Free form shape registration using the barrier method

This paper formalizes overlapping free form shape registration as a minimization problem, which minimizes a weighted sum of registration errors of tentative correspondences with the weights subject to boundary conditions. The tentative correspondences are established using the traditional closest point criterion. Then the powerful barrier method is employed to transform the constrained minimization problem to an unconstrained one. Setting the first order derivative of the unconstrained objective function to zero results in the weights being solved with a closed form solution. The weights are finally globally optimized using the deterministic annealing scheme. Outliers due to occlusion, appearance and disappearance of points in either free form shape are explicitly modelled using a constant. The camera motion parameters are updated in the weighted least squares sense. A comparative study based on both synthetic data and real images shows that the proposed algorithm is promising for the accurate and robust automatic registration of overlapping free form shapes.

Research highlights
► We have formulated the automatic overlapping free form shape registration problem as a constrained one, subject to simple and natural boundary conditions. While it is challenging to solve, it may be formulated as one simpler than we expected.
► A novel algorithm has been developed for the automatic registration of overlapping free form shapes. It possesses a number of desirable properties simultaneously: equalizing the weights of the tentative correspondences, minimizing the registration error of any tentative correspondence, penalizing those correspondences with large registration errors, maximizing the overlapping area between the free form shapes being registered, etc.
► On the whole, the proposed algorithm is more accurate and stable than three existing ones for the automatic registration of overlapping free form shapes with various complexities of geometry.