In this paper, the problem of estimating automatically the symmetry plane of bilateral objects (having perfect or imperfect mirror symmetry) in point clouds is reexamined. Classical methods, mostly based on the ICP algorithm, are shown to be limited and complicated by an inappropriate parameterization of the problem. First, we show how an adequate parameterization, used in an ICP-like scheme, can lead to a simpler, more accurate and faster algorithm. Then, using this parameterization, we reinterpret the problem in a probabilistic framework, and use the maximum likelihood principle to define the optimal symmetry plane. This problem can be solved efficiently using an EM algorithm. The resulting iterative scheme can be seen as an ICP-like algorithm with multiple matches between the two sides of the object. This new algorithm, implemented using a multiscale, multiresolution approach, is evaluated in terms of accuracy, robustness and speed on ground truth data, and some results on real data are presented.