CONTINUUM SHAPE CONSTRAINT ANALYSIS: A CLASS OF INTEGRAL SHAPE PROPERTIES APPLICABLE TO LIDAR/ICP-BASED POSE ESTIMATION

Abstract

Surface registration involving the estimation of a rigid transformation (pose) which aligns a model provided as a triangulated mesh with a set of discrete points (range data) sampled from the actual object is a core task in computer vision. This paper refines and explores the previously introduced notion of Continuum Shape Constraint Analysis (CSCA) which allows the assessment of object shape towards predicting the performance of surface registration algorithms. Conceived for computer-vision assisted spacecraft rendezvous analysis, the approach was developed for blanket or localized scanning by LIDAR or similar range-finding scanner that samples non-specific points from the object across an area. Based on the use of Iterative Closest-Point Algorithm (ICP) for pose estimation, CSCA is applied to a surface-based self-registration cost function which takes into account the direction from which the surface is scanned. The continuum nature of the CSCA formulation generates a registration cost matrix and any derived metrics as pure shape properties of the object. For the context of directional scanning as considered in the paper, these properties also become functions of viewing direction and is directly applicable to the best view problem for LIDAR/ICP pose estimation. This paper introduces the Expectivity Index and uses it to illustrate the ability of the CSCA approach to identify productive views via the expected stability of the global minimum solution. Also demonstrated through the examples, CSCA can be used to produce visual maps of geometric constraint that facilitate human interpretation of the information about the shape. Like the ICP algorithm it supports, the CSCA approach processes shape information without the need for specific feature identification and is applicable to any type of object.