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We can easily rewrite Equation 10 in matrix shape, for instance by expressing the convolution as the sequence of a direct Fourier Transform, a masking in the frequency domain (using a diagonal matrix multiplication), and an inverse Fourier transform.
They focus instead on the more interesting differences in matrix shape and orientation.
Similarly, the comparison between rows A, D and E shows that the effect of changes in shape depends on the matrices' orientation, and that changes in matrix shape become irrelevant (in this two-variables example) when the first eigenvectors of the two matrices are perpendicular (row D).
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It could be arranged in a matrix shape ranging from 12 lines (one cell in each line) to 1 line.
As shown in [59], that the co-ocurrence matrix shape is linked to the fractal dimension of the signal or image.
Moreover, we have shown that d' and H2' are largely robust against variation in matrix size, shape, and sampling effort.
Finally, plot A shows that, in the same way as the effect of orientation depends on matrix shape, the effect of shape depends on orientation.
The statistics also measure the influence of matrix shape and orientation on that differentiation, but not differences in shape and orientation directly.
In this interporosity equation, α is a constant in Warren and Root's model, but differs with the changes in matrix blocks' shapes.
The computer simulations shown in Figure 4 are limited to measure the power of the considered procedures to detect the consequences of changes in matrix orientation and shape.
The S-statistics procedure provides a simple and continuously-varying overall measure of differentiation that is distribution free and interpretable in terms of changes in matrix orientation and shape.
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