Estimation of multiple objects at unknown locations with active contours Margarida Silveira and Jorge S. Marques IST - Instituto Superior T´ ecnico, Technical University of Lisbon and ISR - Instituto de Sistemas e Rob´otica, Portugal Abstract. This paper presents an algorithm for the estimation of multi- ple regions with unknown shapes and positions using multiple active con- tour models (ACM’s). The algorithm organizes edge points into strokes and computes the association between those strokes and the ACM’s us- ing the component wise EM algorithm (CEM) for MAP estimation. The algorithm is randomly initialized with a high number of ACM’s and per- forms online model selection using importance sampling. Experimental results show the effectiveness of the proposed technique. 1 Introduction Active contour models (ACM’s) or snakes [1] have been extensively used to esti- mate object boundaries in images. However, their difficulties with initialization and outlier rejection are still unsolved problems. In addition, most of the re- search done on ACM’s tries to estimate a single region using one elastic model (for e.g. see [2] [3]) and little research has addressed estimation of multiple elastic models. Some examples include [4] where multiple regions are estimated but the approach is restricted to regions that have some common characteristic or prop- erty and weighting parameters are defined heuristically. In [5] several ACM’s are initialized in the centers of divergence of the gradient vector flow field. Some of the centers are discarded using heuristic rules and the method is unable to deal with regions inside other regions. In [6] a single contour can break automatically to represent the contours of multiple objects. In [7] multiple level set contours are also used but they evolve independently. The initial segmentation and num- ber of ACM’s is determined by fuzzy c-means clustering. In [8] gradient vector diffusion is used for the evolution and also the initialization of multiple contours. After the contours evolution region merging reduces the number of contours. In this paper we present a method for the automatic segmentation of multiple regions which, in simultaneous with shape estimation, deals with the problem of sensitivity to the initialization and robustness to outliers. The algorithm builds on the work proposed in [9] in which multiple ACM’s compete for the boundaries of multiple regions, using the EM algorithm for MAP estimation. The algorithm proposed in this paper includes three major contributions 1) it automatically selects the number of ACM’s 2) it uses a different observation model which makes it less sensitive to initialization and more robust to outliers and 3) initialization of the ACM’s is fully automatic.