Abstract. An N-dimensional image is divided into “object ” and “background” segments using a graph cut approach. A graph is formed by connecting all pairs of neighboring image pixels (voxels) by weighted edges. Certain pixels (voxels) have to be a priori identified as object or background seeds providing necessary clues about the image content. Our objective is to find the cheapest way to cut the edges in the graph so that the object seeds are completely separated from the background seeds. If the edge cost is a decreasing function of the local intensity gradient then the minimum cost cut should produce an object/background segmentation with compact boundaries along the high intensity gradient values in the image. An efficient, globally optimal solution is possible via standard min-cut/max-flow algorithms for graphs with two terminals. We applied this technique to interactively segment organs in various 2D and 3D medical images. 1

. We present a new algorithm for the non-rigid registration of 3D Magnetic Resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces (cortical surface and the lateral ventricles) in the image sequence using an active surface algorithm. The volumetric deformation field of the objects the surfaces are embedded in is then inferred from the displacements at the boundary surfaces using a biomechanical finite element model of these objects. The biomechanical model allows us to analyse characteristics of the deformed tissues, such as stress measures. Initial experiments on an intraoperative sequence of brain shift show a good correlation of the internal brain structures after deformation using our algorithm, and a good capability of measuring surface as well as subsurface shift. We measured distances between landmarks in the deformed initial image and the corresponding landmarks in the target scan. The surface shift was recovered from up ...

Recovery of unstructured 3D data with deformable models has been the subject of many studies over the last ten years. In particular, in medical image understanding, deformable models are useful to get a precise representation of anatomical structures. However, general deformable models involve large linear systems to solve when dealing with high resolution 3D images. The advantage of parametric deformable models like superquadrics is their small number of parameters to describe a shape combined with a better robustness in the presence of noise or sparse data. Also, at the expense of a reasonable number of additional parameters, free form deformations provide a much closer fit and a volumetric deformation field. This article introduces such a model to fit unstructured 3D points with a parametric deformable surface based on a superquadric fit followed by a free form deformation to describe the cardiac left ventricle. We present the mathematical and algorithmic details of the method, as wel...

We present a new approach to analyse the deformation of the left ventricle of the heart based on a parametric model that gives a compact representation of a set of points in a 3-D image. We present a strategy for tracking surfaces in a sequence of 3-D cardiac images. Following tracking, we then infer quantitative parameters which characterize: left ventricle motion, volume of left ventricle, ejection fraction, amplitude and twist component of cardiac motion. We explain the computation of these parameters using our model. Experimental results are shown in time sequences of two modalities of medical images, nuclear medicine and X-ray computed tomography (CT). Video sequences presenting these results are on the CD-ROM.

The use of energy-minimizing curves, known as "snakes" to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos [10]. A balloon model was introduced in [5] as a way to generalize and solve some of the problems encountered with the original method. We present a

We present a new mathematical formulation of some curve and surface reconstruction algorithms by the introduction of auxiliary variables. For deformable models and templates, the extraction of a shape is obtained through the minimization of an energy composed of an internal regularization term (not necessary in the case of parametric models) and an external attraction potential. Two-step iterative algorithms have been often used where, at each iteration, the model is first locally deformed according to the potential data attraction and then globally smoothed (or fitted in the parametric case). We show how these approaches can be interpreted as the introduction of auxiliary variables and the minimization of a two-variables energy. The first variable corresponds to the original model we are looking for, while the second variable represents an auxiliary shape close to the first one. This permits to transform an implicit data constraint defined by a non convex potential into an explicit co...

We address the problem of finding a set of contour curves in an image.

. Image matching has emerged as an important area of investigation in medical image analysis. In particular, much attention has been focused on the atlas problem, in which a template representing the structural anatomy of the human brain is deformed to match anatomic brain images from a given individual. The problem is made difficult because there are important differences in both the gross and local morphology of the brain among normal individuals. We have formulated the image matching problem under a Bayesian framework. The Bayesian methodology facilitates a principled approach to the development of a matching model. Of special interest is its capacity to deal with uncertainty in the estimates, a potentially important but generally ignored aspect of the solution. In the construction of a reference system for the human brain, the Bayesian approach is well suited to the task of modeling variation in morphology. Statistical information about morphological variability, accumulated over p...

Feature detection is important in various mesh processing techniques, such as mesh editing, mesh morphing, mesh compression, and mesh signal processing. In spite of much research in computer vision, automatic feature detection even for images still remains a difficult problem. To avoid this difficulty, semi-automatic or interactive techniques for image feature detection have been investigated. In this paper, we propose a geometric snake as an interactive tool for feature detection on a 3D triangular mesh. A geometric snake is an extension of an image snake, which is an active contour model that slithers from its initial position specified by the user to a nearby feature while minimizing an energy functional. To constrain the movement of a geometric snake onto the surface of a mesh, we use the parameterization of the surrounding region of a geometric snake. Although the definition of a feature may vary among applications, we use the normal changes of faces to detect features on a mesh. Experimental results demonstrate that geometric snakes can successfully capture nearby features from user-specified initial positions.

We present in this paper a new curve and surface implicit model. This implicit model based on hyperquadrics allows a local and global control of the shape and a wide variety of allowable shapes. We define a hybrid hyperquadric model by introducing implicitly some local properties on a global shape model. The advantage of our model is that it describes global and local properties through a unique implicit equation yielding a representation of the shape by means of its parameters, independently of the chosen numerical resolution. The data fitting is obtained through the minimization of an energy, modelling the attraction to data independently of the implicit description of the shape. After studying the geometry of hyperquadrics and how the shape deforms when we modify slightly its implicit equation, we are able to define an algorithm for automatic refining of the fit by adding an adequate term to the implicit representation. This geometric approach allows an efficient description of th...