Related papers: Voronoi binning: Optimal adaptive tessellations of…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…
votess is a library for computing parallel 3D Voronoi tessellations on heterogeneous platforms, from CPUs and GPUs, to future accelerator architectures. To do so, it leverages the SYCL abstraction layer to achieve portability and…
Optimized spatial partitioning algorithms are the corner stone of many successful experimental designs and statistical methods. Of these algorithms, the Centroidal Voronoi Tessellation (CVT) is the most widely utilized. CVT based methods…
Identifying Blaschke-Santal\'o diagrams is an important topic that essentially consists in determining the image $Y=F(X)$ of a map $F:X\to{\mathbb{R}}^d$, where the dimension of the source space $X$ is much larger than the one of the target…
Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly…
Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space,…
Digital co-addition of astronomical images is a common technique for increasing signal-to-noise and image depth. A modification of this simple technique has been applied to the detection of minor bodies in the Solar System: first stationary…
Voronoi diagrams are highly compact representations that are used in various Graphics applications. In this work, we show how to embed a differentiable version of it -- via a novel deep architecture -- into a generative deep network. By…
The purpose of this note is to clarify the effect of the finite size of spherical particles upon the characteristics of their spatial distribution through a random Poisson process (RPP). This information is of special interest when using…
In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic…
We present an objective and automated procedure for detecting clusters of galaxies in imaging galaxy surveys. Our Voronoi Galaxy Cluster Finder (VGCF) uses galaxy positions and magnitudes to find clusters and determine their main features:…
The transition from ordered to disordered structures in Voronoi tessellation is obtained by perturbing the seeds that were originally identified with two types of lattice in 2D and one type in 3D. The area in 2D and the volume in 3D are…
Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly…
We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the…
Accurate segmentation of orbital bones in facial computed tomography (CT) images is essential for the creation of customized implants for reconstruction of defected orbital bones, particularly challenging due to the ambiguous boundaries and…
We present medial parametrization, a new approach to parameterizing any compact planar domain bounded by simple closed curves. The basic premise behind our proposed approach is to use two close Voronoi sites, which we call dipoles, to…
The core challenge of hyperspectral image denoising is striking the right balance between data fidelity and noise prior modeling. Most existing methods place too much emphasis on the intrinsic priors of the image while overlooking diverse…
This paper presents a range of results in partial differential equations (PDEs) in which Voronoi patterns arise. We investigate the connection between the solution to an elliptic equation and its probabilistic interpretation as a stochastic…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…