3D shape modeling has received enormous attention in computer graphics and computer vision over the past decade. Several shape modeling techniques have been proposed in literature, some are local (distributed parameter) while others are global (lumped parameter) in terms of the parameters required to describe the shape. Hybrid models that combine both ends of this parameter spectrum have been in vogue only recently. However, they do not allow a smooth transition between the two extremes of this parameter spectrum. We introduce a new shape-modeling scheme that can transform smoothly from local to global models or vice versa. The modeling scheme utilizes a hybrid primitive called the deformable superquadric constructed in an orthonormal wavelet basis . The multiresolution wavelet basis provides the power to continuously transform from local to global shape deformations and thereby allow for a continuum of shape models—from those with local to those with global shape descriptive power—to be created. The multiresolution wavelet basis allows us to generate fractal surfaces of arbitrary order that can be useful in describing natural detail. We embed these multiresolution shape models in a probabilistic framework and use them for recovery of anatomical structures in the human brain from MRI data. A salient feature of our modeling scheme is that it can naturally allow for the incorporation of prior statistics of a rich variety of shapes. This stems from the fact that, unlike other modeling schemes, in our modeling, we require relatively few parameters to describe a large class of shapes.

A new shape modeling scheme is introduced. It can transform smoothly from local (distributed parameter) to global (lumped parameter) models or vice-versa. The modeling scheme makes use of a hybrid primitive, called the deformable superquadric, constructed in an orthonormal wavelet basis. This multiresolution basis provides the power to continuously transform from local to global shape deformations, and thereby allow for a continuum of shape models-from those with local to those with global shape descriptive power-to be created. The characteristic of continuously transforming from local to global shape deformations allows the generation of fractal surfaces of arbitrary degree that can be useful in describing natural detail. These multiresolution shape models reembedded in a probabilistic framework and used for segmenting anatomical structures in the human brain from magnetic resonance imaging (MRI) data.>