Functional Maps Representation on Product Manifolds

by   Emanuele Rodolà, et al.

We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace--Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.


Manifold Diffusion Fields

We present Manifold Diffusion Fields (MDF), an approach to learn generat...

Local inference for functional data on manifold domains using permutation tests

Pini and Vantini (2017) introduced the interval-wise testing procedure w...

Complex Functional Maps : a Conformal Link Between Tangent Bundles

In this paper, we introduce complex functional maps, which extend the fu...

Windowed Fourier Analysis for Signal Processing on Graph Bundles

We consider the task of representing signals supported on graph bundles,...

Registration-free localization of defects in 3-D parts from mesh metrology data using functional maps

Spectral Laplacian methods, widely used in computer graphics and manifol...

Shape And Structure Preserving Differential Privacy

It is common for data structures such as images and shapes of 2D objects...

Please sign up or login with your details

Forgot password? Click here to reset