Spherical parameterization for 3D surface analysis in volumetric images

We propose a new spherical parameterization algorithm for general genus-zero surfaces that aims to control the area and length distortions at the same time. Prior work either considers only the length distortion or applies only to volumetric surfaces. Our algorithm starts from an initial parameterization, performs local and global smoothing steps alternately to improve the mapping quality, and converges to the solution. The local method minimizes the area distortion at a local submesh by solving a linear system as well as controls the length distortion. The global method attempts to reduce the area distortion by equalizing its distribution over the whole sphere. We perform experimental studies showing the effectiveness of the technique. Our new algorithm has many applications in medical image analysis, computer vision, graphics and multimedia databases.