We propose a novel multi-scale template matching method which is robust against both scaling and rotation in unconstrained environments. The key component behind is a similarity measure referred to as scalable diversity similarity (SDS). Specifically, SDS exploits bidirectional diversity of the nearest neighbor (NN) matches between two sets of points. To address the scale-robustness of the similarity measure, local appearance and rank information are jointly used for the NN search. Furthermore, by introducing penalty term on the scale change, and polar radius term into the similarity measure, SDS is shown to be a well-performing similarity measure against overall size and rotation changes, as well as non-rigid geometric deformations, background clutter, and occlusions. The properties of SDS are statistically justified, and experiments on both synthetic and real-world data show that SDS can significantly outperform state-of-the-art methods.
An eye-catching family of similarity measures in recent years is to explore a global statistic property over the two point sets. Bi-directional similarity (BDS) @cite_1 proposes that two point sets are considered similar if all points of one set are contained in the other, and vice versa. Best-buddies-similarity (BBS) @cite_8 @cite_3 counts the two-side NNs as a similarity statistic. Deformable diversity similarity (DDIS) @cite_11 measures the diversity of feature matches between the two sets and is reported to outperform BBS by revealing the deformation'' of the NN field. Despite the robustness of BBS and DDIS against the transformations within the search windows, scaling and rotation on the whole search windows have not been considered. In this paper, we propose a scaling and rotation independent similarity measure which leads to a significant improvement and allows multi-scale template matching in unconstrained environments.
@cite_11 @cite_1 @cite_3 @cite_8
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We propose a novel method for template matching in unconstrained environments. Its essence is the Best-Buddies Similarity (BBS), a useful, robust, and parameter-free similarity measure between two sets of points. BBS is based on counting the number of Best-Buddies Pairs (BBPs)—pairs of points in source and target sets, where each point is the nearest neighbor of the other. BBS has several key features that make it robust against complex geometric deformations and high levels of outliers, such as those arising from background clutter and occlusions. We study these properties, provide a statistical analysis that justifies them, and demonstrate the consistent success of BBS on a challenging real-world dataset. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). We consider the non-metric multidimensional scaling problem: given a set of dissimilarities ∆, find an embedding whose inter-point Euclidean distances have the same ordering as ∆. In this paper, we look at a generalization of this problem in which only a set of order relations of the form dij < dkl are provided. Unlike the original problem, these order relations can be contradictory and need not be specified for all pairs of dissimilarities. We argue that this setting is more natural in some experimental settings and propose an algorithm based on convex optimization techniques to solve this problem. We apply this algorithm to human subject data from a psychophysics experiment concerning how reflectance properties are perceived. We also look at the standard NMDS problem, where a dissimilarity matrix ∆ is provided as input, and show that we can always find an orderrespecting embedding of ∆. Abstract When dealing with the registration of information from different image sources, the de facto similarity measure used is Mutual Information (MI). Although MI gives good performance in many image registration applications, recent works in thermal–visible registration have shown that other similarity measures can give results that are as accurate, if not more than MI. Furthermore, some of these measures also have the advantage of being calculated independently from each image to register, which allows them to be integrated more easily in energy minimization frameworks. In this article, we investigate the accuracy of similarity measures for thermal–visible image registration of human silhouettes, including MI, Sum of Squared Differences (SSD), Normalized Cross-Correlation (NCC), Histograms of Oriented Gradients (HOG), Local Self-Similarity (LSS), Scale-Invariant Feature Transform (SIFT), Speeded-Up Robust Features (SURF), Census, Fast Retina Keypoint (FREAK), and Binary Robust Independent Elementary Feature (BRIEF). We tested the various similarity measures in dense stereo matching tasks over 25,000 windows to have statistically significant results. To do so, we created a new dataset in which one to five humans are walking in a scene in various depth planes. Results show that even if MI is a very strong performer, particularly for large regions of interest (ROI), LSS gives better accuracies when ROI are small or segmented into small fragments because of its ability to capture shape. The other tested similarity measures did not give consistently accurate results. Techniques for multidimensional scaling visualize objects as points in a low-dimensional metric map. As a result, the visualizations are subject to the fundamental limitations of metric spaces. These limitations prevent multidimensional scaling from faithfully representing non-metric similarity data such as word associations or event co-occurrences. In particular, multidimensional scaling cannot faithfully represent intransitive pairwise similarities in a visualization, and it cannot faithfully visualize "central" objects. In this paper, we present an extension of a recently proposed multidimensional scaling technique called t-SNE. The extension aims to address the problems of traditional multidimensional scaling techniques when these techniques are used to visualize non-metric similarities. The new technique, called multiple maps t-SNE, alleviates these problems by constructing a collection of maps that reveal complementary structure in the similarity data. We apply multiple maps t-SNE to a large data set of word association data and to a data set of NIPS co-authorships, demonstrating its ability to successfully visualize non-metric similarities. Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper. Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data are popular to analyze complicated data objects and to cover domain specific data properties. Without an underlying vector space these data are given as pairwise (dis-)similarities only. The few available methods for such data focus widely on similarities and do not scale to large datasets. Kernel methods are very effective for metric similarity matrices, also at large scale, but costly transformations are necessary starting with non-metric (dis-) similarities. We propose an integrative combination of Nystrom approximation, potential double centering and eigenvalue correction to obtain valid kernel matrices at linear costs in the number of samples. By the proposed approach effective kernel approaches become accessible. Experiments with several larger (dis-)similarity datasets show that the proposed method achieves much better runtime performance than the standard strategy while keeping competitive model accuracy. The main contribution is an efficient and accurate technique, to convert (potentially non-metric) large scale dissimilarity matrices into approximated positive semi-definite kernel matrices at linear costs. HighlightsWe propose a linear time and memory efficient approach for converting low rank dissimilarity matrices to similarity matrices and vice versa.Our approach is applicable for proximities obtained from non-metric proximity measures (indefinite kernels, non-standard dissimilarity measures).The presented approach also comprises a generalization of Landmark MDS - the presented approach is in general more accurate and flexible than Landmark MDS.We provide an alternative derivation of the Nystrom approximation together with a convergence proof, also for indefinite kernels not given in the workshop paper as a core element of the approach. Existing billion-scale nearest neighbor search systems have mostly been compared on a single dataset of a billion of SIFT vectors, where systems based on the Inverted Multi-Index (IMI) have been performing very well, achieving state-of-the-art recall in several milliseconds. SIFT-like descriptors, however, are quickly being replaced with descriptors based on deep neural networks (DNN) that provide better performance for many computer vision tasks. In this paper, we introduce a new dataset of one billion descriptors based on DNNs and reveal the relative inefficiency of IMI-based indexing for such descriptors compared to SIFT data. We then introduce two new indexing structures, the Non-Orthogonal Inverted Multi-Index (NO-IMI) and the Generalized Non-Orthogonal Inverted Multi-Index (GNO-IMI). We show that due to additional flexibility, the new structures are able to adapt to DNN descriptor distribution in a better way. In particular, extensive experiments on the new dataset demonstrate that these data structures provide considerably better trade-off between the speed of retrieval and recall, given similar amount of memory, as compared to the standard Inverted Multi-Index. We propose a novel measure for template matching named Deformable Diversity Similarity &#x2013; based on the diversity of feature matches between a target image window and the template. We rely on both local appearance and geometric information that jointly lead to a powerful approach for matching. Our key contribution is a similarity measure, that is robust to complex deformations, significant background clutter, and occlusions. Empirical evaluation on the most up-to-date benchmark shows that our method outperforms the current state-of-the-art in its detection accuracy while improving computational complexity. For similarity search in high-dimensional vector spaces (or ‘HDVSs’), researchers have proposed a number of new methods (or adaptations of existing methods) based, in the main, on data-space partitioning. However, the performance of these methods generally degrades as dimensionality increases. Although this phenomenon-known as the ‘dimensional curse’-is well known, little or no quantitative a.nalysis of the phenomenon is available. In this paper, we provide a detailed analysis of partitioning and clustering techniques for similarity search in HDVSs. We show formally that these methods exhibit linear complexity at high dimensionality, and that existing methods are outperformed on average by a simple sequential scan if the number of dimensions exceeds around 10. Consequently, we come up with an alternative organization based on approximations to make the unavoidable sequential scan as fast as possible. We describe a simple vector approximation scheme, called VA-file, and report on an experimental evaluation of this and of two tree-based index methods (an R*-tree and an X-tree). Comparing two sets of multivariate samples is a central problem in data analysis. From a statistical standpoint, the simplest way to perform such a comparison is to resort to a non-parametric two-sample test (TST), which checks whether the two sets can be seen as i.i.d. samples of an identical unknown