We present a novel method of integrating motion and appearance cues for foreground object segmentation in unconstrained videos. Unlike conventional methods encoding motion and appearance patterns individually, our method puts particular emphasis on their mutual assistance. Specifically, we propose using an interactively constrained encoding (ICE) scheme to incorporate motion and appearance patterns into a graph that leads to a spatiotemporal energy optimization. The reason of utilizing ICE is that both motion and appearance cues for the same target share underlying correlative structure, thus can be exploited in a deeply collaborative manner. We perform ICE not only in the initialization but also in the refinement stage of a two-layer framework for object segmentation. This scheme allows our method to consistently capture structural patterns about object perceptions throughout the whole framework. Our method can be operated on superpixels instead of raw pixels to reduce the number of graph nodes by two orders of magnitude. Moreover, we propose to partially explore the multi-object localization problem with inter-occlusion by weighted bipartite graph matching. Comprehensive experiments on three benchmark datasets (i.e., SegTrack, MOViCS, and GaTech) demonstrate the effectiveness of our approach compared with extensive state-of-the-art methods.
The problem of cross-platform binary code similarity detection aims at detecting whether two binary functions coming from different platforms are similar or not. It has many security applications, including plagiarism detection, malware detection, vulnerability search, etc. Existing approaches rely on approximate graph matching algorithms, which are inevitably slow and sometimes inaccurate, and hard to adapt to a new task. To address these issues, in this work, we propose a novel neural network-based approach to compute the embedding, i.e., a numeric vector, based on the control flow graph of each binary function, then the similarity detection can be done efficiently by measuring the distance between the embeddings for two functions. We implement a prototype called Gemini. Our extensive evaluation shows that Gemini outperforms the state-of-the-art approaches by large margins with respect to similarity detection accuracy. Further, Gemini can speed up prior art's embedding generation time by 3 to 4 orders of magnitude and reduce the required training time from more than 1 week down to 30 minutes to 10 hours. Our real world case studies demonstrate that Gemini can identify significantly more vulnerable firmware images than the state-of-the-art, i.e., Genius. Our research showcases a successful application of deep learning on computer security problems.
Label estimation is an important component in an unsupervised person re-identification (re-ID) system. This paper focuses on cross-camera label estimation, which can be subsequently used in feature learning to learn robust re-ID models. Specifically, we propose to construct a graph for samples in each camera, and then graph matching scheme is introduced for cross-camera labeling association. While labels directly output from existing graph matching methods may be noisy and inaccurate due to significant cross-camera variations, this paper proposes a dynamic graph matching (DGM) method. DGM iteratively updates the image graph and the label estimation process by learning a better feature space with intermediate estimated labels. DGM is advantageous in two aspects: 1) the accuracy of estimated labels is improved significantly with the iterations; 2) DGM is robust to noisy initial training data. Extensive experiments conducted on three benchmarks including the large-scale MARS dataset show that DGM yields competitive performance to fully supervised baselines, and outperforms competing unsupervised learning methods.
While many multiple graph inference methodologies operate under the implicit assumption that an explicit vertex correspondence is known across the vertex sets of the graphs, in practice these correspondences may only be partially or errorfully known. Herein, we provide an information theoretic foundation for understanding the practical impact that errorfully observed vertex correspondences can have on subsequent inference, and the capacity of graph matching methods to recover the lost vertex alignment and inferential performance. Working in the correlated stochastic blockmodel setting, we establish a duality between the loss of mutual information due to an errorfully observed vertex correspondence and the ability of graph matching algorithms to recover the true correspondence across graphs. In the process, we establish a phase transition for graph matchability in terms of the correlation across graphs, and we conjecture the analogous phase transition for the relative information loss due to shuffling vertex labels. We demonstrate the practical effect that graph shuffling---and matching---can have on subsequent inference, with examples from two sample graph hypothesis testing and joint spectral graph clustering.
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives few attention. In this paper, we first formalize the problem of simultaneously cutting a graph into two partitions i.e. graph cuts and establishing their correspondence i.e. graph matching. Then we develop an optimization algorithm by updating matching and cutting alternatively, provided with theoretical analysis. The efficacy of our algorithm is verified on both synthetic dataset and real-world images containing similar regions or structures.
In this work we study convex relaxations of quadratic optimisation problems over permutation matrices. While existing semidefinite programming approaches can achieve remarkably tight relaxations, they have the strong disadvantage that they lift the original $n {\times} n$-dimensional variable to an $n^2 {\times} n^2$-dimensional variable, which limits their practical applicability. In contrast, here we present a lifting-free convex relaxation that is provably at least as tight as existing (lifting-free) convex relaxations. We demonstrate experimentally that our approach is superior to existing convex and non-convex methods for various problems, including image arrangement and multi-graph matching.
