Registration of Uncertain Geometric Features: Estimating the Pose and its Accuracy

We provide in this article a generic framework for the pose estimation from geometric features. We propose more particularly three algorithms: a gradient descent on the Rie-mannian least square distance and on the Mahalanobis distance , and an Extended Kalman Filter. For all these methods , we provide a way to compute the uncertainty of the resulting transformation. The analysis and comparison of the algorithms show how to combine them in a powerful and high level statistical registration algorithm. An application in medical image analysis demonstrate the usefulness of the method. 1 Introduction In computer vision, most registration algorithms rely on feature extracted from the images. In this framework, the problem can generally be separated into two steps: (1) nd-ing the correspondences between features (matches) and (2) computing the geometric transformation that maps one set of features to the other. In this article, we do not discuss matching methods per se, but the estimation of the geometric transformation and its accuracy. We rst review the existing methods for computing the 3D rigid motion from two sets of matched points and how one can estimate its uncertainty. However, models of the real world often lead to consider more complex features like lines Gri90], planes, oriented points FA96] or frames PA94] and no traditional method easily extends to such features. Moreover, we have shown in PA98] that geometric features generally do not belong to a vector space but rather to a manifold and that it induces paradoxes if we try to use the standard techniques on points with them. Thus, we have developed in Pen96] a rigorous theory of uncertainty on geometric features. The basic idea is that our measures on features should be invariant by the action of a given transformation group. In the geometric framework, this can be ensured by using an invariant Riemannian distance on the manifold (which means that the transformation group is a kind of rigidd one for the features). We have developed the