Feature-based object matching is a fundamental problem for many applications in computer vision, such as object recognition, 3D reconstruction, tracking, and motion segmentation. In this work, we consider simultaneously matching object instances in a set of images, where both inlier and outlier features are extracted. The task is to identify the inlier features and establish their consistent correspondences across the image set. This is a challenging combinatorial problem, and the problem complexity grows exponentially with the image number. To this end, we propose a novel framework, termed ROML, to address this problem. ROML optimizes simultaneously a partial permutation matrix (PPM) for each image, and feature correspondences are established by the obtained PPMs. Two of our key contributions are summarized as follows. (1) We formulate the problem as rank and sparsity minimization for PPM optimization, and treat simultaneous optimization of multiple PPMs as a regularized consensus problem in the context of distributed optimization. (2) We use the ADMM method to solve the thus formulated ROML problem, in which a subproblem associated with a single PPM optimization appears to be a difficult integer quadratic program (IQP). We prove that under wildly applicable conditions, this IQP is equivalent to a linear sum assignment problem (LSAP), which can be efficiently solved to an exact solution. Extensive experiments on rigid non-rigid object matching, matching instances of a common object category, and common object localization show the efficacy of our proposed method.
Recently, a low-dimensional embedding method was proposed in @cite_15 for feature matching. Given feature points extracted from each of a set of images, it can learn an embedded feature space, which encodes information of both region descriptors and the geometric structure of points in each image. @cite_15 used k-means clustering in the embedded space for feature matching. As we will show in Section , k-means based on Euclidean distances of embedded features is not a good way to establish correspondences. There is no explicit outlier rejection mechanism in @cite_15 either. Compared to @cite_15 , our method uses the low-rank and sparse constraints to optimize PPMs, which integrates correspondence and outlier rejection in a single step.
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Object recognition can be formulated as matching image features to model features. When recognition is exemplar-based, feature correspondence is one-to-one. However, segmentation errors, articulation, scale difference, and within-class deformation can yield image and model features which don't match one-to-one but rather many-to-many. Adopting a graph-based representation of a set of features, we present a matching algorithm that establishes many-to-many correspondences between the nodes of two noisy, vertex-labeled weighted graphs. Our approach reduces the problem of many-to-many matching of weighted graphs to that of many-to-many matching of weighted point sets in a normed vector space. This is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure. Many-to-many vector correspondences established by the Earth Mover's Distance framework are mapped back into many-to-many correspondences between graph nodes. Empirical evaluation of the algorithm on an extensive set of recognition trials, including a comparison with two competing graph matching approaches, demonstrates both the robustness and efficacy of the overall approach. Despite significant recent advances in the field of face recognition [10, 14, 15, 17], implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity. Once this space has been produced, tasks such as face recognition, verification and clustering can be easily implemented using standard techniques with FaceNet embeddings as feature vectors. The literature currently provides two ways to establish point correspondences between images with moving objects. On one side, there are energy minimization methods that yield very accurate, dense flow fields, but fail as displacements get too large. On the other side, there is descriptor matching that allows for large displacements, but correspondences are very sparse, have limited accuracy, and due to missing regularity constraints there are many outliers. In this paper we propose a method that can combine the advantages of both matching strategies. A region hierarchy is established for both images. Descriptor matching on these regions provides a sparse set of hypotheses for correspondences. These are integrated into a variational approach and guide the local optimization to large displacement solutions. The variational optimization selects among the hypotheses and provides dense and subpixel accurate estimates, making use of geometric constraints and all available image information. A novel multi-criteria optimization framework for matching of partially visible shapes in multiple images using joint geometric graph embedding is proposed. The proposed framework achieves matching of partial shapes in images that exhibit extreme variations in scale, orientation, viewpoint and illumination and also instances of occlusion; conditions which render impractical the use of global contour-based descriptors or local pixel-level features for shape matching. The proposed technique is based on optimization of the embedding distances of geometric features obtained from the eigenspectrum of the joint image graph, coupled with regularization over values of the mean pixel intensity or histogram of oriented gradients. It is shown to obtain successfully the correspondences denoting partial shape similarities as well as correspondences between feature points in the images. A new benchmark dataset is proposed which contains disparate image pairs with extremely challenging variations in viewing conditions when compared to an existing dataset [18]. The proposed technique is shown to significantly outperform several state-of-the-art partial shape matching techniques on both datasets. Embedding algorithms search for a low dimensional continuous representation of data, but most algorithms only handle objects of a single type for which pairwise distances are specified. This paper describes a method for embedding objects of different types, such as images and text, into a single common Euclidean