The scope of this paper is the guaranteed fitting of specified types of quadratic surfaces to scattered 3D point clouds. Since we chose quadrics to account for articular surfaces of various shapes in medical images, the models thus estimated usefully extract global symmetry-related intrinsic features in human joints: centers, axes, extremal curvatures. The unified type-enforcing method is based on a constrained weighted least-squares minimization of algebraic residuals which uses a robust and bias- corrected metric. Provided that at most one quadratic constraint is involved, every step produces closed-form eigenvector solutions. In this framework, guaranteeing the occurrence of 3D primitives of certain types among this eigendecomposition is not a straightforward transcription of the priorly handled 2D case. To explore possibilities, we re-exploit a mapping to a 2D space called the quadric shape map (QSM) where the influence of any constraint on shape and type can in fact be studied visually. As a result, we provide a new enforceable quadratic constraint that practically ensures types such as hyperboloids, which helps characterize saddle-like articular surfaces. Application to a database shows how this guarantee is needed to coherently extract the center and axes of the ankle joint.

The quantitative analysis of three-dimensional (3-D) shapes in terms of morphology and functionality is one of the most challenging problems in medical image analysis. This paper proposes a general methodology that aims at solving part of this problem. It introduces a nonparametric hierarchical partitioning approach that operates on any arbitrary 3-D shape described as a triangle mesh. It first extends the concept of basin districts to the case of curved spaces through a partitioning process on a valuation representing the main curvatures over a polyhedral support. A hierarchical construction of basin districts is obtained from a watershed transform. The speed of the front propagation on the polyhedral surface is controlled by the local characteristics of the surface geometry. As a prerequisite, a set of co-processing tools has been developed that operates directly on a triangulated domain. This includes classical signal processing tasks (e.g., re-sampling, filtering) on a polyhedral support performing a trade-off between accuracy and efficiency. The ability to provide an intrinsic shape partition from any triangular mesh is useful in a wide range of applications from accurate geometric modeling, and hierarchical shape dissection to robust mesh compression. Examples are presented in the paper to illustrate the principles and methodology.

The aim of this paper is to present an original usage of genetic algorithms as a robust search space sampler in application to 3-D medical image elastic registration. An overview of the standard steps of a registration algorithm is given. We focus on the genetic algorithms use and particularly on the problem of extraction of the optimal solution among the final genetic population. We provide an original encoding scheme relying on a structural approach of point matching and then point out the need for a local optimization process. We then illustrate the algorithm with a concrete registration example and assert the results with a direct multivolume rendering tool. Finally, the algorithm is applied on the vanderbilt medical image database to assert the robustness and in order to compare it with other techniques.

We present a new method for direct volume rendering of multiple three-dimensional (3-D) functions using a density emitter model. This work aims at obtaining visual assessment of the results of a 3-D image registration algorithm which operates on anisotropic and non segmented medical data. We first discuss the fundamentals associated with direct, simultaneous rendering of such datasets. Then, we recall the fuzzy classification and fuzzy surface rendering theory within the density emitter model terminology, and propose an extension of standard direct volume rendering that can handle the rendering of two or more 3-D functions; this consists of the definition of merging rules that are applied on emitter clouds. The included rendering applications are related on one hand, to volume-to-volume registration, and on the other hand, to surface-to-volume registration: the first case is concerned with global elastic registration of CT data, and the second one presents fitting of an implicit surface over a CT data subset. In these two medical imaging application cases, our rendering scheme offers a comprehensive appreciation of the relative position of structural information.

A new approach is presented for the detection of linear structures boundaries. The initial objective is the structure detection and its analysis, especially the diameter estimation. The main idea of the method is to use a uniform cost algorithm adapted to the two borders simultaneous tracking. The node represents a set of two edges (a right border and a left border linked by a diameter vector). The cost of the node is calculated from the contrast of the structure border, the angle between the diameter vector and the local edge gradient vectors and the curvature of the path. In order to reduce the search complexity, some heuristics are introduced. For each detected structure, a starting node and research area are defined. The preliminary results obtained on synthetic images and on DSA images are very interesting. The method allows the detection to be performed through the branching structures and overlapping ones. In addition, simulation studies show the robustness of the method with respect to noise.>