Related papers: Higher-Order Minimum Cost Lifted Multicuts for Mot…
In recent years, hypergraph generalizations of many graph cut problems have been introduced and analyzed as a way to better explore and understand complex systems and datasets characterized by multiway relationships. Recent work has made…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…
The study of genome rearrangement has many flavours, but they all are somehow tied to edit distances on variations of a multi-graph called the breakpoint graph. We study a weighted 2-break distance on Eulerian 2-edge-colored multi-graphs,…
Sampling-based planning methods often become inefficient due to narrow passages. Narrow passages induce a higher runtime, because the chance to sample them becomes vanishingly small. In recent work, we showed that narrow passages can be…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
We study the Minimum Submodular-Cost Allocation problem (MSCA). In this problem we are given a finite ground set $V$ and $k$ non-negative submodular set functions $f_1 ,..., f_k$ on $V$. The objective is to partition $V$ into $k$ (possibly…
We propose a mid-level image segmentation framework that combines multiple figure-ground hypothesis (FG) constrained at different locations and scales, into interpretations that tile the entire image. The problem is cast as optimization…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
The goal of this paper is to discover, segment, and track independently moving objects in complex visual scenes. Previous approaches have explored the use of optical flow for motion segmentation, leading to imperfect predictions due to…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…
Motion segmentation is currently an active area of research in computer Vision. The task of comparing different methods of motion segmentation is complicated by the fact that researchers may use subtly different definitions of the problem.…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
The balanced hypergraph partitioning problem is to partition a hypergraph into $k$ disjoint blocks of bounded size such that the sum of the number of blocks connected by each hyperedge is minimized. We present an improvement to the…
Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded…
The graph partitioning problem is a well-known NP-hard problem. In this paper, we formulate a 0-1 quadratic integer programming model for the graph partitioning problem with vertex weight constraints and fixed vertex constraints, and…
Motivated by the classic Generalized Assignment Problem, we consider the Graph Balancing problem in the presence of orientation costs: given an undirected multi-graph G = (V,E) equipped with edge weights and orientation costs on the edges,…
We propose a new approach to learn to segment multiple image objects without manual supervision. The method can extract objects form still images, but uses videos for supervision. While prior works have considered motion for segmentation, a…
While Structure from Motion (SfM) achieves great success in 3D reconstruction, it still meets challenges on large scale scenes. In this work, large scale SfM is deemed as a graph problem, and we tackle it in a divide-and-conquer manner.…
Given their flexibility and encouraging performance, deep-learning models are becoming standard for motion prediction in autonomous driving. However, with great flexibility comes a lack of interpretability and possible violations of…