DSLib is an open-source implementation of the Dominant Set (DS) clustering algorithm written entirely in Matlab. The DS method is a graph-based clustering technique rooted in the evolutionary game theory that starts gaining lots of interest in the computer science community. Thanks to its duality with game theory and its strict relation to the notion of maximal clique, has been explored in several directions not only related to clustering problems. Applications in graph matching, segmentation, classification and medical imaging are common in literature. This package provides an implementation of the original DS clustering algorithm since no code has been officially released yet, together with a still growing collection of methods and variants related to it. Our library is integrable into a Matlab pipeline without dependencies, it is simple to use and easily extendable for upcoming works. The latest source code, the documentation and some examples can be downloaded from https://xwasco.github.io/DominantSetLibrary.
Graph matching pairs corresponding nodes across two or more graphs. The problem is difficult as it is hard to capture the structural similarity across graphs, especially on large graphs. We propose to incorporate high-order information for matching large-scale graphs. Iterated line graphs are introduced for the first time to describe such high-order information, based on which we present a new graph matching method, called High-order Graph Matching Network (HGMN), to learn not only the local structural correspondence, but also the hyperedge relations across graphs. We theoretically prove that iterated line graphs are more expressive than graph convolution networks in terms of aligning nodes. By imposing practical constraints, HGMN is made scalable to large-scale graphs. Experimental results on a variety of settings have shown that, HGMN acquires more accurate matching results than the state-of-the-art, verifying our method effectively captures the structural similarity across different graphs.
Unlabeled sensing is a linear inverse problem where the measurements are scrambled under an unknown permutation leading to loss of correspondence between the measurements and the rows of the sensing matrix. Motivated by practical tasks such as mobile sensor networks, target tracking and the pose and correspondence estimation between point clouds, we study a special case of this problem restricting the class of permutations to be local and allowing for multiple views. In this setting, namely unlabeled multi-view sensing with local permutation, previous results and algorithms are not directly applicable. In this paper, we propose a computationally efficient algorithm that creatively exploits the machinery of graph alignment and Gromov-Wasserstein alignment and leverages the multiple views to estimate the local permutations. Simulation results on synthetic data sets indicate that the proposed algorithm is scalable and applicable to the challenging regimes of low to moderate SNR.
Analog layout synthesis requires some elements in the circuit netlist to be matched and placed symmetrically. However, the set of symmetries is very circuit-specific and a versatile algorithm, applicable to a broad variety of circuits, has been elusive. This paper presents a general methodology for the automated generation of symmetry constraints, and applies these constraints to guide automated layout synthesis. While prior approaches were restricted to identifying simple symmetries, the proposed method operates hierarchically and uses graph-based algorithms to extract multiple axes of symmetry within a circuit. An important ingredient of the algorithm is its ability to identify arrays of repeated structures. In some circuits, the repeated structures are not perfect replicas and can only be found through approximate graph matching. A fast graph neural network based methodology is developed for this purpose, based on evaluating the graph edit distance. The utility of this algorithm is demonstrated on a variety of circuits, including operational amplifiers, data converters, equalizers, and low-noise amplifiers.
Due to the difficulty in generating the effective descriptors which are robust to occlusion and viewpoint changes, place recognition for 3D point cloud remains an open issue. Unlike most of the existing methods that focus on extracting local, global, and statistical features of raw point clouds, our method aims at the semantic level that can be superior in terms of robustness to environmental changes. Inspired by the perspective of humans, who recognize scenes through identifying semantic objects and capturing their relations, this paper presents a novel semantic graph based approach for place recognition. First, we propose a novel semantic graph representation for the point cloud scenes by reserving the semantic and topological information of the raw point cloud. Thus, place recognition is modeled as a graph matching problem. Then we design a fast and effective graph similarity network to compute the similarity. Exhaustive evaluations on the KITTI dataset show that our approach is robust to the occlusion as well as viewpoint changes and outperforms the state-of-the-art methods with a large margin. Our code is available at: \url{https://github.com/kxhit/SG_PR}.
Scene Graph, as a vital tool to bridge the gap between language domain and image domain, has been widely adopted in the cross-modality task like VQA. In this paper, we propose a new method to edit the scene graph according to the user instructions, which has never been explored. To be specific, in order to learn editing scene graphs as the semantics given by texts, we propose a Graph Edit Distance Reward, which is based on the Policy Gradient and Graph Matching algorithm, to optimize neural symbolic model. In the context of text-editing image retrieval, we validate the effectiveness of our method in CSS and CRIR dataset. Besides, CRIR is a new synthetic dataset generated by us, which we will publish it soon for future use.
