What are the image comparision methods based on shape?

What are the comparision methods available to compare 2 images, based ONLY on the SHAPE?

Without considering about pixel values, mean, median, etc.

Answer 1

[Image Analyst]

A common one is circularity or roundness. See Wikipedia on roundness for a bunch of metrics. For example you can use

circularity = perimeter .^ 2  ./ (4 * pi * Area);

You can also look at Euler number, Feret Diameters Click here, morphometrics (see Wikipedia), blob count per unit area, area fraction, blob orientation (rose of orientations), class adjacency (how likely it is for one type of blob to be next to another type of blob), etc.