Facial surface registration is an important research problem in computer vision and graphics, and has broad applications in the industries of gaming and movie. However, it is still challenging to accurately and efficiently register dense surfaces that undergo intense expression change. In this paper, we propose a novel registration method for facial meshes. By leveraging geometry images as the 3D representation, we reduce the 3D mesh registration problem to a 2D image registration problem. A Transformer-based neural network is trained to obtain a 2D deformation field and a Teichmüller map is calculated to smooth the deformation. During the inference stage, our method does not require human-prescribed landmarks and can explicitly output the correspondence between the source and the target faces. The experimental results show that our method surpasses compared methods in registration accuracy and achieves better smoothness of the induced mapping on the testing samples.
Sizing fields stored on triangular background grids control the quality and cost of unstructured mesh generation. Piecewise-linear interpolation on raw Stereolithography (STL) background grids can introduce high-density banding artifacts near discrete geometric transitions, leading to unnecessary local over-refinement. We propose GCN-HOSF, a two-stage framework in which a Graph Convolutional Network (GCN) approximates an expensive rule-based numerical detector, and a High-Order Sizing Field (HOSF) corrects the predicted banding conditions without changing the original STL connectivity. This design avoids global refinement and topological subdivision while preserving a lightweight background-grid representation. Across 179 paired validation cases, GCN-HOSF reduced the mean number of generated surface-mesh elements by 62.01% relative to the initial STL-derived sizing field while leaving the background-grid cell count unchanged. In the four computational-performance cases, it reduced the stage-summed workflow time by 3.57%–97.06% compared with LIU and by 3.11%–72.50% compared with GCN-SF, although extreme mesh-quality degradation may still occur for pathological geometries.
In this work, for a kind of univariate C1 rational cubic B-spline-like basis functions, we deduce the conversion matrix between the local tensor-product (TP for short) rational bicubic B-spline-like basis functions and the TP rational bicubic Bernstein basis functions. Based on these, we further give the construction of C1 rational bicubic splines over hierarchical T-meshes, succinctly termed as RHT-splines. The nestedness and dimension of the RHT-spline space are also discussed. For each cell in the hierarchical T-meshes, RHT-splines are expressed by rational bicubic Bernstein basis functions, and possess some desirable properties such as the non-negativity, partition of unity, local support, local adjustable weights, local refinement and include the C1 bicubic PHT-splines as a special case. The exact representation for 1 8 sphere using RHT-splines is given. Additionally, the expression for the geometric information of basis vertices in RHT-splines is proposed. Experimental results on adaptive fitting of open 3D triangular mesh models using RHT-splines demonstrate the advantages of the adjustable weights. Without changing the tolerance of fitting error, we can adaptively generate a simpler hierarchical T-mesh by using weights, and the surfaces fitted using this simpler hierarchical T-mesh retain a shape almost identical to those fitted using PHTsplines, with errors remaining within the tolerance. The RHT-spline quasi-interpolant operator with two constructions of linear functionals is given, which reproduces the RHT-spline space and the bilinear polynomial space.
