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We propose a novel semantic segmentation algorithm by learning a deconvolution network. We learn the network on top of the convolutional layers adopted from VGG 16-layer net. The deconvolution network is composed of deconvolution and…
We present an edge labeling of order-$k$ Voronoi diagrams, $V_k(S)$, of point sets $S$ in the plane, and study properties of the regions defined by them. Among them, we show that $V_k(S)$ has a small orientable cycle and path double cover,…
Supervised object detection and semantic segmentation require object or even pixel level annotations. When there exist image level labels only, it is challenging for weakly supervised algorithms to achieve accurate predictions. The accuracy…
Let $S$ be a planar $n$-point set. A triangulation for $S$ is a maximal plane straight-line graph with vertex set $S$. The Voronoi diagram for $S$ is the subdivision of the plane into cells such that all points in a cell have the same…
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 Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…
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 study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…
Weakly supervised semantic segmentation produces pixel-level localization from class labels; however, a classifier trained on such labels is likely to focus on a small discriminative region of the target object. We interpret this phenomenon…
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional…
Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up…
Surprisingly, the order-$k$ Voronoi diagram of line segments had received no attention in the computational-geometry literature. It illustrates properties surprisingly different from its counterpart for points; for example, a single…
We introduce an algorithm to estimate the redshift distribution of a sample of galaxies selected photometrically given a subsample with measured spectroscopic redshifts. The approach uses a non-parametric Voronoi tessellation density…
In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal…
In this paper, we show that recent advances in self-supervised feature learning enable unsupervised object discovery and semantic segmentation with a performance that matches the state of the field on supervised semantic segmentation 10…
Most current results on coverage control using mobile sensors require that one partitioned cell is associated with precisely one sensor. In this paper, we consider a class of coverage control problems involving higher order Voronoi…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…