Multiresolution stochastic hybrid shape models with fractal priors

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Abstract
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.

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