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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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
