Concept
Invariance of domain
Related publications (8)
Generalised Implicit Neural Representations
We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...
2022Smooth Shapes with Spherical Topology: Beyond Traditional Modeling, Efficient Deformation, and Interaction
Michaël Unser, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter
Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models a ...
2017Smoothly Deformable Spheres: Modeling, Deformation, and Interaction
Michaël Unser, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter
Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as NURBS. Polygon models and subdivision metho ...
ACM2016Sampling Models in Light Fields
What is the actual information contained in light rays filling the 3-D world? Leonardo da Vinci saw the world as an infinite number of radiant pyramids caused by the objects located in it. Nowadays, the radiant pyramid is usually described as a set of ligh ...
EPFL2016Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks
Pierre Vandergheynst, Michael Bronstein
In this paper, we propose a generalization of convolutional neural networks (CNN) to non-Euclidean domains for the analysis of deformable shapes. Our construction is based on localized frequency analysis (a generalization of the windowed Fourier transform ...
Wiley-Blackwell2015A note on topological amenability
A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established. ...
Oxford University Press2010DNA Topology
This thesis explores different aspects of DNA topology through experimental and numerical techniques. Topology is a vast mathematical field, that deals with the spatial properties of objects undergoing continuous deformations, but here it is restricted to ...
EPFL2010The Contourlet Transform: An Efficient Directional Multiresolution Image Representation
The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can c ...
2005