Image Segmentation Using Weak Shape Priors

The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. In the case when the segmentation is performed by means of active contours, a typical way to overcome the above difficulties is to impose an a priori model on the shape of the contours – a model which can be either analytical or probabilistic in its nature. Effectively, the model represents some shape constraints, which are intended to regularize the segmenting contour in the case when imagery data alone fails to provide sufficient information for determination of its optimal configuration. In practice, the shape models are typically learned based on training sets of examples of the object(s) of interest. In such cases, the goodness of modeling depend on the size of the training set, with more examples leading to more reliable and accurate models. Unfortunately, when the number of training samples is relatively small, the resulting model can be inadequate, thereby tending to bias the segmenting contour towards a suboptimal solution. To overcome this deficiency, the present paper introduces a novel approach to modeling of shape priors. Specifically, in the proposed method, an active contour is constrained to converge to a configuration at which its geometric parameters attain their empirical probability densities closely matching the corresponding model densities that are learned based on training samples. It is shown through numerical experiments that the proposed shape modeling can be regarded as “weak” in the sense that it minimally influences the segmentation, which is allowed to be dominated by data-related forces. On the other hand, the priors provide sufficient constraints to regularize the convergence of segmentation, while requiring substantially smaller training sets to yield less biased results as compared to the case of PCA-based regularization methods. The main advantages of the proposed technique over some existing alternatives is demonstrated in a series of experiments. ∗This research was supported by a Discovery grant from NSERC – The Natural Sciences and Engineering Research Council of Canada. Information on various NSERC activities and programs can be obtained from http://www.nserc.ca. †R. Xu, O. Michailovich, and M. Salama are with the School of Electrical and Computer Engineering, University of Waterloo, Canada N2L 3G1 (phone: 519-888-4567; e-mails: rsxu, olegm, [email protected]). 1 ar X iv :1 00 6. 27 00 v1 [ cs .C V ] 1 4 Ju n 20 10