distribution (the null hypothesis). If the null is rejected, one wishes to identify regions accounting for this difference. This paper presents a two-stage method providing feedback on this difference, based upon a combination of statistical learning (regression) and computational topology methods. Consider two populations, each given as a point cloud in Rd. In the first step, we assign a label to each set and we compute, for each sample point, a discrepancy measure based on comparing an estimate of the conditional probability distribution of the label given a position versus the global unconditional label distribution. In the second step, we study the height function defined at each point by the aforementioned estimated discrepancy. Topological persistence is used to identify persistent local minima of this height function, their basins defining regions of points with high discrepancy and in spatial proximity. Experiments are reported both on synthetic and real data (satellite images and handwritten digit images), ranging in dimension from d = 2 to d = 784, illustrating the ability of our method to localize discrepancies. On a general perspective, the ability to provide feedback downstream TST may prove of ubiquitous interest in exploratory statistics and data science. We introduce a new probabilistic proximity search algorithm for range and A"-nearest neighbor (A"-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a linear scan when the space is intrinsically high dimensional, as is the case in many pattern recognition tasks. This, for example, renders the A"-NN approach to classification rather slow in large databases. Our novel idea is to predict closeness between elements according to how they order their distances toward a distinguished set of anchor objects. Each element in the space sorts the anchor objects from closest to farthest to it and the similarity between orders turns out to be an excellent predictor of the closeness between the corresponding elements. We present extensive experiments comparing our method against state-of-the-art exact and approximate techniques, both in synthetic and real, metric and nonmetric databases, measuring both CPU time and distance computations. The experiments demonstrate that our technique almost always improves upon the performance of alternative techniques, in some cases by a wide margin. An alternative form to multidimensional projections for the visual analysis of data represented in multidimensional spaces is the deployment of similarity trees, such as Neighbor Joining trees. They organize data objects on the visual plane emphasizing their levels of similarity with high capability of detecting and separating groups and subgroups of objects. Besides this similarity-based hierarchical data organization, some of their advantages include the ability to decrease point clutter; high precision; and a consistent view of the data set during focusing, offering a very intuitive way to view the general structure of the data set as well as to drill down to groups and subgroups of interest. Disadvantages of similarity trees based on neighbor joining strategies include their computational cost and the presence of virtual nodes that utilize too much of the visual space. This paper presents a highly improved version of the similarity tree technique. The improvements in the technique are given by two procedures. The first is a strategy that replaces virtual nodes by promoting real leaf nodes to their place, saving large portions of space in the display and maintaining the expressiveness and precision of the technique. The second improvement is an implementation that significantly accelerates the algorithm, impacting its use for larger data sets. We also illustrate the applicability of the technique in visual data mining, showing its advantages to support visual classification of data sets, with special attention to the case of image classification. We demonstrate the capabilities of the tree for analysis and iterative manipulation and employ those capabilities to support evolving to a satisfactory data organization and classification. Local learning of sparse image models has proved to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we consider the underlying geometry of the data. The first algorithm, called adaptive geometry-driven nearest neighbor search (AGNN), is an adaptive scheme, which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called geometry-driven overlapping clusters (GOCs), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image superresolution and shown to outperform spectral clustering, soft clustering, and geodesic distance-based subset selection in most settings. We consider the problem of approximate set similarity search under Braun-Blanquet similarity B(x, y) = |x ∩ y| max(|x|, |y|). The (b1, b2)-approximate Braun-Blanquet similarity search problem is to preprocess a collection of sets P such that, given a query set q, if there exists x E P with B(q, x) ≥ b1, then we can efficiently return x′ E P with B(q, x′) > b2. We present a simple data structure that solves this problem with space usage O(n1+ρlogn + ∑x e P|x|) and query time O(|q|nρ logn) where n = |P| and ρ = log(1 b1) log(1 b2). Making use of existing lower bounds for locality-sensitive hashing by O' (TOCT 2014) we show that this value of ρ is tight across the parameter space, i.e., for every choice of constants 0 In the case where all sets have the same size our solution strictly improves upon the value of ρ that can be obtained through the use of state-of-the-art data-independent techniques in the Indyk-Motwani locality-sensitive hashing framework (STOC 1998) such as Broder's MinHash (CCS 1997) for Jaccard similarity and 's