A New Model for the Segmentation of Multiple, Overlapping, Near-Circular Objects

Some of the most difficult image segmentation problems involve an unknown number of object instances that can touch or overlap in the image, e.g. microscopy imaging of cells in biology. In an important set of cases, the nature of the objects and the imaging process mean that when objects overlap, the resulting image is approximately given by the sum of intensities of individual objects; and, in addition, the objects of interest are `blob-like' or near-circular. We propose a new model for the segmentation of the objects in such images. The posterior energy is the sum of a prior energy modelling shape and a likelihood energy modelling the image. The prior is a multi-layer nonlocal phase field energy that favours configurations consisting of a number of possibly overlapping or touching near-circular object instances. The likelihood energy models the additive nature of image intensity in regions corresponding to overlapping objects. We use variational methods to compute a MAP estimate of the object instances in an image. We test the resulting model on synthetic data and on fluorescence microscopy images of cell nuclei.