Related papers: Sampling Superquadric Point Clouds with Normals
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the…
We investigate the problem of learning to generate 3D parametric surface representations for novel object instances, as seen from one or more views. Previous work on learning shape reconstruction from multiple views uses discrete…
There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
Source coding is the canonical problem of data compression in information theory. In a locally encodable source coding, each compressed bit depends on only few bits of the input. In this paper, we show that a recently popular model of…
The popularisation of acquisition devices capable of capturing volumetric information such as LiDAR scans and depth cameras has lead to an increased interest in point clouds as an imaging modality. Due to the high amount of data needed for…
Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…
A central problem in hyperspectral image classification is obtaining high classification accuracy when using a limited amount of labelled data. In this paper we present a novel graph-based framework, which aims to tackle this problem in the…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
A new method for improving the resolution of astronomical images is presented. It is based on the principle that sampled data cannot be fully deconvolved without violating the sampling theorem. Thus, the sampled image should not be…
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…
The shape of crystalline nanoparticles (NP) can often be described by polyhedra with flat facet surfaces. Thus, structural studies of polyhedral bodies can help to describe geometric details of NPs. Here we consider compact polyhedra of…
The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…
Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the…