space, based on their co-occurrence statistics. The joint distributions are modeled as exponentials of Euclidean distances in the low-dimensional embedding space, which links the problem to convex optimization over positive semidefinite matrices. The local structure of the embedding corresponds to the statistical correlations via random walks in the Euclidean space. We quantify the performance of our method on two text data sets, and show that it consistently and significantly outperforms standard methods of statistical correspondence modeling, such as multidimensional scaling, IsoMap and correspondence analysis. We introduce a new transformation estimation algorithm using the @math estimator and apply it to non-rigid registration for building robust sparse and dense correspondences. In the sparse point case, our method iteratively recovers the point correspondence and estimates the transformation between two point sets. Feature descriptors such as shape context are used to establish rough correspondence. We then estimate the transformation using our robust algorithm. This enables us to deal with the noise and outliers which arise in the correspondence step. The transformation is specified in a functional space, more specifically a reproducing kernel Hilbert space. In the dense point case for nonrigid image registration, our approach consists of matching both sparsely and densely sampled SIFT features, and it has particular advantages in handling significant scale changes and rotations. The experimental results show that our approach greatly outperforms state-of-the-art methods, particularly when the data contains severe outliers. Given the size and confidence of pairwise local orderings, angular embedding (AE) finds a global ordering with a near-global optimal eigensolution. As a quadratic criterion in the complex domain, AE is remarkably robust to outliers, unlike its real domain counterpart LS, the least squares embedding. Our comparative study of LS and AE reveals that AE's robustness is due not to the particular choice of the criterion, but to the choice of representation in the complex domain. When the embedding is encoded in the angular space, we not only have a nonconvex error function that delivers robustness, but also have a Hermitian graph Laplacian that completely determines the optimum and delivers efficiency. The high quality of embedding by AE in the presence of outliers can hardly be matched by LS, its corresponding L1 norm formulation, or their bounded versions. These results suggest that the key to overcoming outliers lies not with additionally imposing constraints on the embedding solution, but with adaptively penalizing inconsistency between measurements themselves. AE thus significantly advances statistical ranking methods by removing the impact of outliers directly without explicit inconsistency characterization, and advances spectral clustering methods by covering the entire size-confidence measurement space and providing an ordered cluster organization. We present a method to automatically learn object categories from unlabeled images. Each image is represented by an unordered set of local features, and all sets are embedded into a space where they cluster according to their partial-match feature correspondences. After efficiently computing the pairwise affinities between the input images in this space, a spectral clustering technique is used to recover the primary groupings among the images. We introduce an efficient means of refining these groupings according to intra-cluster statistics over the subsets of features selected by the partial matches between the images, and based on an optional, variable amount of user supervision. We compute the consistent subsets of feature correspondences within a grouping to infer category feature masks. The output of the algorithm is a partition of the data into a set of learned categories, and a set of classifiers trained from these ranked partitions that can recognize the categories in novel images. We propose a real-time, robust to outliers and accurate solution to the Perspective-n-Point (PnP) problem. The main advantages of our solution are twofold: first, it in- tegrates the outlier rejection within the pose estimation pipeline with a negligible computational overhead, and sec- ond, its scalability to arbitrarily large number of correspon- dences. Given a set of 3D-to-2D matches, we formulate pose estimation problem as a low-rank homogeneous sys- tem where the solution lies on its 1D null space. Outlier correspondences are those rows of the linear system which perturb the null space and are progressively detected by projecting them on an iteratively estimated solution of the null space. Since our outlier removal process is based on an algebraic criterion which does not require computing the full-pose and reprojecting back all 3D points on the image plane at each step, we achieve speed gains of more than 100× compared to RANSAC strategies. An extensive exper- imental evaluation will show that our solution yields accu- rate results in situations with up to 50 of outliers, and can process more than 1000 correspondences in less than 5ms. We propose a new methodology for reliably solving the correspondence problem between sparse sets of points of two or more images. This is a key step inmost problems of computer vision and, so far, no general method exists to solve it. Our methodology is able to handle most of the commonly used assumptions in a unique formulation, independent of the domain of application and type of features. It performs correspondence and outlier rejection in a single step and achieves global optimality with feasible computation. Feature selection and correspondence are first formulated as an integer optimization problem. This is a blunt formulation, which considers the whole combinatorial space of possible point selections and correspondences. To find its global optimal solution, we build a concave objective function and relax the search domain into its convex-hull. The special structure of this extended problem assures its equivalence to the original one, but it can be optimally solved by efficient algorithms that avoid combinatorial search. This methodology can use any criterion provided it can be translated into cost functions with continuous second derivatives. In computer