Detecting the Prescence of a "Tail" on an Object

Question

I have a set of objects, which may be spherical or elongated, which may or may not have a tail like structure attached to one or two ends. The tail may be long or short. It may also have a curve to it.

I'm currently looking over the information returned by regionprops and trying to see if anything jumps out at me which could be used to discriminate between normals and tails. I am also playing around with some morphological operations.

An opening operation followed by a comparison to the original mask is my current thought, but I'm not certain that this will be reliable enough in the presence of elongated cells, and I haven't yet found the "perfect" structuring element.

As I am not highly experienced in the IA field (more of an intermediate level), I am thinking that it may be a good idea to reach out and see if others have any ideas that I have not yet considered.

Test images are below. The effective dynamic range is 12-bits, but I've normalized them so that they can be viewed more easily.

And here are a few "normals" for comparison:

P.S. I'm not overly concerned about which language is being used, nor do I require a code sample. However, I am using MATLAB in case anyone would like to dive into the implementation.

Answer 1

If you want to use mathematical morphology in your problem, you have two solutions:

1. You already know the tail width (approximately the number of pixels). Then you perform a top-hat with a comparable size, like that only the tail is cut into the opening operation, and consequently appears in the result.
2. The tails have different width (too different to approximate), then you use minimum answer of oriented openings. You apply many opening with an oriented structuring element (but length smaller than the cell nuclei size), and you keep the minimum answer. The tail will disappear, and then you subtract this image to the original one.

An other solution is to compute the cell skeleton and a distance map. If your cell has a tail, then more pixels of the skeleton will have a short distance from the border.

A last solution is to use a shape index. Normally as cited, the ratio between the major and minor axis is enough. But if you cell are really elongated and with twisted tails, then you can replace this shape index using the ratio between the geodesic diameter and the area (Coster and Chermant, 1985, Book): 4/Pi x S / D^2, with S the surface and D the geodesic diameter.