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This paper presents a multiscale framework based on a medial representation for the segmentation and shape characterization of anatomical objects in medical imagery. The segmentation procedure is based on a Bayesian deformable templates methodology in which the prior information about the geometry and shape of anatomical objects is incorporated via the construction of exemplary templates. The anatomical variability is accommodated in the Bayesian framework by defining probabilistic transformations on these templates. The transformations, thus, defined are parameterized directly in terms of natural shape operations, such as growth and bending, and their locations. A preliminary validation study of the segmentation procedure is presented. We also present a novel statistical shape analysis approach based on the medial descriptions that examines shape via separate intuitive categories, such as global variability at the coarse scale and localized variability at the fine scale. We show that the method can be used to statistically describe shape variability in intuitive terms such as growing and bending.

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.

We present an approach to computing a curve atlas based on deriving a correspondence between two curves. This correspondence is based on a notion of an alignment curve and on a measure of similarity between the intrinsic properties of the curve, namely, length and curvature. The optimal correspondence is found by an efficient dynamicprogramming method. This is then used to compute an average for a set of curves and applied to computing the averages of bone shapes and corpus callosum as examples, towards constructing a computational atlas. The proposed notion of alignment also leads to a registration method, which is illustrated with several examples. 1

Knowledge about the biological variability of anatomical objects is essential for statistical shape analysis and discrimination between healthy and pathological structures. This paper describes a novel approach that incorporates variability of an object population into the generation of a characteristic 3D shape model. The proposed shape representation is based on a fine-scale spherical harmonics (SPHARM) boundary description and a coarse-scale sampled medial description. The medial description is composed of a net of medial samples (m-rep) with fixed graph properties. The medial model is computed automatically from a predefined shape space using pruned 3D Voronoi skeletons to determine the stable medial branching topology. An intrinsic coordinate system and an implicit correspondence between shapes is defined on the medial manifold.

. A new fully automated shape learning method is presented. It is based on clustering a shape training set in the original shape space and performing a Procrustes analysis on each cluster to obtain a cluster prototype and information about shape variation. As a direct application of our shape learning method, a 17-structure shape model of brain substructures was computed from MR image data, an eigen-shape model was automatically trained, and employed in our method for segmentation of those MR brain images not present in the shape-training set. Our approach can serve as a fully valid automated substitute to the tedious and time-consuming manual shape analysis. 1 1 Motivation Automated learning of shape models is an important problem in medical image analysis with direct implications in the area of medical image interpretation. We and others have previously demonstrated the utility of incorporating shape in medical image segmentation and interpretation [1]. However, training a shapebas...

We present a hybrid volume rendering method that uses object shape information provided by multiscale medial models to guide a splatting renderer. Such models can efficiently give large-tolerance versions of object boundaries. Our renderer uses the medially implied boundaries to focus the rendering effort towards the region of detailed boundaries, thereby avoiding occlusion of the objects of interest. Our renderer finds a most likely boundary displacement from the medially implied boundary using a Bayesian approach based on the volume directional derivatives of image intensity in directions normal to the medially implied boundary.

Knowledge about the biological variability of anatomical objects is essential for statistical shape analysis and a discrimination between healthy and pathological structures. This paper describes ongoing research on a novel approach that incorporates variability of a training set into the generation of a characteristic 3D shape model. The proposed shape representation is a hybrid of a fine-scale global boundary description and a coarse-scale local medial description. The hybrid overcomes inherent limitations of pure medial based or pure boundary based descriptions. The medial description composed of a net of medial primitives (M-rep) with fixed graph properties is derived from the shape space spanned by the major deformation eigenmodes of a boundary description based on spherical harmonic descriptors (SPHARM). The topology of the M-rep is determined by studying pruned 3D Voronoi skeletons in the given shape space. Shapes are characterized by its SPHARM descriptors and an individually deformed M-rep model. The hybrid shape description gives an implicit correspondence on the boundary and on the medial manifold, thus enabling a more powerful statistical analysis.

A method is proposed for the automatic, rapid and stable identification and measurement of objects in 3D images. It is based on local shape properties derived statistically from populations of medial primitives sought throughout the image space. These shape properties are measured at medial locations within the object, and include scale, orientation, endness, and medial dimensionality. Medial dimensionality is a local shape property differentiating sphere-like, cylinder-like, and slab-like structures, with intermediate dimensionality also possible. Endness is a property found at the cap of a cylinder or the edge of a slab. In terms of an application, the cardiac left ventricle during systole is modeled as a large dark cylinder with an apical cap, terminated at the other end by a thin bright slab-like mitral valve. Such a model, containing medial shape properties at just a few locations, along with the relative distances and orientations between these locations, is intuitive and robust ...

Abstract.This paper presents a Bayesian multi-scale three dimensional deformable template approach based on a medial representation for the segmentation and shape characterization of anatomical objects in medical imagery. Prior information about the geometry and shape of the anatomical objects under study is incorporated via the construction of exemplary templates. The anatomical variability is accommodated in the Bayesian framework by defining probabilistic transformations on these templates. The modeling approach taken in this paper for building exemplary templates and associated transformations is based on a multi-scale medial representation. The transformations defined in this framework are parameterized directly in terms of natural shape operations, such as thickening and bending, and their location. Quantitative validation results are presented on the automatic segmentation procedure developed for the extraction of the kidney parenchyma-including the renal pelvis-in subjects undergoing radiation treatment for cancer. We show that the segmentation procedure developed in this paper is efficient and accurate to within the voxel resolution of the imaging modality. A