论文标题
基于薄壳能量的隐式表面匹配的对称和缩放极限
Symmetry and scaling limits for matching of implicit surfaces based on thin shell energies
论文作者
论文摘要
在Iglesias，Rumpf和Scherzer的最新论文中，提出了与给出的一对形状相匹配的变形模型的变异模型，提出了与级别集合函数相匹配。它的主要特征是仅在类似于弹性壳行为的高空曲面周围的狭窄带中活跃的各向异性能量。在这项工作中，我们考虑了该模型的一些扩展和进一步分析。首先，我们提出一个对称能量函数，以使给定两个特定的形状，当形状的作用互换时，它将其分配给任何给定的变形与逆变形，并引入足够的参数缩放以恢复窄带宽度消失时恢复表面问题。然后，我们获得了对对称能量的对称能量的最小化变形的存在，用于小宽度的宽度足够小，并且由于宽度趋向于零，因此证明了相应的非对称能量的相应非对称能量的结果$γ$ - 浓度。最后，提出了证明对称能量效果的现实形状匹配应用的数值结果。
In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic energies active only in a narrow band around the hypersurfaces that resemble the behavior of elastic shells. In this work we consider some extensions and further analysis of that model. First, we present a symmetric energy functional such that given two particular shapes, it assigns the same energy to any given deformation as to its inverse when the roles of the shapes are interchanged, and introduce the adequate parameter scaling to recover a surface problem when the width of the narrow band vanishes. Then, we obtain existence of minimizing deformations for the symmetric energy in classes of bi-Sobolev homeomorphisms for small enough widths, and prove a $Γ$-convergence result for the corresponding non-symmetric energies as the width tends to zero. Finally, numerical results on realistic shape matching applications demonstrating the effect of the symmetric energy are presented.
