Related papers: Consistent digital line segments

We formulate the task of detecting lines and paragraphs in a document into a unified two-level clustering problem. Given a set of text detection boxes that roughly correspond to words, a text line is a cluster of boxes and a paragraph is a…

We address the question how a given connection structure (directed graph) can be realised as a heteroclinic network that is complete in the sense that it contains all unstable manifolds of its equilibria. For a directed graph consisting of…

We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a…

In this paper, we prove the entirety of loop group Eisenstein series induced from cusp forms on the underlying finite dimensional group, by demonstrating their absolute convergence on the full complex plane. This is quite in contrast to the…

When using the maximin principle to solve the problem of classifying digital objects according to histograms, generated by this objects, it becomes necessary to take into account all the vertices of the polyhedron, generated by inequalities…

Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…

We want to introduce a construction of spherical designs from finite graphs with the theory of crystal lattice. We start from a finite graph, and we consider standard realization of the crystal lattices as the maximal Abelian covering of…

We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued…

In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential problems of the form $\Delta^p u =f$, $p\ge1$. More…

Given a compact basic semi-algebraic set we provide a numerical scheme to approximate as closely as desired, any finite number of moments of the Hausdorff measure on the boundary of this set. This also allows one to approximate interesting…

Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space…

We prove that for all positive integers $n$ and $k$, there exists an integer $N = N(n,k)$ satisfying the following. If $U$ is a set of $k$ direction vectors in the plane and $\mathcal{J}_U$ is the set of all line segments in direction $u$…

The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by uniformly prox-regular sets. After obtaining well-posedness results, we propose a…

Semantic segmentation consists of predicting a semantic label for each image pixel. While existing deep learning approaches achieve high accuracy, they often overlook the ordinal relationships between classes, which can provide critical…

We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to David and Semmes in the case of sufficiently large co-dimension,…

This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann-Beenker tilings as…

Fully convolutional neural networks like U-Net have been the state-of-the-art methods in medical image segmentation. Practically, a network is highly specialized and trained separately for each segmentation task. Instead of a collection of…

Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…

We share our recent findings in an attempt to train a universal segmentation network for various cell types and imaging modalities. Our method was built on the generalized U-Net architecture, which allows the evaluation of each component…

L\"uroth series, like regular continued fractions, provide an interesting identification of real numbers with infinite sequences of integers. These sequences give deep arithmetic and measure-theoretic properties of subsets of numbers…