Statistical Partial Constraints for 3D Model Matching and Pose Estimation Problems

Abstract

We explore the potential of variance matrices to represent not just statistical error on object pose estimates but also partially constrained degrees of freedom. Using an iterated extended Kalman filter as an estimation tool, we generate, combine and predict partially constrained pose estimates from 3D range data. We find that partial constraints on the translation component of pose which occur frequently in practice are handled well by the method. However, coupled partial constraints between rotation and translation are, in general, non-linear and cannot be represented by this method.

Controllability and Observability: Tools for Kalman Filter Design

“…If the estimation process allows accurate evaluation of the mean it is quite correct to use the process covariance to constrain the value of the estimated mean by allowing the estimate variance to reduce to zero (the issue of controllability of this system is discussed in depth in the later work [12]). In [11], where the covariance matrix is used to provide partial constraints on aligning patches of range data, it is noted that in certain degenerate cases there are problems with their algorithm, although this is not named as a controllability problem.…”

Optimal Pose Estimation in Two and Three Dimensions

“…The anisotropy of feature error distribution in 2D data [12] and 3D range data [13] has been represented in covariance matrix form. This corresponds to an oriented weighting on the error measure so that position errors transverse to the edge direction are given a higher weighting than axial errors along the edge direction.…”