vision and multimedia search, it is common to use multiple features from different views to represent an object. For example, to well characterize a natural scene image, it is essential to find a set of visual features to represent its color, texture, and shape information and encode each feature into a vector. Therefore, we have a set of vectors in different spaces to represent the image. Conventional spectral-embedding algorithms cannot deal with such datum directly, so we have to concatenate these vectors together as a new vector. This concatenation is not physically meaningful because each feature has a specific statistical property. Therefore, we develop a new spectral-embedding algorithm, namely, multiview spectral embedding (MSE), which can encode different features in different ways, to achieve a physically meaningful embedding. In particular, MSE finds a low-dimensional embedding wherein the distribution of each view is sufficiently smooth, and MSE explores the complementary property of different views. Because there is no closed-form solution for MSE, we derive an alternating optimization-based iterative algorithm to obtain the low-dimensional embedding. Empirical evaluations based on the applications of image retrieval, video annotation, and document clustering demonstrate the effectiveness of the proposed approach. Local features have been widely used in computer vision tasks, e.g., human action recognition, but it tends to be an extremely challenging task to deal with large-scale local features of high dimensionality with redundant information. In this paper, we propose a novel fully supervised local descriptor learning algorithm called discriminative embedding method based on the image-to-class distance (I2CDDE) to learn compact but highly discriminative local feature descriptors for more accurate and efficient action recognition. By leveraging the advantages of the I2C distance, the proposed I2CDDE incorporates class labels to enable fully supervised learning of local feature descriptors, which achieves highly discriminative but compact local descriptors. The objective of our I2CDDE is to minimize the I2C distances from samples to their corresponding classes while maximizing the I2C distances to the other classes in the low-dimensional space. To further improve the performance, we propose incorporating a manifold regularization based on the graph Laplacian into the objective function, which can enhance the smoothness of the embedding by extracting the local intrinsic geometrical structure. The proposed I2CDDE for the first time achieves fully supervised learning of local feature descriptors. It significantly improves the performance of I2C-based methods by increasing the discriminative ability of local features while greatly reducing the computational burden by dimensionality reduction to handle large-scale data. We apply the proposed I2CDDE algorithm to human action recognition on four widely used benchmark datasets. The results have shown that I2CDDE can significantly improve I2C-based classifiers and achieves state-of-the-art performance. This paper focuses on structured-output learning using deep neural networks for 3D human pose estimation from monocular images. Our network takes an image and 3D pose as inputs and outputs a score value, which is high when the image-pose pair matches and low otherwise. The network structure consists of a convolutional neural network for image feature extraction, followed by two sub-networks for transforming the image features and pose into a joint embedding. The score function is then the dot-product between the image and pose embeddings. The image-pose embedding and score function are jointly trained using a maximum-margin cost function. Our proposed framework can be interpreted as a special form of structured support vector machines where the joint feature space is discriminatively learned using deep neural networks. We test our framework on the Human3.6m dataset and obtain state-of-the-art results compared to other recent methods. Finally, we present visualizations of the image-pose embedding space, demonstrating the network has learned a high-level embedding of body-orientation and pose-configuration. In this paper, we propose a novel method for solving single-image super-resolution problems. Given a low-resolution image as input, we recover its high-resolution counterpart using a set of training examples. While this formulation resembles other learning-based methods for super-resolution, our method has been inspired by recent manifold teaming methods, particularly locally linear embedding (LLE). Specifically, small image patches in the lowand high-resolution images form manifolds with similar local geometry in two distinct feature spaces. As in LLE, local geometry is characterized by how a feature vector corresponding to a patch can be reconstructed by its neighbors in the feature space. Besides using the training image pairs to estimate the high-resolution embedding, we also enforce local compatibility and smoothness constraints between patches in the target high-resolution image through overlapping. Experiments show that our method is very flexible and gives good empirical results. A new architecture, denoted spatial pyramid matching on the semantic manifold (SPMSM), is proposed for scene recognition. SPMSM is based on a recent image representation on a semantic probability simplex, which is now augmented with a rough encoding of spatial information. A connection between the semantic simplex and a Riemmanian manifold is established, so as to equip the architecture with a similarity measure that respects the manifold structure of the semantic space. It is then argued that the closed-form geodesic distance between two manifold points is a natural measure of similarity between images. This leads to a conditionally positive definite kernel that can be used with any SVM classifier. An approximation of the geodesic distance reveals connections to the well-known Bhattacharyya kernel, and is explored to derive an explicit feature embedding for this kernel, by simple square-rooting. This enables a low-complexity SVM implementation, using a linear SVM on the embedded features. Several experiments are reported, comparing SPMSM to state-of-the-art recognition methods. SPMSM is shown to achieve the best recognition