Efficient Globally Optimal 2D-to-3D Deformable Shape Matching
Efficient Globally Optimal 2D-to-3D Deformable Shape Matching
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DOI：
10.1109/cvpr.2016.240
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发表时间：
2016-01
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影响因子：
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通讯作者：
Zorah Lähner;E. Rodolà;Frank R. Schmidt;M. Bronstein;D. Cremers
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文献类型：
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作者：
Zorah Lähner;E. Rodolà;Frank R. Schmidt;M. Bronstein;D. Cremers
我们提出了第一个用于非刚性2D到3D形状匹配的算法，其中输入是2D查询形状和3D目标形状，输出是表示为3D形状上的闭合轮廓的连续匹配曲线。我们把这个问题转化为在两个形状的乘积3流形上寻找最短的圆形路径。我们证明了最优匹配可以在多项式时间内计算，（最坏情况下）复杂度为O（mn2 log（n）），其中m和n分别表示2D和3D形状上的顶点数。定量评价证实，该方法提供了良好的效果，基于草图的可变形三维形状检索。
We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D query shape as well as a 3D target shape and the output is a continuous matching curve represented as a closed contour on the 3D shape. We cast the problem as finding the shortest circular path on the product 3-manifold of the two shapes. We prove that the optimal matching can be computed in polynomial time with a (worst-case) complexity of O(mn2 log(n)), wherem and n denote the number of vertices on the 2D and the 3D shape respectively. Quantitative evaluation confirms that the method provides excellent results for sketch-based deformable 3D shape retrieval.