Dense Elastic 3D Shape Matching
Dense Elastic 3D Shape Matching
复制标题
密集弹性 3D 形状匹配
DOI：
10.1007/978-3-642-54774-4_1
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. Cremers
中科院分区：
文献类型：
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作者：
F. R. Schmidt;T. Windheuser;U. Schlickewei;D. Cremers
我们提出了一种新的方法来计算两个三维形状之间的几何一致和空间密集的匹配，并通过凸松弛来实现。我们不是点对点的映射，而是在保持几何结构的同时匹配无限小的曲面片。在这种精神下，我们认为物体表面之间的匹配是定义为几何一致的微分同胚。由于这种微分同胚可以表示为乘积空间中的闭曲面，因此我们在四维空间中就会遇到一个极小曲面问题。所提出的离散公式描述了具有线性约束的搜索空间，从而导致二元线性规划。对于这一潜在的NP-难问题，我们提出了一种近似方法。为了克服内存限制，我们还提出了一种多尺度方法，对粗略匹配进行细化，直到达到最精细的水平。作为匹配的代价函数，我们考虑薄壳能量，测量将一个形状变形为另一个形状所需的物理能量。实验结果表明，所提出的LP松弛算法可以计算出高质量的匹配，并可靠地输入到对应的关节3D形状中。据我们所知，这是稠密弹性曲面匹配的第一个解，它不需要初始化，并且提供了有界最优解。
We propose a novel method for computing a geometrically consistent and spatially dense matching between two 3D shapesandby means of a convex relaxation. Rather than mapping points to points we match infinitesimal surface patches while preserving the geometric structures. In this spirit, we consider matchings between objects’ surfaces as diffeomorphisms which are by definition geometrically consistent. Since such diffeomorphisms can be represented as closed surfaces in the product space, we are led to a minimal surface problem in a four-dimensional space. The proposed discrete formulation describes the search space with linear constraints which leads to a binary linear program. We propose an approximation approach to this potentially NP-hard problem. To overcome memory limitations, we also propose a multi-scale approach that refines a coarse matching until it reaches the finest level. As cost function for matching, we consider a thin shell energy, measuring the physical energy necessary to deform one shape into the other. Experimental results demonstrate that the proposed LP relaxation allows to compute high-quality matchings which reliably put into correspondence articulated 3D shapes. To our knowledge, this is the first solution to dense elastic surface matching which does not require an initialization and provides solutions of bounded optimality.
DOI：
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发表时间：
1990
期刊：
影响因子：
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作者：
H. Huppertz
通讯作者：
H. Huppertz
使用黎曼表面结构进行脑表面参数化
DOI：
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发表时间：
2005
期刊：
International Conference on Medical Image Computing and Computer-Assisted Intervention
影响因子：
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作者：
Yalin Wang;X. Gu;Kiralee M. Hayashi;T. Chan;P. Thompson;S. Yau
通讯作者：
S. Yau
使用黎曼表面结构进行表面参数化
DOI：
10.1109/iccv.2005.233
发表时间：
2005
期刊：
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1
影响因子：
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作者：
Yalin Wang;X. Gu;Kiralee M. Hayashi;T. Chan;P. Thompson;S. Yau
通讯作者：
S. Yau