Hello David, May you please let me know how to export all the angles with coordinates in a text or excel file? I am pretty unfamiliar to Mathematica so struggling to get it.

Regards, Mirtunjay

Thanks for you insight on this. I understand tolerably well in "concept" the challenge and believe that some more work on the portion of the code that fits the data will produce results. However, I'm not confident that my skills in the Wolfram language will allow me to work constructively on such a problem, at least not yet. I would like to ask if you may consider collaborating on this problem in a more formal way, perhaps with the benefit of being published or for a consulting fee. Any arrangement I might make will need approval by my adademic advisor, but I believe this can happen. My contact information is as follows: Phillip Green, gt9226a@gatech.edu

This is an interesting problem. I have been thinking of an approach based disks of successive radii. Looking at the top image, begin at a vertex and define a disk region of a small radius. Count the black pixels within the disk. Do the same for successively greater radii. At each step, the rate at which the black pixel count grows is a function of the arc subtended by the black region at that radius. For any given radius, this may be a noisy number. But if the curve could be fit, perhaps from the fit could be determined an estimate of the angle of separation at the start. It would help if some assumption could be made regarding the form of the function to be fit.

Hi Phillip,

Would you mind posting some source data, for example one of your input images at max resolution.

My immediate commentary regards data cleanliness. The sample image you're working from contains four areas that are aligned with varied precision. You are examining corners along these boundaries, along with corners at the edges of the image (notably some noise in the top right has created at least one erroneous corner.)

I would suggest partitioning your input into each separate image, and then extracting the shapes entirely contained in each image. If you're expecting high variance this suggestion may be inappropriate, as it may skew your corner data towards that of smaller 'blobs'.

Finally, all of these corners feature highly curved edges, thus the higher resolution we examine the smaller the output angles will be. Will all the input data be at a consistent resolution? Is there a specific pixel radius you want to specify measuring at?

David