I think you need to compare the performance of the methods to a reference. We normally use the ground truth (manually labelled data set). You could however, implement the best method reported in the literature and compare the the 3 algorithms to that but again you are not comparing to the optimum solution.

The other thing that I could think of in case you are working on life science data is to gain access to priori knowledge of your data (e.g, number of cells in a tissue, distributions of their sizes, etc) and then you see which segmentation method approaches that "number" or best matches the size distributions. In short you really need some side information to help you compare the methods.

Hi Khadidja,

Otherwise, without GT you can measure "how much" your segmentation methods are different from each other without knowing if they are good or not.

For doing so you can perform pairwise comparison based on contours, Jaccard Index, Dice coefficient or other. May be your conclusion will be something like your three systems are very close but you will not have any indications regarding their respective accuracy.

An alternative would be to define a subjective scale. For that, you would ask two or three observers to rate in a binary or ternary fashion a subset. Each readers will be asked to rate the outcome of the three segmentation computing the same data until kappa coefficient will disclose significant difference (pVal

If the three methods are each doing a fair job, you might create a rating of the methods in this way. For each test image, sum (pixelwise) the binary (0/1) segmentation images, then for each of the 3 binary segmentation images multiply it by that sum image and then compute the average intensity of the result. The values show the degree to which each segmentation result agrees with the consensus of all three methods. This is a quick and easy relative ordering. In principle, you could threshold the sum image to get a consensus segmentation at some degree of confidence. Not perfect, but gives a nice ordering of the methods.

Still, how to know that the three methods are each doing a fair job?

If there is no other side information that could be helpful, I would recommend trying the visual quality scale (e.g., Human visual system scoring) as Tom suggested above. We have used that to rank common methods, including our own, for image fusion, see the below paper, particularly section 3.4:

https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-21-14-16584&id=258484