Abstract

We present a closed form solution for symmetrizing two and three-dimensional models, by solving for the optimal deformation that reconciles a set of local bilateral symmetries. Our main motivation is the symmetrization of digitized fossils, which often undergo affine compression and bending. Given a set of symmetric point-pairs, we compute local transformations which approximate bilateral symmetries over small neighborhoods. We then combine these local symmetries and solve for a global symmetry across the $y$-$z$ plane, while maintaining the shapes of the local neighborhoods. We present results on 2D and 3D objects that are deformed by compression and bending. We easily extend the technique to articulated models, for which the local symmetries are rotations.

Paper (pdf) in Proceedings of Symposium of Geometry Processing 2010

Abstract

Establishing reliable correspondences between object surfaces is a fundamental operation, required in many contexts such as cleaning up and completing imperfect captured data, texture and deformation transfer, shape space analysis and exploration, and the automatic generation of realistic distributions of objects. We present a method for matching a template to a collection of possibly target meshes. Our method uses a very small number of user-placed landmarks, which we augment with automatically detected feature correspondences, found using spin images. We deform the template onto the data using an ICP-like framework, smoothing the noisy correspondences at each step so as to produce an averaged motion. The deformation uses a differential representation of the mesh, with which the deformation can be computed at each iteration by solving a sparse linear system.

We have applied our algorithm to a variety of data sets. Using only 11 landmarks between a template and one of the scans from the CEASAR data set, we are able to deform the template, and correctly identify and transfer distinctive features, which are not identified by user-supplied landmarks. We have also successfully established
correspondences between several scans of monkey skulls, which have dangling triangles, non- manifold vertices, and self intersections. Our algorithm does not require a clean target mesh, and can even generate correspondence without trimming our extraneous pieces from the target mesh, such as scans of teeth.

Paper (pdf) in Proceedings of SPIE Medical Imaging 2009