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Digital Image Processing (2000)

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4.4 Matrix Manipulation

In addition to the typical geometric operations of zooming and rotation/warping, a number of functions for padding and combining matrices are included in the Digital Image Processing package. Edge padding operations occur naturally in the context of any linear or morphological filtering operation. Matrix concatenation and threading functions add to the already impressive library of matrix manipulation functions found in Mathematica.
This loads the package.
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This gives three example arrays.
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Five methods of padding images and multidimensional arrays are available. Arrays may be extended by appending zeros, by appending any user selected constant, by periodic repetition of the elements of the array, by periodic repetition of the elements of the array in reverse order, and by replication of the edge elements.

List padding functions.

This demonstrates padding 1D lists with zeros.
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This contrasts periodic and reflected padding of a 1D list.
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This shows all the padding methods using a small example matrix.
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In addition to padding, a number of matrix manipulation operators are available, which allow for a variety of methods of concatenating and combining arrays.

Matrix combine, join, and thread functions.

Here are examples of threading and concatenating matrices and . First we demonstrate row-only operations.
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Here are the results of joining and threading both rows and columns.
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Reflection is a form of rotation. In the case of a matrix, it is equivalent to a rotation by 180 degrees. For multidimensional arrays it is more conveniently implemented as a reversal of the elements at each level of the array. Reflections naturally occur in convolution operations and many morphological operators.

Reflect function.

Here is an example of the reflection of a matrix.
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