Abstract:
We propose a new technique for use in the visualization of sparse,
fuzzy, or noisy 3D data. This technique incorporates the methods of deformable
or active models that have been developed in 2D computer vision.
In this paper we generalize such models to 3D
in a manner that is both practical and
mathematically elegant, and we thereby
avoid many of the problems associated with previous attempts to
generalize deformable models.
When generalizing to 3D, deformable models have several drawbacks---including their acute sensitivity to topology, parameterization, and initial conditions---which limit their effectiveness. Many of these problems stem from the underlying parameterization of the model. This paper presents an {\em implicit representation} of deformable models. The implicit representation is an embedding of objects as level sets of greyscale functions which serve as templates. The evolution equation associated with the energy minimization process for a model has an analogous partial differential equation which governs the behavior of the corresponding greyscale template.
We show that the ``active blobs'' associated with the embedding of active models have several useful properties. First, they are topologically flexible. Second, greyscale images represent {\em families} of models. Third, when surfaces are embedded as greyscale images, they are described by a natural scale space. This scale space provides the ability to solve these equations in a multi-scale manner. Several 2D examples of technique are presented, as well as some visualization results from 3D ultrasound.