A keyframe summary, or "static storyboard", is a collection of frames from a video designed to summarise its semantic content. Many algorithms have been proposed to extract such summaries automatically. How best to evaluate these outputs is an important but little-discussed question. We review the current methods for matching frames between two summaries in the formalism of graph theory. Our analysis revealed different behaviours of these methods, which we illustrate with a number of case studies. Based on the results, we recommend a greedy matching algorithm due to Kannappan et al.
We present an efficient and scalable algorithm for segmenting 3D RGBD point clouds by combining depth, color, and temporal information using a multistage, hierarchical graph-based approach. Our algorithm processes a moving window over several point clouds to group similar regions over a graph, resulting in an initial over-segmentation. These regions are then merged to yield a dendrogram using agglomerative clustering via a minimum spanning tree algorithm. Bipartite graph matching at a given level of the hierarchical tree yields the final segmentation of the point clouds by maintaining region identities over arbitrarily long periods of time. We show that a multistage segmentation with depth then color yields better results than a linear combination of depth and color. Due to its incremental processing, our algorithm can process videos of any length and in a streaming pipeline. The algorithm's ability to produce robust, efficient segmentation is demonstrated with numerous experimental results on challenging sequences from our own as well as public RGBD data sets.
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a decomposition of the matching constraints. Graph matching is then reformulated as a non-convex non-separable optimization problem that can be split into smaller and much-easier-to-solve subproblems, by means of the alternating direction method of multipliers. The proposed framework is modular, scalable, and can be instantiated into different variants. Two instantiations are studied exploring pairwise and higher-order constraints. Experimental results on widely adopted benchmarks involving synthetic and real examples demonstrate that the proposed solutions outperform existing pairwise graph matching methods, and competitive with the state of the art in higher-order settings.
The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to {\it Drosophila} and human connectomes that this approach can achieve good performance.
We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified framework. The main contribution of this paper is twofold. First, we formulate the global correspondence search problem of multi-attributed graphs by utilizing a set of multi-layer structures. The proposed formulation describes each pair of graphs as a multi-layer structure, and jointly considers whole matching pairs. Second, we propose a robust multiple graph matching method based on the multi-layer random walks framework. The proposed framework synchronizes movements of random walkers, and leads them to consistent matching candidates. In our extensive experiments, the proposed method exhibits robust and accurate performance over the state-of-the-art multiple graph matching algorithms.
Neuronal cell bodies mostly reside in the cerebral cortex. The study of this thin and highly convoluted surface is essential for understanding how the brain works. The analysis of surface data is, however, challenging due to the high variability of the cortical geometry. This paper presents a novel approach for learning and exploiting surface data directly across surface domains. Current approaches rely on geometrical simplifications, such as spherical inflations, a popular but costly process. For instance, the widely used FreeSurfer takes about 3 hours to parcellate brain surfaces on a standard machine. Direct learning of surface data via graph convolutions would provide a new family of fast algorithms for processing brain surfaces. However, the current limitation of existing state-of-the-art approaches is their inability to compare surface data across different surface domains. Surface bases are indeed incompatible between brain geometries. This paper leverages recent advances in spectral graph matching to transfer surface data across aligned spectral domains. This novel approach enables a direct learning of surface data across compatible surface bases. It exploits spectral filters over intrinsic representations of surface neighborhoods. We illustrate the benefits of this approach with an application to brain parcellation. We validate the algorithm over 101 manually labeled brain surfaces. The results show a significant improvement in labeling accuracy over recent Euclidean approaches, while gaining a drastic speed improvement over conventional methods.
In this paper, we propose a graph correspondence transfer (GCT) approach for person re-identification. Unlike existing methods, the GCT model formulates person re-identification as an off-line graph matching and on-line correspondence transferring problem. In specific, during training, the GCT model aims to learn off-line a set of correspondence templates from positive training pairs with various pose-pair configurations via patch-wise graph matching. During testing, for each pair of test samples, we select a few training pairs with the most similar pose-pair configurations as references, and transfer the correspondences of these references to test pair for feature distance calculation. The matching score is derived by aggregating distances from different references. For each probe image, the gallery image with the highest matching score is the re-identifying result. Compared to existing algorithms, our GCT can handle spatial misalignment caused by large variations in view angles and human poses owing to the benefits of patch-wise graph matching. Extensive experiments on five benchmarks including VIPeR, Road, PRID450S, 3DPES and CUHK01 evidence the superior performance of GCT model over other state-of-the-art methods.
In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the Laplacian family signature (LFS) on the nodes, and the pairwise heat kernel map on the edges. In this paper, without assuming an explicit form of parametric dependence nor a distance metric between node signatures, we formulate an optimization problem which incorporates the knowledge of anchor nodes. Solving this problem gives us an optimized proximity measure specific to the graphs under consideration. Using this as a first order compatibility term, we then set up an integer quadratic program (IQP) to solve for a near optimal graph matching. Our experiments demonstrate the superior performance of our approach on randomly generated graphs and on two widely-used image sequences, when compared with other existing signature and adjacency matrix based graph matching methods.
