相关论文: Solving Jigsaw Puzzles By the Graph Connection Lap…

Cartoon face recognition is challenging as they typically have smooth color regions and emphasized edges, the key to recognize cartoon faces is to precisely perceive their sparse and critical shape patterns. However, it is quite difficult…

In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…

We prove the computational intractability of rotating and placing $n$ square tiles into a $1 \times n$ array such that adjacent tiles are compatible--either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as…

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…

We present an algorithm that efficiently computes nearly-optimal solutions to a class of combinatorial reconfiguration problems on weighted, undirected graphs. Inspired by societally relevant applications in networked infrastructure…

We devise methods for finding approximations of the generalized inverse of the graph Laplacian matrix, which arises in many graph-theoretic applications. Finding this matrix in its entirety involves solving a matrix inversion problem, which…

In the graph signal processing (GSP) literature, it has been shown that signal-dependent graph Laplacian regularizer (GLR) can efficiently promote piecewise constant (PWC) signal reconstruction for various image restoration tasks. However,…

We consider the problem of matrix completion with graphs as side information depicting the interrelations between variables. The key challenge lies in leveraging the similarity structure of the graph to enhance matrix recovery. Existing…

This paper addresses the problem of reassembling images from disjointed fragments. More specifically, given an unordered set of fragments, we aim at reassembling one or several possibly incomplete images. The main contributions of this work…

Reassembling real-world archaeological artifacts from fragmented pieces poses significant challenges due to erosion, missing regions, irregular shapes, and large-scale ambiguity. Traditional jigsaw puzzle solvers, often designed for clean…

This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…

We present a method for the automatic assembly of apictorial jigsaw puzzles. This method relies on integral area invariants for shape matching and an optimization process to aggregate shape matches into a final puzzle assembly. Assumptions…

We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…

Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…

Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics. We apply some…

In recent years, improvements in various image acquisition techniques gave rise to the need for adaptive processing methods, aimed particularly for large datasets corrupted by noise and deformations. In this work, we consider datasets of…

In reinforcement learning, the graph Laplacian has proved to be a valuable tool in the task-agnostic setting, with applications ranging from skill discovery to reward shaping. Recently, learning the Laplacian representation has been framed…

We propose a method by which to recover an underlying graph from a set of multivariate wave signals that is discretely sampled from a solution of the graph wave equation. Herein, the graph wave equation is defined with the graph Laplacian,…