Abstract. This paper presents a novel processing scheme for the automatic and robust computation of a medial shape model, which represents an object population with shape variability. The sensitivity of medial descriptions to object variations and small boundary perturbations are fundamental problems of any skeletonization technique. These problems are approached with the computation of a model with common medial branching topology and grid sampling. This model is then used for a medial shape description of individual objects via a constrained model fit. The process starts from parametric 3D boundary representations with existing point-to-point homology between objects. The Voronoi skeleton of each sampled object boundary is partitioned into non-branching medial sheets and simplified by a novel pruning algorithm using a volumetric contribution criterion. Using the surface homology, medial sheets are combined to form a common medial branching topology. Finally, the medial sheets are sampled and represented as meshes of medial primitives. Results on populations of up to 184 biological objects clearly demonstrate that the common medial branching topology can be described by a small number of medial sheets and that even a coarse sampling leads to a close approximation of individual objects.

This paper presents a novel processing scheme for the automatic computation of a medial shape model which is representative for an object population with shape variability. The sensitivity of medial descriptions to object variations and small boundary perturbations are fundamental problems of any skeletonization technique. These problems are approached with the computation of a model with common medial branching topology and grid sampling. This model is then used for a medial shape description of individual objects via a constrained model fit. The process starts from parametric 3D boundary representations with existing point-to-point homology between objects. The Voronoi diagram of each sampled object boundary is grouped into medial sheets and simplified by a pruning algorithm using a volumetric contribution criterion. Medial sheets are combined to form a common medial branching topology. Finally, the medial sheets are sampled and represented as meshes of medial primitives. We present new results on populations of up to 184 biological objects. For these objects the common medial branching topology is described by a small number of sheets. Despite the coarse medial sampling, a close approximation of individual objects is achieved. 1.

We describe a novel continuous medial representation for object geometry and a deformable templates method for fitting the representation to images. Our representation simultaneously describes the boundary and medial loci of geometrical objects, always maintaining Blum’s symmetric axis transform (SAT) relationship. Cubic b-splines define the continuous medial locus and the associated thickness field, which in turn generate the object boundary. We present geometrical properties of the representation and derive a set of constraints on the b-spline parameters. The 2D representation encompasses branching medial loci; the 3D version can model objects with a single medial surface, and the extension to branching medial surfaces is a subject of ongoing research. We present preliminary results of segmenting 2D and 3D medical images. The representation is ultimately intended for use in statistical shape analysis.

Feature selection methodology from machine learning literature is adapted and applied to the problem of statistical shape-based classification of biological objects. The feature selection paradigm is used to discover the regions of objects where the di#erence between classes is most pronounced.

Abstract. There is a frequent need to compute medial shape representations of each of a group of structures, e.g. for use in a medical study of anatomical shapes. We present a novel approach to skeletonization that leverages information provided from such a group. We augment the traditional medial axis transform with an additional coordinate stored at each medial locus, indicating the confidence that the branch on which that locus lies represents signal and not noise. This confidence is calculated based on the support given to that branch by corresponding branches in other skeletons in the group. We establish the aforementioned correspondence by a set of bipartite graph matchings using the Hungarian algorithm, and compute branch support based on similarity of computed geometric and topological features at each branch. This groupwise skeletonization approach supports an intelligent pruning algorithm, which we show to operate quickly and provide pruning in an intuitive manner. We show that the method is amenable to automatic detection of skeletal configurations with one, or more than one, topological class of skeletons. This is useful to medical studies which often involve patient groups whose structures may differ topologically. 1

In this paper we develop a method to parameterize tubular surfaces onto the cylinder. The cylinder can be seen as the natural parameterization domain for tubular surfaces since they share the same topology. Most present algorithms are designed to parameterize disc-like surfaces onto the plane. Surfaces with a different topology are cut into disc-like patches and the patches are parameterized separately. This introduces discontinuities and constrains the parameterization. Also the semantics of the surface are lost. We avoid this by parameterizing tubular surfaces on, their natural domain, the cylinder. Since the cylinder is locally isometric to the plane we can do calculations on the cylinder without loosing efficiency. For speeding up the calculation we use a progressive parameterization technique, as suggested in recent literature. Together, this results in a robust, efficient, continuous, and semantics preserving parameterization method for arbitrary tubular surfaces.

Abstract. Local symmetry axis based schemes have been used for generic shape recognition as they lead to articulation insensitive representations. Despite their strengths, purely syntactic level of axial representations precludes the possibility of distinguishing a likely articulation from an unlikely one. In order to overcome this weakness, syntax should be combined with pragmatics and/or semantics. As a solution we propose a novel articulation space which enables inferences on the likelihood of possible articulations. Articulation priors can be constructed directly from examples (pragmatics) or set externally (semantics). We incorporate articulation priors to a skeletal matching scheme to arrive at an enriched axial representation which is sensitive to unlikely articulations but insensitive to likely ones. 2 1