Intrinsic spatial pyramid matching for deformable 3D shape retrieval

Abstract

In this paper, we present an intrinsic spatial pyramid matching approach for 3D shape retrieval. Motivated by the fact that the second eigenfunction of Laplace-Beltrami operator not only can capture the global topological structure information, but also is intrinsic, we propose to adopt its level sets as cuts to perform surface partition. The resulting matching scheme is able to consistently estimate the approximate global geometric correspondence among 3D shapes. In particular, we can leverage recent developments in intrinsic shape analysis and perform intrinsic spatial pyramid matching based on dense spectral shape descriptors such as scaleinvariant heat kernel signature. Our experiments demonstrate a significant improvement of 3D shape retrieval on two standard benchmarks.

Retrieval and classification methods for textured 3D models: a comparative study

“…Also, these eigenbases serve as ingredients for two further steps: feature extraction, detailed in Section 4.2.1, and spatial sensitive shape comparison via intrinsic spatial pyramid matching [39], discussed in Section 4.2.2. The cotangent weight scheme [14] was used to discretize LBO.…”

Persistence-Based Structural Recognition

“…The subsequent research on spatial aggregation get compelling performance because of two seemingly independent advantages: the better design of (1) spatial regions and (2) aggregating operator. The spatial pyramids manually define the multi-scale grid-structured regions over the image space, and many excellent visual recognition methods either directly use them [25,44], or modify the spatial decomposition to fit their data [9,26]. Recently, Jia et al [23] proposed to learn more adaptive regions by the receptive fields.…”

“…SIHKS is a scale-invariant version of HKS. We compare our method to BoF-based approach, spatially-sensitive BoF (SSBoF) [7] and ISPM [26], which is a spatial pyramid approach on surfaces. …”

A statistical model of Riemannian metric variation for deformable shape analysis

“…For this purpose, the Bag-of-Features (BoF) paradigm is quite popular and has been successfully applied to 3D shape description [10,12,23,48]. Li and Hamza [27] used the BoF paradigm combining the exploitation of hierarchical structures of the shape, such as pyramid matching [16] and spatial relationship [10,12,23]. They proposed to adopt the eigenfunction associated with the second-smallest eigenvector of the Laplace-Beltrami operator in order to build a global surface coordinate system which is insensitive to shape deformation, showing that the introduction of global spatial context could improve the effectiveness of their descriptor in 3D shape recognition.…”

“…They proposed to adopt the eigenfunction associated with the second-smallest eigenvector of the Laplace-Beltrami operator in order to build a global surface coordinate system which is insensitive to shape deformation, showing that the introduction of global spatial context could improve the effectiveness of their descriptor in 3D shape recognition. Spatial pyramid [30,27,24], is the term used to identify this approach. Other approaches inspired by text-analysis have been proposed.…”