IEEE Trans Pattern Anal Mach Intell. 2017 May;39(5):965-980. doi: 10.1109/TPAMI.2016.2567398. Epub 2016 May 12.
Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture industries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquers this problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We employ our algorithm to study the constrained surface registration problem which applies to both computer vision and medical imaging applications. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic and achieve relatively high performance when evaluated with some popular surface registration evaluation standards.
通过调和映射进行曲面对应自动计算是计算机视觉、计算机图形学和计算几何领域的一个活跃研究领域。它有助于记录和理解物理和生物现象，并且在生物识别、医学成像和运动捕捉等行业也有广泛的应用。尽管已经有许多研究致力于调和映射的研究，但在具有地标约束的一般拓扑曲面上计算保形调和映射的进展有限。通过将目标曲面的黎曼度量更改为双曲度量，本工作解决了这个问题，从而保证在地标约束下调和映射是一个微分同胚。计算算法基于 Ricci 流和非线性热扩散方法。该方法具有通用性和鲁棒性。我们将算法应用于研究约束曲面配准问题，该问题适用于计算机视觉和医学成像应用。实验结果表明，通过改变黎曼度量，配准总是微分同胚的，并且在使用一些流行的曲面配准评估标准进行评估时，性能相对较高。
