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  2. Multidimensional discrete convolution - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_discrete...

    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:

  3. Kernel (image processing) - Wikipedia

    en.wikipedia.org/wiki/Kernel_(image_processing)

    2D Convolution Animation. Convolution is the process of adding each element of the image to its local neighbors, weighted by the kernel. This is related to a form of mathematical convolution. The matrix operation being performed—convolution—is not traditional matrix multiplication, despite being similarly denoted by *.

  4. Minkowski addition - Wikipedia

    en.wikipedia.org/wiki/Minkowski_addition

    In 2D image processing the Minkowski sum and difference are known as dilation and erosion. An alternative definition of the Minkowski difference is sometimes used for computing intersection of convex shapes. [3] This is not equivalent to the previous definition, and is not an inverse of the sum operation.

  5. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    For example, convolution of digit sequences is the kernel operation in multiplication of multi-digit numbers, which can therefore be efficiently implemented with transform techniques (Knuth 1997, §4.3.3.C; von zur Gathen & Gerhard 2003, §8.2).

  6. Line integral convolution - Wikipedia

    en.wikipedia.org/wiki/Line_integral_convolution

    In scientific visualization, line integral convolution (LIC) is a method to visualize a vector field (such as fluid motion) at high spatial resolutions. [1] The LIC technique was first proposed by Brian Cabral and Leith Casey Leedom in 1993.

  7. Convolutional layer - Wikipedia

    en.wikipedia.org/wiki/Convolutional_layer

    In artificial neural networks, a convolutional layer is a type of network layer that applies a convolution operation to the input. Convolutional layers are some of the primary building blocks of convolutional neural networks (CNNs), a class of neural network most commonly applied to images, video, audio, and other data that have the property of uniform translational symmetry.

  8. Gabor filter - Wikipedia

    en.wikipedia.org/wiki/Gabor_filter

    Its impulse response is defined by a sinusoidal wave (a plane wave for 2D Gabor filters) multiplied by a Gaussian function. [6] Because of the multiplication-convolution property (Convolution theorem), the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function (sinusoidal function) and the Fourier transform of the Gaussian ...

  9. Savitzky–Golay filter - Wikipedia

    en.wikipedia.org/wiki/Savitzky–Golay_filter

    These functions are shown in the plot at the right. For example, with a 9-point linear function (moving average) two thirds of the noise is removed and with a 9-point quadratic/cubic smoothing function only about half the noise is removed. Most of the noise remaining is low-frequency noise(see Frequency characteristics of convolution filters ...