This paper describes a viewpoint-robust object-based change detection network (OBJ-CDNet). Mobile cameras such as drive recorders capture images from different viewpoints each time due to differences in camera trajectory and shutter timing. However, previous methods for pixel-wise change detection are vulnerable to the viewpoint differences because they assume aligned image pairs as inputs. To cope with the difficulty, we introduce a deep graph matching network that establishes object correspondence between an image pair. The introduction enables us to detect object-wise scene changes without precise image alignment. For more accurate object matching, we propose an epipolar-guided deep graph matching network (EGMNet), which incorporates the epipolar constraint into the deep graph matching layer used in OBJCDNet. To evaluate our network's robustness against viewpoint differences, we created synthetic and real datasets for scene change detection from an image pair. The experimental results verified the effectiveness of our network.
We propose and study a method called FLOT that estimates scene flow on point clouds. We start the design of FLOT by noticing that scene flow estimation on point clouds reduces to estimating a permutation matrix in a perfect world. Inspired by recent works on graph matching, we build a method to find these correspondences by borrowing tools from optimal transport. Then, we relax the transport constraints to take into account real-world imperfections. The transport cost between two points is given by the pairwise similarity between deep features extracted by a neural network trained under full supervision using synthetic datasets. Our main finding is that FLOT can perform as well as the best existing methods on synthetic and real-world datasets while requiring much less parameters and without using multiscale analysis. Our second finding is that, on the training datasets considered, most of the performance can be explained by the learned transport cost. This yields a simpler method, FLOT$_0$, which is obtained using a particular choice of optimal transport parameters and performs nearly as well as FLOT.
The semantic segmentation of parts of objects in the wild is a challenging task in which multiple instances of objects and multiple parts within those objects must be detected in the scene. This problem remains nowadays very marginally explored, despite its fundamental importance towards detailed object understanding. In this work, we propose a novel framework combining higher object-level context conditioning and part-level spatial relationships to address the task. To tackle object-level ambiguity, a class-conditioning module is introduced to retain class-level semantics when learning parts-level semantics. In this way, mid-level features carry also this information prior to the decoding stage. To tackle part-level ambiguity and localization we propose a novel adjacency graph-based module that aims at matching the relative spatial relationships between ground truth and predicted parts. The experimental evaluation on the Pascal-Part dataset shows that we achieve state-of-the-art results on this task.
While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to the task of graph similarity learning. Recent work on graph similarity learning has considered either global-level graph-graph interactions or low-level node-node interactions, however ignoring the rich cross-level interactions (e.g., between each node of one graph and the other whole graph). In this paper, we propose a multi-level graph matching network (MGMN) framework for computing the graph similarity between any pair of graph-structured objects in an end-to-end fashion. In particular, the proposed MGMN consists of a node-graph matching network for effectively learning cross-level interactions between each node of one graph and the other whole graph, and a siamese graph neural network to learn global-level interactions between two input graphs. Furthermore, to compensate for the lack of standard benchmark datasets, we have created and collected a set of datasets for both the graph-graph classification and graph-graph regression tasks with different sizes in order to evaluate the effectiveness and robustness of our models. Comprehensive experiments demonstrate that MGMN consistently outperforms state-of-the-art baseline models on both the graph-graph classification and graph-graph regression tasks. Compared with previous work, MGMN also exhibits stronger robustness as the sizes of the two input graphs increase.
Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention mechanisms to simulate soft alignment, with no training signals to explicitly encourage alignment. The learned attention matrices are also dense and lacks interpretability. We propose Graph Optimal Transport (GOT), a principled framework that germinates from recent advances in Optimal Transport (OT). In GOT, cross-domain alignment is formulated as a graph matching problem, by representing entities into a dynamically-constructed graph. Two types of OT distances are considered: (i) Wasserstein distance (WD) for node (entity) matching; and (ii) Gromov-Wasserstein distance (GWD) for edge (structure) matching. Both WD and GWD can be incorporated into existing neural network models, effectively acting as a drop-in regularizer. The inferred transport plan also yields sparse and self-normalized alignment, enhancing the interpretability of the learned model. Experiments show consistent outperformance of GOT over baselines across a wide range of tasks, including image-text retrieval, visual question answering, image captioning, machine translation, and text summarization.
