Representing clumps of cell nuclei as unions of elliptic shapes by using the MDL principle

We discuss the problem of interpreting clumps (or clusters) of nuclei in histological images as unions of elliptical shapes, each ellipse representing one nucleus. The difficult part is to rank various interpretations, involving different numbers of ellipses, and our approach is an information theoretic one where the score for each interpretation is computed using the minimum description length (MDL) principle for a simple parametric family of models. We show how to evaluate MDL for the proposed family using the code-length of an implementable method, which does not involve any asymptotic approximations. We then show how to locally improve the ellipse parameters of a given initial interpretation so that its MDL score is minimized. The initial and final MDL scores of each competing interpretation are then used for deciding which interpretation is the least redundant. We perform a preliminary study involving human subjects for proposing interpretations of the clumps and we also obtain interpretations by an improved version of the existing ellipse fitting algorithm SNEF. We study the variability between the human subject interpretations and compare it with the variability of SNEF algorithm. Finally, the results are examined by a pathology expert for assessing the quality of the MDL based decisions.