Surface Representation with Deformable Splines: Using Decoupled Variables

• Authors: André Guéziec
• Venue: IEEE Computational Science & Engineering
• Year: 1995

When we work with three-dimensional digital data, such as medical data from computer-tomography or magnetic-resonance scans, we repeatedly address the topic of surface representation. Surface models can be used for registration, for visualization, for performing statistical measurements or for simulations. This research introduces a new representation that is particularly computationally efficient for segmentation and registration. In order to convert 3D data points into a useful surface representation, my approach is to start with a simple surface and progressively deform it into a shape which is able to approximate the data points within a given tolerance. I use deformable spline surfaces for modeling surface structures embedded in 3D data. This approach builds upon existing methods that minimize the "energy" of a deformable surface in an external potential field. I introduce an efficient algorithmic modification which decouples surface variables, thereby allowing me to treat the large meshes necessary for a detailed representation with an acceptable computational burden. A major advantage of the spline representation is that it naturally induces a differentiable structure for the surface. Hence we can measure differential properties such as principal curvatures and directions, and extract lines of maximum curvature, which are stable and salient three-dimensional features, for use in a novel surface-matching method. I validated this method by demonstrating experimentally that lines of maximum curvature can be used to register different surface models, thereby registering the associated volumetric data sets.