This past week, I have been working on solving for the gaussian which fits the intensity plots of my glitter pieces, and using this to solve for the center of the receptive field of the glitter. Below is an example of an intensity plot of a centroid:
Below are the equations I am using to write the optimization function to solve for the receptive field. Here I am computing the integral of the response of a piece of glitter at every location on the monitor, where I(x,y) is a binary of whether the monitor is lit or not at each location:
Right now, I am solving this using the circular gaussian with a single sigma, and I spent a few days working through writing the optimization function. Yesterday I was able to write it in a way that speeds it up (each iteration is looking at 200 frames and ~700 centroids, so it was very slow).
My next step is to work on analyzing the final error that I am getting and looking at the optimal solution for the center of the receptive field and the sigma value (I am getting a solution, but have not spent too much time trying to understand its validity).