Deformable Fourier models for surface finding in 3-D images

This paper describes a new global shape parametrization for smoothly deformable three- dimensional objects, such as those found in biomedical images, whose diversity and irregularity make them difficult to represent in terms of fixed features or parts. This representation is used for geometric surface matching to three-dimensional image data. The parametrization decomposes the surface into sinusoidal basis functions. Four types of surfaces are modeled: tori, open surfaces, closed surfaces, and tubes. This parametrization allows a wide variety of smooth surfaces to be described with a small number of parameters. Surface finding is formulated as an optimization problem. Results of the method applied to synthetic and medical three-dimensional images are presented.