Proprioceptive localization refers to a new class of robot egocentric localization methods that do not rely on the perception and recognition of external landmarks. These methods are naturally immune to bad weather, poor lighting conditions, or other extreme environmental conditions that may hinder exteroceptive sensors such as a camera or a laser ranger finder. These methods depend on proprioceptive sensors such as inertial measurement units (IMUs) and/or wheel encoders. Assisted by magnetoreception, the sensors can provide a rudimentary estimation of vehicle trajectory which is used to query a prior known map to obtain location. Named as graph-based proprioceptive localization (GBPL), we provide a low cost fallback solution for localization under challenging environmental conditions. As a robot/vehicle travels, we extract a sequence of heading-length values for straight segments from the trajectory and match the sequence with a pre-processed heading-length graph (HLG) abstracted from the prior known map to localize the robot under a graph-matching approach. Using the information from HLG, our location alignment and verification module compensates for trajectory drift, wheel slip, or tire inflation level. We have implemented our algorithm and tested it in both simulated and physical experiments. The algorithm runs successfully in finding robot location continuously and achieves localization accurate at the level that the prior map allows (less than 10m).
Graph similarity computation aims to predict a similarity score between one pair of graphs to facilitate downstream applications, such as finding the most similar chemical compounds similar to a query compound or Fewshot 3D Action Recognition. Recently, some graph similarity computation models based on neural networks have been proposed, which are either based on graph-level interaction or node-level comparison. However, when the number of nodes in the graph increases, it will inevitably bring about reduced representation ability or high computation cost. Motivated by this observation, we propose a graph partitioning and graph neural network-based model, called PSimGNN, to effectively resolve this issue. Specifically, each of the input graphs is partitioned into a set of subgraphs to extract the local structural features directly. Next, a novel graph neural network with an attention mechanism is designed to map each subgraph into an embedding vector. Some of these subgraph pairs are automatically selected for node-level comparison to supplement the subgraph-level embedding with fine-grained information. Finally, coarse-grained interaction information among subgraphs and fine-grained comparison information among nodes in different subgraphs are integrated to predict the final similarity score. Experimental results on graph datasets with different graph sizes demonstrate that PSimGNN outperforms state-of-the-art methods in graph similarity computation tasks using approximate Graph Edit Distance (GED) as the graph similarity metric.
Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set of seeds, i.e., pre-mapped vertex-pairs, is given in advance. While most previous work requires all seeds to be correct, we focus on the setting where the seeds are partially correct. Specifically, consider two correlated graphs whose edges are sampled independently from a parent \ER graph $\mathcal{G}(n,p)$. A mapping between the vertices of the two graphs is provided as seeds, of which an unknown $\beta$ fraction is correct. We first analyze a simple algorithm that matches vertices based on the number of common seeds in the $1$-hop neighborhoods, and then further propose a new algorithm that uses seeds in the $2$-hop neighborhoods. We establish non-asymptotic performance guarantees of perfect matching for both $1$-hop and $2$-hop algorithms, showing that our new $2$-hop algorithm requires substantially fewer correct seeds than the $1$-hop algorithm when graphs are sparse. Moreover, by combining our new performance guarantees for the $1$-hop and $2$-hop algorithms, we attain the best-known results (in terms of the required fraction of correct seeds) across the entire range of graph sparsity and significantly improve the previous results in \cite{10.14778/2794367.2794371,lubars2018correcting} when $p\ge n^{-5/6}$. For instance, when $p$ is a constant or $p=n^{-3/4}$, we show that only $\Omega(\sqrt{n\log n})$ correct seeds suffice for perfect matching, while the previously best-known results demand $\Omega(n)$ and $\Omega(n^{3/4}\log n)$ correct seeds, respectively. Numerical experiments corroborate our theoretical findings, demonstrating the superiority of our $2$-hop algorithm on a variety of synthetic and real graphs.
