CODEWITHSUNDEEP
pythonmachine-learningdeep-learninggaussianblurautomatic-differentiation
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Reputation: 11

Derivative of Gaussian Blur with respect to the pixels

I'm applying a Gaussian blur to an image where each pixel of the original image is being optimized for some purpose and the Gaussian blur is an intermediate transformation. For several reasons, it is important for me to be able to get the Jacobian of this transformation.

For instance if the transformation of the pixels can be given as G(p) then I need to be able to find dG/dp.

I'm stumped about how to actually find this though. It doesn't have to be analytical, it can be numerical through a Python program.

I don't really even know where to start.

I have an input image of 150x150 pixels. I am applying Gaussian blur through OpenCV. I understand how to find the Gaussian X and Y derivatives, but I don't understand how to find the Jacobian of the entire transformation with respect to the pixels.

Numerically, I suppose the finite difference method would work (change the pixel slightly and see the effect), but there probably is a better way no?

Upvotes: 1

Views: 130

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