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.

我们提出了一种新的基于稀疏建模方法的非刚性形状匹配算法，通过检测可重复区域，建立形状间的精确对应关系，并以非常完美的表现在标准基准数据集上得到了定量和定性的评估。