This is a good question with many possible answers.   

Here is a selection of important shape descriptors:

Edge strength of a pixel:  Let f(x,y) be the intensity of a pixel in a digital image f and let $\frac{\partial f(x,y)}{\partial y}$ be the discrete partial derivative of f(x,y) with respect to y (denoted by Dy) and let $\frac{\partial f(x,y)}{\partial x}$ (denoted by Dx) be the discrete partial derivative of f(x,y) with respect to x.   Then the edge strength of f(x,y) is defined by

\[

E(x,y) = |Dx| + |Dy|.

\]

Edge strength is used in John Canny's approach to determining when a pixel is an edge pixel relative to a hysteresis interval and the principle of non-maximal suppression.

Gradient orientation of a pixel: arctan [Dy/Dx].

Connectedness: 4-connected and 8-connected pixels.

Adjacency: adjacent pixels and adjacent neighbouhoods.

Convexity: Set of pixels that form a convex set.

Hole: A set of low (zero) intensity pixels in a binary image.

There are some very good papers on shape descriptors on RG.  Here are examples:

https://www.researchgate.net/publication/224135303_Intrinsic_shape_signatures_A_shape_descriptor_for_3D_object_recognition

https://www.researchgate.net/publication/253282688_Spherical_Harmonics_as_a_Shape_Descriptor_for_Hyperspectral_Image_Classification

https://www.researchgate.net/publication/4141418_A_comparative_study_of_three_moment-based_shape_descriptors

Conference Paper Intrinsic shape signatures: A shape descriptor for 3D object...

Article Spherical Harmonics as a Shape Descriptor for Hyperspectral ...

Conference Paper A comparative study of three moment-based shape descriptors

Hi Muhammad,

Thanks for the great question. If you happen to be able to post an example image (i.e. use case), I'd be happy to use our new and powerful software package MIPAR, available at http://MIPAR.us, to identify your features of interest based on many of the available segmentation tools, many of which involve advanced feature shape metrics. These can include convex area/area ratio, eccentricity, and moment invariants.

Cheers,

John

Hi Muhammed,

I just want to add my personal experience to the good advices above.

We are working on colorectal polyp classification and found that the simple, scale invariant parameters, such as solidity (=convex_area/area), circularity (=4*pi*area/perimeter^2), and Hu moments are good enough for our purposes. Of course, not all of them is needed, and we could reach more than 95% accuracy in spot classification using only 3 of them. (solidity, circularity, Hu_0). But this is problem-dependent.

I'd like to suggest to try the very simple scale-invariant properties. Solidity, circularity, Hu moments are usually supported by image processing libraries. If they are not enough, you can try the more sophisticated. (See, e.g., the suggested papers above.)

(Note however, that an adequate preprocessing is a must for trustworthy identification.)

Article Preprocessing Endoscopic Images of Colorectal Polyps

Hi.

I am using fiji mostly and to my experience on biological objects the easiest parameter like elongation, sphericity, volume/area work the best.

Though I have a habit to turn on all possible parameters when first seeing a new type of objects and checking if any of it works. Though I always go back to "easy" one in the end.