross-Correlation, Probability, Statistics, Computer Vision, Natural Language Processing, Image Processing.
References
2017
- (Gibson & Patterson, 2017) ⇒ Adam Gibson, Josh Patterson (2017). "Chapter 4. Major Architectures of Deep Networks". In: "Deep Learning" ISBN: 9781491924570.
- QUOTE: A convolution is defined as a mathematical operation describing a rule for how to merge two sets of information. It is important in both physics and mathematics and defines a bridge between the space/time domain and the frequency domain through the use of Fourier transforms. It takes input, applies a convolution kernel, and gives us a feature map as output.
The convolution operation, shown in Figure 4-12, is known as the feature detector of a CNN. The input to a convolution can be raw data or a feature map output from another convolution. It is often interpreted as a filter in which the kernel filters input data for certain kinds of information; for example, an edge kernel lets pass through only information from the edge of an image.
Figure 4-12. The convolution operation
The figure illustrates how the kernel is slid across the input data to produce the convoluted feature (output) data. At each step, the kernel is multiplied by the input data values within its bounds, creating a single entry in the output feature map. In practice the output is large if the feature we’re looking for is detected in the input(...)
- QUOTE: A convolution is defined as a mathematical operation describing a rule for how to merge two sets of information. It is important in both physics and mathematics and defines a bridge between the space/time domain and the frequency domain through the use of Fourier transforms. It takes input, applies a convolution kernel, and gives us a feature map as output.
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/convolution Retrieved:2015-11-7.
- In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated. Convolution is similar to cross-correlation. It has applications that include probability, statistics, computer vision, natural language processing, image and signal processing, engineering, and differential equations.
The convolution can be defined for functions on groups other than Euclidean space. For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 10 at DTFT#Properties.) A discrete convolution can be defined for functions on the set of integers. Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.
Computing the inverse of the convolution operation is known as deconvolution.
- In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated. Convolution is similar to cross-correlation. It has applications that include probability, statistics, computer vision, natural language processing, image and signal processing, engineering, and differential equations.