  Evaluating the similarity of non-rigid shapes with significant partiality is
a fundamental task in numerous computer vision applications. Here, we propose a
novel axiomatic method to match similar regions across shapes. Matching similar
regions is formulated as the alignment of the spectra of operators closely
related to the Laplace-Beltrami operator (LBO). The main novelty of the
proposed approach is the consideration of differential operators defined on a
manifold with multiple metrics. The choice of a metric relates to fundamental
shape properties while considering the same manifold under different metrics
can thus be viewed as analyzing the underlying manifold from different
perspectives. Specifically, we examine the scale-invariant metric and the
corresponding scale-invariant Laplace-Beltrami operator (SI-LBO) along with the
regular metric and the regular LBO. We demonstrate that the scale-invariant
metric emphasizes the locations of important semantic features in articulated
shapes. A truncated spectrum of the SI-LBO consequently better captures locally
curved regions and complements the global information encapsulated in the
truncated spectrum of the regular LBO. We show that matching these dual spectra
outperforms competing axiomatic frameworks when tested on standard benchmarks.
We introduced a new dataset and compare the proposed method with the
state-of-the-art learning based approach in a cross-database configuration.
Specifically, we show that, when trained on one data set and tested on another,
the proposed axiomatic approach which does not involve training, outperforms
the deep learning alternative.