Occluded person re-identification is a challenging task as the appearance varies substantially with various obstacles, especially in the crowd scenario. To address this issue, we propose a Pose-guided Visible Part Matching (PVPM) method that jointly learns the discriminative features with pose-guided attention and self-mines the part visibility in an end-to-end framework. Specifically, the proposed PVPM includes two key components: 1) pose-guided attention (PGA) method for part feature pooling that exploits more discriminative local features; 2) pose-guided visibility predictor (PVP) that estimates whether a part suffers the occlusion or not. As there are no ground truth training annotations for the occluded part, we turn to utilize the characteristic of part correspondence in positive pairs and self-mining the correspondence scores via graph matching. The generated correspondence scores are then utilized as pseudo-labels for visibility predictor (PVP). Experimental results on three reported occluded benchmarks show that the proposed method achieves competitive performance to state-of-the-art methods. The source codes are available at https://github.com/hh23333/PVPM
Graph matching (GM), as a longstanding problem in computer vision and pattern recognition, still suffers from numerous cluttered outliers in practical applications. To address this issue, we present the zero-assignment constraint (ZAC) for approaching the graph matching problem in the presence of outliers. The underlying idea is to suppress the matchings of outliers by assigning zero-valued vectors to the potential outliers in the obtained optimal correspondence matrix. We provide elaborate theoretical analysis to the problem, i.e., GM with ZAC, and figure out that the GM problem with and without outliers are intrinsically different, which enables us to put forward a sufficient condition to construct valid and reasonable objective function. Consequently, we design an efficient outlier-robust algorithm to significantly reduce the incorrect or redundant matchings caused by numerous outliers. Extensive experiments demonstrate that our method can achieve the state-of-the-art performance in terms of accuracy and efficiency, especially in the presence of numerous outliers.
Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of heavily optimized combinatorial solvers together with some improvements in architecture design, we advance state-of-the-art on deep graph matching benchmarks for keypoint correspondence. In addition, we highlight the conceptual advantages of incorporating solvers into deep learning architectures, such as the possibility of post-processing with a strong multi-graph matching solver or the indifference to changes in the training setting. Finally, we propose two new challenging experimental setups. The code is available at https://github.com/martius-lab/blackbox-deep-graph-matching
Occluded person re-identification (ReID) aims to match occluded person images to holistic ones across dis-joint cameras. In this paper, we propose a novel framework by learning high-order relation and topology information for discriminative features and robust alignment. At first, we use a CNN backbone and a key-points estimation model to extract semantic local features. Even so, occluded images still suffer from occlusion and outliers. Then, we view the local features of an image as nodes of a graph and propose an adaptive direction graph convolutional (ADGC)layer to pass relation information between nodes. The proposed ADGC layer can automatically suppress the message-passing of meaningless features by dynamically learning di-rection and degree of linkage. When aligning two groups of local features from two images, we view it as a graph matching problem and propose a cross-graph embedded-alignment (CGEA) layer to jointly learn and embed topology information to local features, and straightly predict similarity score. The proposed CGEA layer not only take full use of alignment learned by graph matching but also re-place sensitive one-to-one matching with a robust soft one. Finally, extensive experiments on occluded, partial, and holistic ReID tasks show the effectiveness of our proposed method. Specifically, our framework significantly outperforms state-of-the-art by6.5%mAP scores on Occluded-Duke dataset.
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high computational complexity and therefore do not have good scalability with respect to graph size. For matching two weighted graphs of $n$ nodes, our algorithm has time complexity only $O(n^3)$ per iteration and space complexity $O(n^2)$. In addition to its scalability, our algorithm is easy to implement, robust, and able to match undirected weighted attributed graphs of different sizes. While the convergence rate of previous iterative graph matching algorithms is unknown, our algorithm is theoretically guaranteed to converge at a linear rate. Extensive experiments on large synthetic and real graphs (more than 1,000 nodes) were conducted to evaluate the performance of various algorithms. Results show that in most cases our proposed algorithm achieves better performance than previous state-of-the-art algorithms in terms of both speed and accuracy in large graph matching. In particular, with high accuracy, our algorithm takes only a few seconds (in a PC) to match two graphs of 1,000 nodes.
Graph generation is an extremely important task, as graphs are found throughout different areas of science and engineering. In this work, we focus on the modern equivalent of the Erdos-Renyi random graph model: the graph variational autoencoder (GVAE). This model assumes edges and nodes are independent in order to generate entire graphs at a time using a multi-layer perceptron decoder. As a result of these assumptions, GVAE has difficulty matching the training distribution and relies on an expensive graph matching procedure. We improve this class of models by building a message passing neural network into GVAE's encoder and decoder. We demonstrate our model on the specific task of generating small organic molecules