rates in the literature for two large datasets (MIT Indoor and SUN) and rates equivalent or superior to the state-of-the-art on a number of smaller datasets. In all cases, the resulting SVM also has much smaller dimensionality and requires much fewer support vectors than previous classifiers. This guarantees much smaller complexity and suggests improved generalization beyond the datasets considered. We propose a novel framework to build descriptors of local intensity that are invariant to general deformations. In this framework, an image is embedded as a 2D surface in 3D space, with intensity weighted relative to distance in x-y. We show that as this weight increases, geodesic distances on the embedded surface are less affected by image deformations. In the limit, distances are deformation invariant. We use geodesic sampling to get neighborhood samples for interest points, and then use a geodesic-intensity histogram (GIH) as a deformation invariant local descriptor. In addition to its invariance, the new descriptor automatically finds its support region. This means it can safely gather information from a large neighborhood to improve discriminability. Furthermore, we propose a matching method for this descriptor that is invariant to affine lighting changes. We have tested this new descriptor on interest point matching for two data sets, one with synthetic deformation and lighting change, and another with real non-affine deformations. Our method shows promising matching results compared to several other approaches This paper focuses on structured-output learning using deep neural networks for 3D human pose estimation from monocular images. Our network takes an image and 3D pose as inputs and outputs a score value, which is high when the image-pose pair matches and low otherwise. The network structure consists of a convolutional neural network for image feature extraction, followed by two sub-networks for transforming the image features and pose into a joint embedding. The score function is then the dot-product between the image and pose embeddings. The image-pose embedding and score function are jointly trained using a maximum-margin cost function. Our proposed framework can be interpreted as a special form of structured support vector machines where the joint feature space is discriminatively learned using deep neural networks. We also propose an efficient recurrent neural network for performing inference with the learned image-embedding. We test our framework on the Human3.6m dataset and obtain state-of-the-art results compared to other recent methods. Finally, we present visualizations of the image-pose embedding space, demonstrating the network has learned a high-level embedding of body-orientation and pose-configuration. This paper improves recent methods for large scale image search. State-of-the-art methods build on the bag-of-features image representation. We, first, analyze bag-of-features in the framework of approximate nearest neighbor search. This shows the sub-optimality of such a representation for matching descriptors and leads us to derive a more precise representation based on 1) Hamming embedding (HE) and 2) weak geometric consistency constraints (WGC). HE provides binary signatures that refine the matching based on visual words. WGC filters matching descriptors that are not consistent in terms of angle and scale. HE and WGC are integrated within the inverted file and are efficiently exploited for all images, even in the case of very large datasets. Experiments performed on a dataset of one million of images show a significant improvement due to the binary signature and the weak geometric consistency constraints, as well as their efficiency. Estimation of the full geometric transformation, i.e., a re-ranking step on a short list of images, is complementary to our weak geometric consistency constraints and allows to further improve the accuracy. This paper proposes an efficient mixture model for establishing robust point correspondences between two sets of points under multi-layer motion. Our algorithm starts by creating a set of putative correspondences which can contain a number of false correspondences, or outliers, in addition to the true correspondences (inliers). Next we solve for correspondence by interpolating a set of spatial transformations on the putative correspondence set based on a mixture model, which involves estimating a consensus of inlier points whose matching follows a non-parametric geometrical constraint. We formulate this as a maximum a posteriori (MAP) estimation of a Bayesian model with hidden latent variables indicating whether matches in the putative set are outliers or inliers. We impose non-parametric geometrical constraints on the correspondence, as a prior distribution, in a reproducing kernel Hilbert space (RKHS). MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We further provide a fast implementation based on sparse approximation which can achieve a significant speed-up without much performance degradation. We illustrate the proposed method on 2D and 3D real images for sparse feature correspondence, as well as a public available dataset for shape matching. The quantitative results demonstrate that our method is robust to non-rigid deformation and multi-layer large discontinuous motion. To reliably determine the camera pose of an image relative to a 3D point cloud of a scene, correspondences between 2D features and 3D points are needed. Recent work has demonstrated that directly matching the features against the points outperforms methods that take an intermediate image retrieval step in terms of the number of images that can be localized successfully. Yet, direct matching is inherently less scalable than retrievalbased approaches. In this paper, we therefore analyze the algorithmic factors that cause the performance gap and identify false positive votes as the main source of the gap. Based on a detailed experimental evaluation, we show that retrieval methods using a selective voting scheme are able to outperform state-of-the-art direct matching methods. We explore how both selective voting and correspondence computation can be accelerated by using a Hamming embedding of feature descriptors. Furthermore, we introduce a new dataset with challenging query images for the evaluation of image-based localization.