内在对应的稀疏建模
Sparse Modeling of Intrinsic Correspondences
摘要：
我们提出了一种新的稀疏建模方法，非刚性形状匹配只使用检测可重复区域的能力。作为我们算法的输入，我们只得到两个形状中的两组区域;没有提供描述符，因此不知道区域之间的对应关系，也不知道两个形状中有多少区域对应。我们表明，即使这样的稀缺信息，它是可能的，以建立非常准确的对应关系的形状，通过使用稀疏建模领域的方法，这是第一个非平凡的使用稀疏模型的形状对应。我们制定的置换稀疏编码的问题，在其中，我们同时解决一个未知的置换排序的两个形状和功能表示的一个未知的对应关系的区域。我们还提出了一个强大的变种能够处理不完全匹配。数值上，该问题是有效地解决交替的线性分配和稀疏编码问题的解决方案。所提出的方法进行了定性和定量评价标准基准包含合成和扫描对象。
英文摘要：
We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to establish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of permuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects.
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