Spatial-Stiffness Analysis of Surface-Based Registration

Abstract

Abstract. We have developed a new approach for preoperative selection of points from a surface model for rigid shape-based registration. This approach is based on an extension of our earlier spatial-stiffness model of fiducial registration. We compared our approach with the maximization of the noise-amplification index (NAI), using target registration accuracy (TRE) as our comparison measure, on models derived from computed tomography scans of volunteers. In this study, our approach was substantially less expensive to compute than maximizing the NAI and produced similar TREs with smaller variances. Optimal incremental selection shows promise for improving the preoperative selection of registration points for image-guided surgical procedures.

Unified Point Selection and Surface-Based Registration Using a Particle Filter

“…We [9] proposed an algorithm for sequentially constructing a set of model registration points by greedily maximizing a quality measure derived from a stiffness model of shape-based registration. Our approach considers the N registration points p i to be the attachment locations for unloaded linear springs with orientations given by the surface normal vectors n i .…”

“…Q characterizes the least constrained displacement of the mechanism; maximizing Q will minimize the worstcase displacement of the mechanism. Our algorithm [9] takes as input a set of N model registration points p i with normal vectors n i and a surface model from which to select points. The quality measure Q is calculated and heuristics are used to find the model point p N +1 that maximizes the increase in Q.…”

“…of the increase in quality measure if point p k with normal n k is added to the current set of estimated model registration points P; see [9] for details. • Find the model points with ∆Q in the range [lo, hi] (lo and hi might be the 95 th and 100 th percentiles, for example) defining regions on the model that contain good registration points.…”

“…Uniform sampling of the sphere of normal vectors was proposed by Rusinkiewicz and Levoy [12] as a method of point selection for registering pairs of range images. We [9] showed that Simon's scatter matrix was equivalent to the well known spatial-stiffness matrix of an unactuated, kinematically unconstrained elastic mechanism; we proposed a pointselection algorithm based on the coordinate frame invariant analysis of Lin et al [8].…”

“…In this article we unify our point selection algorithm [9] with our sampling-based registration algorithm [10] to produce a filter-selection algorithm that estimates the distribution of the registration parameters (instead of only the covariance) and computes which regions of the model are likely to contain good registration points.…”