Related papers: The Offset Filtration of Convex Objects
We have recently developed a mean-field theory to estimate the packing fraction of non-spherical particles [A. Baule et al., Nature Commun. (2013)]. The central quantity in this framework is the Voronoi excluded volume, which generalizes…
We introduce Topological Offsets, a novel approach to generate manifold and self-intersection-free offset surfaces that are topologically equivalent to an offset infinitesimally close to the surface. Our approach, by construction, creates a…
We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property (that is, the smallest fraction of pixels that need to change in…
When the boundary of a familiar object is shown by a series of isolated dots, humans can often recognize the object with ease. This ability can be sustained with addition of distracting dots around the object. However, such capability has…
In this paper, we present an approach for minimizing the computational complexity of trained Convolutional Neural Networks (ConvNet). The idea is to approximate all elements of a given ConvNet and replace the original convolutional filters…
Inspired by the conclusion that humans choose the visual cortex regions corresponding to the real size of an object to analyze its features when identifying objects in the real world, this paper presents a framework, SizeNet, which is based…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
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…
We present a geometric perspective on sparse filtrations used in topological data analysis. This new perspective leads to much simpler proofs, while also being more general, applying equally to Rips filtrations and Cech filtrations for any…
In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on…
We formulate object segmentation in video as a graph partitioning problem in space and time, in which nodes are pixels and their relations form local neighborhoods. We claim that the strongest cluster in this pixel-level graph represents…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
We define and study error detection and correction tasks that are useful for 3D reconstruction of neurons from electron microscopic imagery, and for image segmentation more generally. Both tasks take as input the raw image and a binary mask…
We introduce a notion of $k$-convexity and explore polygons in the plane that have this property. Polygons which are \mbox{$k$-convex} can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUM-hard…
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually…
We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the…
This study introduces a method for efficiently detecting objects within 3D point clouds using convolutional neural networks (CNNs). Our approach adopts a unique feature-centric voting mechanism to construct convolutional layers that…
Consider a set represented by an inequality. An interesting phenomenon which occurs in various settings in mathematics is that the interior of this set is the subset where strict inequality holds, the boundary is the subset where equality…
Efficient fine-tuning methods are critical to address the high computational and parameter complexity while adapting large pre-trained models to downstream tasks. Our study is inspired by prior research that represents each convolution…