The last couple of days, I have focused on formally writing up the derivation in 2D of the constraints on the glitter that I am using in defining ellipses. I believe there is something wrong/incomplete in how I am thinking about the magnitude of the surface normals when using them to calculate the gradient vector. The difference in magnitude of the surface normals for each piece of glitter definitely has a bearing on the size of the ellipse associated with that piece of glitter.
I have attached my write-up to this post. In the write-up, there is a derivation of the constraints as well as my initial attempt at motivating this problem. I think I need to tie the motivation into the overall camera calibration problem instead of just talking about how the glitter can define ellipses.
My immediate next steps include re-working the last part of the derivation, the part which involves the magnitude of the surface normals (the ratio). I am also going to try to find other approaches to this problem. I REALLY believe the surface normals of the lit glitter is enough to determine the set of ellipses, so perhaps this implicit equation approach isn't the correct one! In the next day or so, I will put up a more comprehensive post on what results (including pretty/not-so-pretty pictures) I have achieved so far using the technique outlined in the write-up attached to this post.