Smooth point-set registration using neighboring constraints

We present an approach for Maximum Likelihood estimation of correspondence and alignment parameters that benefits from the representational skills of graphs. We pose the problem as one of mixture modeling within the framework of the Expectation–Maximization algorithm. Our mixture model encompasses a Gaussian density to model the point-position errors and a Bernoulli density to model the structural errors. The Gaussian density components are parameterized by the alignment parameters which constrain their means to move according to a similarity transformation model. The Bernoulli density components are parameterized by the continuous correspondence indicators which are updated within an annealing procedure using Softassign. Outlier rejection is modeled as a gradual assignment to the null node. We highlight the analogies of our method to some existing methods.We investigate the benefits of using structural and geometrical information by presenting results of the full rigid version of our method together with its pure geometrical and its pure structural versions. We compare our method to other point-set registration methods as well as to other graph matching methods which incorporate geometric information. We also present a non-rigid version of our method and compare to state-of-the-art non-rigid registration methods.Results show that our method gets either the best performance or similar performance than state-of-the-art methods.

► We present a rigid point-set registration method that uses neighboring relations.
► Two well-known registration methods can be derived from the proposed method.
► We present a non-rigid extension of the proposed method.
► We compare to state-of-the-art rigid and non-rigid point-set registration and graph matching.
► Our method performs similarly or better than state-of-the-art methods in both synthetic and real-data experiments.