Matchability of heterogeneous networks pairs

We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability is almost surely lost when matching the networks directly, and is almost perfectly recovered when first centering the networks using Universal Singular Value Thresholding before matching. These theoretical results are then demonstrated in both real and synthetic simulation settings. We also recover analogous core-matchability results in a very general core-junk network model, wherein some vertices do not correspond between the graph pair.First author draf

Maximum Likelihood Estimation and Graph Matching in Errorfully Observed Networks

Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study this problem from a statistical framework in which one of the graphs is an errorfully observed copy of the other. We introduce a corrupting channel model, and show that in this model framework, the solution to the graph matching problem is a maximum likelihood estimator. Necessary and sufficient conditions for consistency of this MLE are presented, as well as a relaxed notion of consistency in which a negligible fraction of the vertices need not be matched correctly. The results are used to study matchability in several families of random graphs, including edge independent models, random regular graphs and small-world networks. We also use these results to introduce measures of matching feasibility, and experimentally validate the results on simulated and real-world networks

Ship Detection and Segmentation using Image Correlation

There have been intensive research interests in ship detection and segmentation due to high demands on a wide range of civil applications in the last two decades. However, existing approaches, which are mainly based on statistical properties of images, fail to detect smaller ships and boats. Specifically, known techniques are not robust enough in view of inevitable small geometric and photometric changes in images consisting of ships. In this paper a novel approach for ship detection is proposed based on correlation of maritime images. The idea comes from the observation that a fine pattern of the sea surface changes considerably from time to time whereas the ship appearance basically keeps unchanged. We want to examine whether the images have a common unaltered part, a ship in this case. To this end, we developed a method - Focused Correlation (FC) to achieve robustness to geometric distortions of the image content. Various experiments have been conducted to evaluate the effectiveness of the proposed approach.Comment: 8 pages, to be published in proc. of conference IEEE SMC 201

Learning Feature Matching via Matchable Keypoint-Assisted Graph Neural Network

Accurately matching local features between a pair of images is a challenging computer vision task. Previous studies typically use attention based graph neural networks (GNNs) with fully-connected graphs over keypoints within/across images for visual and geometric information reasoning. However, in the context of feature matching, considerable keypoints are non-repeatable due to occlusion and failure of the detector, and thus irrelevant for message passing. The connectivity with non-repeatable keypoints not only introduces redundancy, resulting in limited efficiency, but also interferes with the representation aggregation process, leading to limited accuracy. Targeting towards high accuracy and efficiency, we propose MaKeGNN, a sparse attention-based GNN architecture which bypasses non-repeatable keypoints and leverages matchable ones to guide compact and meaningful message passing. More specifically, our Bilateral Context-Aware Sampling Module first dynamically samples two small sets of well-distributed keypoints with high matchability scores from the image pair. Then, our Matchable Keypoint-Assisted Context Aggregation Module regards sampled informative keypoints as message bottlenecks and thus constrains each keypoint only to retrieve favorable contextual information from intra- and inter- matchable keypoints, evading the interference of irrelevant and redundant connectivity with non-repeatable ones. Furthermore, considering the potential noise in initial keypoints and sampled matchable ones, the MKACA module adopts a matchability-guided attentional aggregation operation for purer data-dependent context propagation. By these means, we achieve the state-of-the-art performance on relative camera estimation, fundamental matrix estimation, and visual localization, while significantly reducing computational and memory complexity compared to typical attentional GNNs