Rigid and affine registration of smooth surfaces using differential properties

Abstract

Recently, several researchers ([BM92], [Zha93], [CM92], [ML92], [CLSB92]) have proposed very interesting methods based on an iterative algorithm to rigidly register surfaces represented by a set of 3d points, when an estimate of the displacement is available. In this paper, we propose to introduce differential informations on points to extend this algorithm. First, we show how to efficiently use curvatures to superpose principal frame at possible corresponding points in order to find the needed rough estimate of the displacement. Then, we explain how to extend this algorithm to look for an affine transformation between two surfaces. We introduce differential informations in points coordinates: this allows us to match locally similar points. We show how this differential information is transformed by an affine transformation. Finally, we introduce curvatures in the best affine transformation criterion and we minimize it using extended Kalman filters. All this extensions are illustrated with experiments on various real biomedical surfaces: teeth, faces, skulls and brains.