From global to local, a continuum of shape models with fractal priors

3D Shape modeling has been a very prominent part of 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. In this paper, 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 superquadrics constructed in an orthonormal wavelet bases. These multi-resolution bases provide 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 us to generate fractal surfaces of arbitrary degree that can be useful in describing natural detail. We embed these multi-resolution shape models in a probabilistic framework and use them for segmenting 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 completely.