Registration of 3D medical images consists in computing the “best” transformation between two acquisitions, or equivalently, determines the point to point correspondence between the images. Registration algorithms are usually based either on features extracted from the image (feature-based approaches) or on the optimization of a similarity measure of the images intensities (intensitybased or iconic approaches). Another classification criterion is the type of transformation sought (e.g. rigid or non-rigid). In this chapter, we concentrate on feature-based approaches for rigid registration, similar approaches for non-rigid registration being reported in another set of publication [35, 36]. We show how to reduce the dimension of the registration problem by first extracting a surface from the 3D image, then landmark curves on this surface and possibly landmark points on these curves. This concept proved its efficiency through many applications in medical image analysis as we will see in the sequel. This work has been for a long time a central investigation topic of the Epidaure team [2] and we can only reflect here on a small part of the research done in this area. We present in the first section the notions of crest lines and extremal points and how these differential geometry features can be extracted from 3D images. In Section 2, we focus on the different rigid registration algorithms that we used to register such features. The last section analyzes the possible errors in this registration scheme and demonstrates that a very accurate registration could be achieved.

INTRODUCTION E PIDAURE is the name of a research project launched in 1989 at INRIA Rocquencourt, close to Paris, France. At that time, after a first experience of research in Computer Vision [1] in the group of O. Faugeras, I was very enthusiastic about the idea of transposing research results of digital image analysis into the medical domain. Visiting hospitals and medical research centers, I was progressively convinced that Medical Image Analysis was an important research domain by itself. In fact I had the impression that a better exploitation of the available medical imaging modalities would require more and more advanced image processing tools in the short and long-term future, not only to assess the diagnosis on more objective and quantitative measurements, but also to better prepare, control and evaluate the therapy. Fig. 1. This image has been the "Logo" of the Epidaure project for a long time. It was also used as a logo of the first CVRMed Conference held in Nice in 1

In this paper, we present a new and efficient multi-modal 3D-3D vascular registration algorithm, which transforms the 3D-3D registration problem into a multiple 2D-3D vascular registration problem. Along each orthogonal axis, projected 2D image from a segmented binary 3D floating volume is compared with maximum intensity projection (MIP) image of the reference volume. At the preprocessing stage of the floating image volume, vessels are segmented and represented by a number of spheres with centers located at the skeleton points of the vessels and radii equal to the distance from the skeleton points to their closest boundary. To generate projected images from the binary 3D volume, instead of using the conventional ray-casting technique, the spheres are projected to the three orthogonal projection planes. The discrepancy between the projected image and the reference MIP image is measured by a relatively simple similarity measure, sum of squared differences (SSD). By visual comparison, we found that the performances of our method and the Mutual Information (MI)-based method are visually comparable. Moreover, based on the experimental results, our method for 3D-3D vascular registration is more computationally efficient than the MI-based method.

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Publication interne n ˚ 1746 — Septembre 2005 — 36 pages Abstract: A unified a contrario detection method is proposed to solve three classical problems in clustering analysis. The first one is to evaluate the validity of a cluster candidate. The second problem is that meaningful clusters can contain or be contained in other meaningful clusters. A rule is needed to define locally optimal clusters by inclusion. The third problem is the definition of a correct merging rule between meaningful clusters, permitting to decide whether they should stay separate or unit. The motivation of this theory is shape recognition. Matching algorithms usually compute correspondences between more or less local features (called shape elements) between images to be compared. This paper intends to form spatially coherent groups between matching shape elements into a shape. Each pair of matching shape elements indeed leads to a unique transformation (similarity or affine map.) As an application, the present theory on the choice of the right clusters is used to group these shape elements into shapes by detecting clusters in the transformation space. Key-words: Cluster validity, merging criterion, number of false alarms, shape recognition (Résumé: tsvp)