Symmetric Shape Morphing for 3D Face and Head Modelling

We propose a shape template morphing approach suitable for any class of shapes that exhibits approximate reflective symmetry over some plane. The human face and full head are examples. A shape morphing algorithm that constrains all morphs to be symmetric is a form of deformation regulation. This mitigates undesirable effects seen in standard morphing algorithms that are not symmetry-aware, such as tangential sliding. Our method builds on the Coherent Point Drift (CPD) algorithm and is called Symmetry-aware CPD (SA-CPD). Global symmetric deformations are obtained by removal of asymmetric shear from CPD's global affine transformations. Symmetrised local deformations are then used to improve the symmetric template fit. These symmetric deformations are followed by Laplace-Beltrami regularized projection which allows the shape template to fit to any asymmetries in the raw shape data. The pipeline facilitates construction of statistical models that are readily factored into symmetrical and asymmetrical components. Evaluations demonstrate that SA-CPD mitigates tangential sliding problem in CPD and outperforms other competing shape morphing methods, in some cases substantially. 3D morphable models are constructed from over 1200 full head scans, and we evaluate the constructed models in terms of age and gender classification. The best performance, in the context of SVM classification, is achieved using the proposed SA-CPD deformation algorithm

SIGGRAPH

We present a method for recovering a temporally coherent, deforming triangle mesh with arbitrarily changing topology from an incoherent sequence of static closed surfaces. We solve this problem using the surface geometry alone, without any prior information like surface templates or velocity fields. Our system combines a proven strategy for triangle mesh improvement, a robust multi-resolution non-rigid registration routine, and a reliable technique for changing surface mesh topology. We also introduce a novel topological constraint enforcement algorithm to ensure that the output and input always have similar topology. We apply our technique to a series of diverse input data from video reconstructions, physics simulations, and artistic morphs. The structured output of our algorithm allows us to efficiently track information like colors and displacement maps, recover velocity information, and solve PDEs on the mesh as a post process

Constrained parameterization with applications to graphics and image processing.

Surface parameterization is to establish a transformation that maps the points on a surface to a specified parametric domain. It has been widely applied to computer graphics and image processing fields. The challenging issue is that the usual positional constraints always result in triangle flipping in parameterizations (also called foldovers). Additionally, distortion is inevitable in parameterizations. Thus the rigid constraint is always taken into account. In general, the constraints are application-dependent. This thesis thus focuses on the various constraints depended on applications and investigates the foldover-free constrained parameterization approaches individually. Such constraints usually include, simple positional constraints, tradeoff of positional constraints and rigid constraint, and rigid constraint. From the perspective of applications, we aim at the foldover-free parameterization methods with positional constraints, the as-rigid-as-possible parameterization with positional constraints, and the well-shaped well-spaced pre-processing procedure for low-distortion parameterizations in this thesis. The first contribution of this thesis is the development of a RBF-based re-parameterization algorithm for the application of the foldover-free constrained texture mapping. The basic idea is to split the usual parameterization procedure into two steps, 2D parameterization with the constraints of convex boundaries and 2D re-parameterization with the interior positional constraints. Moreover, we further extend the 2D re-parameterization approach with the interior positional constraints to high dimensional datasets, such as, volume data and polyhedrons. The second contribution is the development of a vector field based deformation algorithm for 2D mesh deformation and image warping. Many presented deformation approaches are used to employ the basis functions (including our proposed RBF-based re-parameterization algorithm here). The main problem is that such algorithms have infinite support, that is, any local deformation always leads to small changes over the whole domain. Our presented vector field based algorithm can effectively carry on the local deformation while reducing distortion as much as possible. The third contribution is the development of a pre-processing for surface parameterization. Except the developable surfaces, the current parameterization approaches inevitably incur large distortion. To reduce distortion, we proposed a pre-processing procedure in this thesis, including mesh partition and mesh smoothing. As a result, the resulting meshes are partitioned into a set of small patches with rectangle-like boundaries. Moreover, they are well-shaped and well-spaced. This pre-processing procedure can evidently improve the quality of meshes for low-distortion parameterizations