Related papers: Connected Components on Lie Groups and Application…
High-dimensional data with intrinsic low-dimensional structure is ubiquitous in machine learning and data science. While various approaches allow one to learn a data manifold with a Riemannian structure from finite samples, performing…
Robust segmentation for non-elongated tissues in medical images is hard to realize due to the large variation of the shape, size, and appearance of these tissues in different patients. In this paper, we present an end-to-end trainable deep…
The Weisfeiler-Leman (WL) algorithms form a family of incomplete approaches to the graph isomorphism problem. They recently found various applications in algorithmic group theory and machine learning. In fact, the algorithms form a…
This article introduces a new connected component labeling and analysis algorithm for foreground and background labeling that computes the adjacency tree. The computation of features (bounding boxes, first statistical moments, Euler number)…
State-of-the-art detection systems are generally evaluated on their ability to exhaustively retrieve objects densely distributed in the image, across a wide variety of appearances and semantic categories. Orthogonal to this, many real-life…
In this paper we describe a new method for detecting and counting a repeating object in an image. While the method relies on a fairly sophisticated deformable part model, unlike existing techniques it estimates the model parameters in an…
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…
In this paper, left-invariant almost contact metric structures on three-dimensional non-unimodular Lie groups are investigated. It is proved that for every Riemannian Lie group, there is one of these structures. In addition, left-invariant…
This review presents various image segmentation methods using complex networks. Image segmentation is one of the important steps in image analysis as it helps analyze and understand complex images. At first, it has been tried to classify…
In this paper we study the problem of maintaining the strongly connected components of a graph in the presence of failures. In particular, we show that given a directed graph $G=(V,E)$ with $n=|V|$ and $m=|E|$, and an integer value $k\geq…
Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…
This paper is the first from a series of papers that provide a characterization of maximum packings of $T$-cuts in bipartite graphs. Given a connected graph, a set $T$ of an even number of vertices, and a minimum $T$-join, an edge weighting…
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree…
We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions that a large class of totally disconnected locally compact groups acting on trees and…
We study the correlation between different sets of parton distributions (PDFs). Specifically, viewing different PDF sets as distinct determinations, generally correlated, of the same underlying physical quantity, we examine the extent to…
In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the…
The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. Its simplest formulation is in two steps: (1) We cut every edge of G into two halves, thus obtaining a…
Graph Laplacian based algorithms for data lying on a manifold have been proven effective for tasks such as dimensionality reduction, clustering, and denoising. In this work, we consider data sets whose data points lie on a manifold that is…
This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…
Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the…