My general question is, how do I go about performing some differential geometry on Image data? Specifically, I would like to represent the images as a surface defined by its intensity value, and then interpolate a smooth surface over it. After that I would like to examine the various Curvature based properties on this surface.
I can manage the Interpolation and get a surface (using ListPlot3D, my images are expressed as list of lists, row x col). What would the next steps be? Is there a package that I should load, or something that I can download (preferable something that also allows me to calculate the fundamental forms too..)