Structure Matrices and Convolution Kernels
| DiskMatrix[r] | a radius r disk of 1s inside a  matrix of 0s |
| DiskMatrix[{r1,...}] | an ellipsoid of 1s with radii  inside an array of dimension  |
| DiskMatrix[{r1, ...},{n1, ...}] | an ellipsoid with radii  inside an array of dimension  |
| DiamondMatrix[{r1,...},{n1,...}] | a diamond of 1s with radii  inside an array of dimension  |
| BoxMatrix[{r1,...},{n1,...}] | a box of 1s with radii  inside an array of dimension  |
| CrossMatrix[{r1,...},{n1,...}] | a cross of 1s with radii  inside an array of dimension  |
Constructing matrices with special shapes.
This creates a matrix of 0s containing a radius 4 diamond of 1s. The result is a 9×9 matrix.
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The size of the matrix can be explicitly specified.
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This creates a matrix containing an ellipse and displays it graphically.
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Here is the same matrix, converted to an
Image. Note that 1 is
White and 0 is
Black.
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The shape matrix family of functions can make arrays with any rank.
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| GaussianMatrix[r] | A  matrix which samples a Gaussian |
GaussianMatrix[{r, }] | A  matrix which samples a Gaussian with standard deviation |
| GaussianMatrix[{{r1,...},{1,...}}] | A  array which samples a Gaussian with standard deviation  in the  direction |
| GaussianMatrix[{{r1,...},{1,...}},{n1,...}] | A  array which samples the  discrete derivative in the  direction of a Gaussian with standard deviation  in the ith direction |
Gaussian matrices.
This creates a radius 2 Gaussian kernel.
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GaussianMatrix can construct arrays with any rank.
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By default, the matrix elements are numerical and constructed to behave optimally under discrete convolution. Using
WorkingPrecision->Infinity will produce an exact representation.
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Use
Method
to sample a true Gaussian.
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This shows a comparison of the two types of Gaussians.
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This specifies a standard deviation of 1 in both directions of a rectangular Gaussian matrix.
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Plot the second derivative of the Gaussian in the row direction.
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Sum derivatives by using nested
List objects in the second argument. For example, this plots the Laplacian.
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This finds the length of the vector which has a minimum of 95% of the integrated fraction of the Gaussian with standard deviation 1.
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This finds the dimensions of the matrix which, in each direction, has a minimum of 95% of the integrated fraction of the Gaussian with standard deviation 1.
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