In this paper, we consider the approximate weighted graph matching problem and introduce stable and informative first and second order compatibility terms suitable for inclusion into the popular integer quadratic program formulation. Our approach relies on a rigorous analysis of stability of spectral signatures based on the graph Laplacian. In the case of the first order term, we derive an objective function that measures both the stability and informativeness of a given spectral signature. By optimizing this objective, we design new spectral node signatures tuned to a specific graph to be matched. We also introduce the pairwise heat kernel distance as a stable second order compatibility term; we justify its plausibility by showing that in a certain limiting case it converges to the classical adjacency matrix-based second order compatibility function. We have tested our approach on a set of synthetic graphs, the widely-used CMU house sequence, and a set of real images. These experiments show the superior performance of our first and second order compatibility terms as compared with the commonly used ones.
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first given a partial alignment that we are tasked with completing. In this paper, we modify the state-of-the-art approximate graph matching algorithm "FAQ" of Vogelstein et al. (2015) to make it a fast approximate seeded graph matching algorithm, adapt its applicability to include graphs with differently sized vertex sets, and extend the algorithm so as to provide, for each individual vertex, a nomination list of likely matches. We demonstrate the effectiveness of our algorithm via simulation and real data experiments; indeed, knowledge of even a few seeds can be extremely effective when our seeded graph matching algorithm is used to recover a naturally existing alignment that is only partially observed.
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in correlated Erd\H{o}s-R\'enyi graphs. However, very little is known about the existence of efficient algorithms to achieve graph alignment without seeds. In this work we identify a region in which a straightforward $O(n^{11/5} \log n )$-time canonical labeling algorithm, initially introduced in the context of graph isomorphism, succeeds in aligning correlated Erd\H{o}s-R\'enyi graphs. The algorithm has two steps. In the first step, all vertices are labeled by their degrees and a trivial minimum distance alignment (i.e., sorting vertices according to their degrees) matches a fixed number of highest degree vertices in the two graphs. Having identified this subset of vertices, the remaining vertices are matched using a alignment algorithm for bipartite graphs.
We propose a texture template approach, consisting of a set of virtual minutiae, to improve the overall latent fingerprint recognition accuracy. To compensate for the lack of sufficient number of minutiae in poor quality latent prints, we generate a set of virtual minutiae. However, due to a large number of these regularly placed virtual minutiae, texture based template matching has a large computational requirement compared to matching true minutiae templates. To improve both the accuracy and efficiency of the texture template matching, we investigate: i) both original and enhanced fingerprint patches for training convolutional neural networks (ConvNets) to improve the distinctiveness of descriptors associated with each virtual minutiae, ii) smaller patches around virtual minutiae and a fast ConvNet architecture to speed up descriptor extraction, iii) reduce the descriptor length, iv) a modified hierarchical graph matching strategy to improve the matching speed, and v) extraction of multiple texture templates to boost the performance. Experiments on NIST SD27 latent database show that the above strategies can improve the matching speed from 11 ms (24 threads) per comparison (between a latent and a reference print) to only 7.7 ms (single thread) per comparison while improving the rank-1 accuracy by 8.9% against 10K gallery.
This work proposes a multi-image matching method to estimate semantic correspondences across multiple images. In contrast to the previous methods that optimize all pairwise correspondences, the proposed method identifies and matches only a sparse set of reliable features in the image collection. In this way, the proposed method is able to prune nonrepeatable features and also highly scalable to handle thousands of images. We additionally propose a low-rank constraint to ensure the geometric consistency of feature correspondences over the whole image collection. Besides the competitive performance on multi-graph matching and semantic flow benchmarks, we also demonstrate the applicability of the proposed method for reconstructing object-class models and discovering object-class landmarks from images without using any annotation.
We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a pair of $\gamma$-correlated $G(n,p)$ graphs $G_0,G_1$ with average degree between $n^{\varepsilon}$ and $n^{1/153}$ for $\varepsilon = o(1)$, recovers the "ground truth" permutation $\pi\in S_n$ that matches the vertices of $G_0$ to the vertices of $G_n$ in the way that minimizes the number of mismatched edges. We also give a recovery algorithm for a denser regime, and a polynomial-time algorithm for distinguishing between correlated and uncorrelated graphs. Prior work showed that recovery is information-theoretically possible in this model as long the average degree was at least $\log n$, but sub-exponential time algorithms were only known in the dense case (i.e., for $p > n^{-o(1)}$). Moreover, "Percolation Graph Matching", which is the most common heuristic for this problem, has been shown to require knowledge of $n^{\Omega(1)}$ "seeds" (i.e., input/output pairs of the permutation $\pi$) to succeed in this regime. In contrast our algorithms require no seed and succeed for $p$ which is as low as $n^{o(1)-1}$.