Multiscale medial shape-based analysis of image objects

Medial representation of a three-dimensional (3-D) object or an ensemble of 3-D objects involves capturing the object interior as a locus of medial atoms, each atom being two vectors of equal length joined at the tail at the medial point. Medial representation has a variety of beneficial properties, among the most important of which are 1) its inherent geometry, provides an objectintrinsic coordinate system and thus provides correspondence between instances of the object in and near the object(s); 2) it captures the object interior and is, thus, very suitable for deformation; and 3) it provides the basis for an intuitive object-based multiscale sequence leading to efficiency of segmentation algorithms and trainability of statistical characterizations with limited training sets. As a result of these properties, medial representation is particularly suitable for the following image analysis tasks; how each operates will be described and will be illustrated by results: segmentation of objects and object complexes via deformable models; segmentation of tubular trees, e.g., of blood vessels, by following height ridges of measures of fit of medial atoms to target images; object-based image registration via medial loci of such blood vessel trees; statistical characterization of shape differences between control and pathological classes of structures. These analysis tasks are made possible by a new form of medial representation called m-reps, which is described.