Matlab Code for implementing ring partition technique used in Robust Perceptual Image Hashing

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The hashing consists of three steps. First the input image is converted to a normalized image with a standard size.Next, the normalized image is partitioned into different rings which are then used to construct a secondary image. Lastly, NMF ( Nonnegative Matrix Factorization) is applied to the secondary image and image hash is finally formed by NMF coefficients

I have divided a 512*512 square image into 32 rings and calculated their individual radii (r0-r31)

Now how do I obtain the pixel values in each ring and classify them into a set to make a sorted vector in ascending order? The next step is to map this vector into a new vector by linear interpolation to finally obtain a secondary image which is unrelated to rotation.