Point set registration for pose estimation using continuous distance field

An efficient and precise three-dimensional shape registration method using the continuous distance field is described, which reformulates the point set registration as the nonlinear least squares optimization problem. The continuous distance field is proposed by the approximate distance function derived from the implicit formulation of the target model. The registration error with respect to the relative pose is constructed by the sum of the squared distance between the source set to the target model. In this paper, the twist coordinates are adopted to represent the rigid transformation of the 3D object during the registration process. With the property of Lie group and Lie algebra, the optimal registration is formulated concisely as an unconstrained optimization problem. In this way, the best match can be achieved by directly optimizing the six pose parameters of the object. The detailed formulation of the Gauss-Newton method for solving the nonlinear least squares problem is explicitly derived. Experimental results show the proposed approach is capable of aligning the 3D free-form object with faster convergence speed, especially in the presence with a large amount of point cloud, which demonstrates the potential applications of the method such as pose estimation and object tracking.