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  2. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    Download as PDF; Printable version; ... the convolution formula can be described as the area under the function ... Discrete 2D Convolution Animation.

  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. Multidimensional discrete convolution - Wikipedia

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

    This ensures that a two-dimensional convolution will be able to be performed by a one-dimensional convolution operator as the 2D filter has been unwound to a 1D filter with gaps of zeroes separating the filter coefficients. One-Dimensional Filtering Strip after being Unwound. Assuming that some-low pass two-dimensional filter was used, such as:

  5. 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 ...

  6. Savitzky–Golay filter - Wikipedia

    en.wikipedia.org/wiki/Savitzky–Golay_filter

    Two-dimensional smoothing and differentiation can also be applied to tables of data values, such as intensity values in a photographic image which is composed of a rectangular grid of pixels. [17] [18] Such a grid is referred as a kernel, and the data points that constitute the kernel are referred as nodes. The trick is to transform the ...

  7. Gaussian filter - Wikipedia

    en.wikipedia.org/wiki/Gaussian_filter

    The simple moving average corresponds to convolution with the constant B-spline (a rectangular pulse). For example, four iterations of a moving average yield a cubic B-spline as a filter window, which approximates the Gaussian quite well. A moving average is quite cheap to compute, so levels can be cascaded quite easily.

  8. 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.

  9. Richardson–Lucy deconvolution - Wikipedia

    en.wikipedia.org/wiki/Richardson–Lucy...

    This has been written for one spatial dimension, but most imaging systems are two dimensional, with the source, detected image, and point spread function all having two indices. So a two dimensional detected image is a convolution of the underlying image with a two dimensional point spread function P ( Δ x , Δ y ) {\displaystyle P(\Delta x ...