How do I calculate the directional derivative of an image in the north, east, west and south directions?

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nbro
nbro 2019-5-31
To implement the anisotropic diffusion of Perona and Malik (1987), we can use an explicit scheme (Euler forward method), where the formula
Screen Shot 2019-05-31 at 12.09.37.png
where c is the diffusion function, I is the image and x, y and y are the parameters of both c and I (where x and y are the spatial coordinates of the image and t is time).
In this formulation, we need to find the gradient of the image in the north, east, west and south direction and c is also computed as a function of the direction. In Matlab, there are at least two functions to compute the derivative of a function, imgradient and imgradientxy, where the second seems to be the function I am looking for, but it calculates the directional gradient in the x and y direction. However, I am looking for the gradient in the north, east, west and south directions! So, how can I calculate the gradient of an image in the N, E, W and S directions in Matlab?

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