In this paper, we propose and analyze several methods to estimate a rigid transformation from a set of 3-D matched points or matched frames, which are important features in geometric algorithms. We also develop tools to predict and verify the accuracy of these estimations. The theoretical contributions are: an intrinsic model of noise for transformations based on composition rather than addition; a unified formalism for the estimation of both the rigid transformation and its covariance matrix for points or frames correspondences, and a statistical validation method to verify the error estimation, which applies even when no "ground truth" is available. We analyze and demonstrate on synthetic data that our scheme is well behaved. The practical contribution of the paper is the validation of our transformation estimation method in the case of 3-D medical images, which shows that an accuracy of the registration far below the size of a voxel can be achieved, and in the case of protein substructure matching, where frame features drastically improve both selectivity and complexity. 1.

Abstract—Ridges and valleys are useful geometric features for image analysis. Different characterizations have been proposed to formalize the intuitive notion of ridge/valley. In this paper, we review their principal characterizations and propose a new one. Subsequently, we evaluate these characterizations with respect to a list of desirable properties and their purpose in the context of representative image analysis tasks. Index Terms—Creases, separatrices, drainage patterns, comparative analysis. ————————— — F ——————————

Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g a G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(d) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tesselations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for total (Gaussian) and mean curvature estimation, and shows that indeed different alogrithms should be employed to compute the Gaussian and mean curvatures.

Automatic polyp detection is an increasingly important task in medical imaging with virtual colonoscopy [15] being widely used. In this paper, we present a 3D object detection algorithm and show its application on polyp detection from CT images. We make the following contributions: (1) The system adopts Probabilistic Boosting Tree (PBT) to probabilistically detect polyps. Integral volume and 3D Haar filters are introduced to achieve fast feature computation. (2) We give an explicit convergence rate analysis for the AdaBoost algorithm [2] and prove that the error at each step ɛt+1. is tightly bounded by the previous error ɛt. (3) For a 3D polyp template, a generative model is defined. Given the bound and convergence analysis, we analyze the role of “sample alignment ” in the template design and devise a robust and efficient algorithm for polyp detection. The overall system has been tested on 150 volumes and the results obtained are very encouraging. 1 1.

this paper we present an approach to localize semi-automatically landmarks characterized by extremal isocontour curvature. The semi-automatic approach implies that a rough estimate of the landmark position centered at a volume-of-interest is interactively provided by the user as an input. The algorithm then refines this position [10]. Monga and Benayoun [4] presented an approach to compute locally the curvature characteristics of isosurfaces. The gradient direction is used to define locally the tangent plane of the isosurface. Then a local parametrization is defined by setting up two arbitrary orthogonal vectors within this tangent plane. Given this parametrization they show how the principal curvatures of the isosurface and the associated principal directions can be computed. Additionally, they derive an extremality criterion based on the spatial derivative of the principal curvature in direction of the corresponding principal direction. Application of this extremality criterion in maximum curvature direction yields a 1D subset of points on the isosurface which they call ridge (or crest) lines. Thirion [6] proposed an algorithm to extract automatically isocontour curvature extrema, which he denoted extremal points, from 3D images and which then serve as input for a rigid registration algorithm. His algorithm basically uses the extremality criterion of Monga and Benayoun [4] in both principal curvature directions.

Given a smooth surface, a ridge is a curve along which one of the principal curvatures has an extremum along its curvature line. Ridges are curves of extremal curvature and therefore encode important informations used in segmentation, registration, matching and surface analysis. Surprisingly, no method developed so far to report ridges from a mesh approximating a smooth surface comes with a careful analysis, which entails that one does not know whether the ridges are reported in a coherent fashion. To bridge this gap, we make the following contributions. First, we present a careful analysis of the orientation issues arising when one wishes to report the ridges associated to the two principal curvatures separately. The analysis highlights the subtle interplay between ridges, umbilics, and curvature lines. Second, given a triangulation T approximating a smooth generic surface S, we present sufficient conditions on T together with a certified algorithm reporting ridges in a topologically coherent fashion. Third, we develop a heuristic algorithm to process a mesh when no information on an underlying smooth surface is known. Fourth, for coarse models, we provide a filtering mechanism retaining the most stable ridges only. Fifth, we present experimental results of the heuristic algorithm for smooth surfaces as well as coarse models. Our running times improve of at least one order of magnitude state-of-the-art methods. The common

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

Abstract — Multimodal image registration significantly benefits from previous denoising and structure segmentation and vice versa. In particular combined information of different image modalities makes segmentation significantly more robust. Indeed, fundamental tasks in image processing are highly interdependent. A variational approach is presented, which combines the detection of corresponding edges, an edge preserving denoising and the morphological registration via a non-rigid deformation for a pair of images with structural correspondence. The morphology of an image function is split into a singular part consisting of the edge set and a regular part represented by the field of normals on the ensemble of level sets. A Mumford-Shah type free discontinuity problem is applied to treat the singular morphology and the matching of corresponding edges under the deformation. The matching of the regular morphology is quantified by a second contribution which compares deformed normals and normals at deformed positions. Finally, a nonlinear elastic energy controls the deformation itself and ensures smoothness and injectivity. A multi scale approach that is based on a phase field approximation leads to an effective and efficient algorithm. Numerical experiments underline the robustness of the presented approach and show applications on medical images.

this article, we describe the virtual environment we have created in order to develop a simulator of liver surgery including visual and haptic feedback: the surgeon can interact in real time with a image of the virtual organ, and both look and feel the deformations. This work was done in the Epidaure project at INRIA Sophia-Antipolis (France) in collaboration with IRCAD in Strasbourg (France). Epidaure is a research group specialized in medical images analysis, and IRCAD is a multidisciplinary research institute for cancers of the digestive tract, involving among others clinicians, surgeons and scientists