Applying conformal mapping to the vertex correspondence problem for three-dimensional face models.

摘要

In this thesis, we present a new approach to establishing vertex-level correspondences between 3D face models represented as triangular meshes. We then apply this approach to several critical Computer Vision applications, including texture transfer, facial expression cloning and face recognition.; We first generalize and describe the types of vertex correspondence algorithms that have been established to date. Thereafter, we discuss some of the latest research in establishing conformal mappings between a 3D mesh and the 2D plane. This research is of critical importance to our approach because we propose that these planar mappings can be used as an intermediary stage in quickly establishing reliable correspondences between vertices in two 3D meshes. Whereas most other approaches use a measurement system such as geodesic measurements in order to provide an algorithm that is robust to bending in meshes, we propose that conformal mappings, which can be calculated far more quickly, serve equally well and allow for much faster correspondence algorithms. Using conformal parameterization as an approximate invariance to bending as well as scale and resolution, we provide a lightweight approach to establishing a vertex-level correspondence between 2D meshes. By applying this algorithm to these conformal parameterizations, which maintain a one-to-one relationship with the vertices in the original 3D meshes, we can trace our established correspondences back to the 3D meshes instantaneously, thereby reducing the problem scope of 3D vertex correspondence to the 2D spatial domain.; Furthermore, because our approach establishes 3D correspondences using 2D information from 3D meshes, we propose that correspondences can be established between 3D meshes and images. To demonstrate the bridging of this gap, we perform semi-automated texture mapping 2D images with 22 hand-selected feature points to 3D face meshes using our correspondence algorithm.