Unifying deformable model representations through new geometric data structures
Russell H. Taylor, Michael Kazhdan, Blake C. Lucas · 2012
One objective of image analysis is to extract geometric information from images. A modern approach is to start with an initial guess for an object's geometry and deform it to match objects observed in images. Deformable models are commonly used to represent geometry because they change shape due to forces applied at their boundary. In image analysis, deformable models imitate all types of materials: rigid, elastic, plastic, and fluid materials. Meshes and level sets are the two primary deformable model representations. Methods usually favor a particular representation depending on the type of material the model is intended to imitate. For instance, we will describe a new algorithm for 3D reconstruction (SxMAC) with a strong preference for level sets. However, image analysis pipelines that use a mixture of methods are forced to transform one representation into another in order to use the preferred representation for each method. This strategy leads to loss of information and less flexibility in design of the system. Spring Level Sets (SpringLS) merge meshes and level sets into a single representation to provide interoperability between methods designed for either. The key idea is to use a constellation of disconnected triangular surface elements (springls) to define a level set. SpringLS is extended to the multi-object case by coupling it with Multi-Object Geodesic Active Contours (MOGAC). The MOGAC data structure can represent any number of level sets with a label mask and distance field. The combination of SpringLS and MOGAC creates a powerful new type of deformable model (MUSCLE) for representing multiple objects that is parametric, has sub-voxel precision, re-meshes, tracks point correspondences, and guarantees no self-intersections, air-gaps, or overlaps between adjacent structures. Applications to full brain parcellation, whole body segmentation, atlasing, and multi-organ tracking are presented. Finally, a new method is described for warping and combining images in ways that preserve edge strength. It does so by decoupling shape and intensity information, manipulating them independently, and then synthesizing images. The method relies on MUSCLE to represent geometry in an image and enforce geometric constraints (e.g. no air-gaps or overlaps). Applications to registration and atlas construction are presented.