RIGID, AFFINE AND LOCALLY AFFINE REGISTRATION OF FREE-FORM SURFACES

In this paper, we propose a new framework to perform nonrigid surface registration. It is based on various extensions of an iterative algori thm recently presented by several researchers (Besl and McKay, 1992; C hampleboux et al., 1992; Chen and Medioni, 1992; Menq and Lai, 1992; Z hang, 1994) to rigidly register surfaces represented by a set of 3D po ints, when a prior estimate of the displacement is available. Our fram ework consists of three stages: First, we search for the best rigid di splacement to superpose the two surfaces. We show how to efficiently u se curvatures to superpose principal frames at possible corresponding points in order to find a prior rough estimate of the displacement and initialize the iterative algorithm. Second, we search for the best af fine transformation. We introduce differential information in points c oordinates: this allows us to match locally similar points. Then, we s how how principal frames and curvatures are transformed by an affine t ransformation. Finally, we introduce this differential information in a global criterion minimized by extended Kalman filtering in order to ensure the convergence of the algorithm. Third, we locally deform the surface. Instead of computing a global affine transformation, we attac h to each point a local affine transformation varying smoothly along t he surface. We call this deformation a locally affine deformation. All these stages are illustrated with experiments on various real biomedi cal surfaces (teeth, faces, skulls, brains and hearts), which demonstr ate the validity of the approach.