cross-polytope LSH (NIPS 2015) for cosine similarity. Surprisingly, even though our solution is data-independent, for a large part of the parameter space we outperform the currently best data-dependent method by Andoni and Razenshteyn (STOC 2015). One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment. Explicitly solving for the optimal alignment is usually impractical. So, two general methods have been proposed for addressing this issue: (1) Every model is represented using rotation invariant descriptors. (2) Every model is described by a rotation dependent descriptor that is aligned into a canonical coordinate system defined by the model. In this paper, we describe the limitations of canonical alignment and discuss an alternate method, based on spherical harmonics, for obtaining rotation invariant representations. We describe the properties of this tool and show how it can be applied to a number of existing, orientation dependent descriptors to improve their matching performance. The advantages of this tool are two-fold: First, it improves the matching performance of many descriptors. Second, it reduces the dimensionality of the descriptor, providing a more compact representation, which in turn makes comparing two models more efficient. In this paper, we present a new framework for geo-locating an image utilizing a novel multiple nearest neighbor feature matching method using Generalized Minimum Clique Graphs (GMCP). First, we extract local features (e.g., SIFT) from the query image and retrieve a number of nearest neighbors for each query feature from the reference data set. Next, we apply our GMCP-based feature matching to select a single nearest neighbor for each query feature such that all matches are globally consistent. Our approach to feature matching is based on the proposition that the first nearest neighbors are not necessarily the best choices for finding correspondences in image matching. Therefore, the proposed method considers multiple reference nearest neighbors as potential matches and selects the correct ones by enforcing consistency among their global features (e.g., GIST) using GMCP. In this context, we argue that using a robust distance function for finding the similarity between the global features is essential for the cases where the query matches multiple reference images with dissimilar global features. Towards this end, we propose a robust distance function based on the Gaussian Radial Basis Function (G-RBF). We evaluated the proposed framework on a new data set of 102k street view images; the experiments show it outperforms the state of the art by 10 percent. This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground truth measure). Moreover, we obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the consistency to hold. We provide results for two-way and for multiway cuts. Furthermore we provide numerical experiments that illustrate the results and explore the optimality of scaling in dimension two. Many real-world objects described by multiple attributes or features can be decomposed as multiple "views" (e.g., an image can be described by a color view or a shape view), which often provides complementary information to each other. Learning a metric (similarity measures) for multi-view data is primary due to its wide applications in practices. However, leveraging multi-view information to produce a good metric is a great challenge and existing techniques are concerned with pairwise similarities, leading to undesirable fusion metric and high computational complexity. In this paper, we propose a novel Metric Fusion technique via cross-view graph Random Walk, named MFRW, regarding a multi-view based similarity graphs (with each similarity graph constructed under each view). Instead of using pairwise similarities, we seek a high-order metric yielded by graph random walks over constructed similarity graphs. Observing that outlier views" may exist in the fusion process, we incorporate the coefficient matrices representing the correlation strength between any two views into MFRW, named WMFRW. The principle of WMFRW is implemented by exploring the common latent structure" between views. The empirical studies conducted on real-world databases demonstrate that our approach outperforms the state-of-the-art competitors in terms of effectiveness and efficiency. We present a descriptor, called fully convolutional self-similarity (FCSS), for dense semantic correspondence. Unlike traditional dense correspondence approaches for estimating depth or optical flow, semantic correspondence estimation poses additional challenges due to intra-class appearance and shape variations among different instances within the same object or scene category. To robustly match points across semantically similar images, we formulate FCSS using local self-similarity (LSS), which is inherently insensitive to intra-class appearance variations. LSS is incorporated through a proposed convolutional self-similarity (CSS) layer, where the sampling patterns and the self-similarity measure are jointly learned in an end-to-end and multi-scale manner. Furthermore, to address shape variations among different object instances, we propose a convolutional affine transformer (CAT) layer that estimates explicit affine transformation fields at each pixel to transform the sampling patterns and corresponding receptive fields. As training data for semantic correspondence is rather limited, we propose to leverage object candidate priors provided in most existing datasets and also correspondence consistency between object pairs to enable weakly-supervised learning. Experiments demonstrate that FCSS significantly outperforms conventional handcrafted descriptors and CNN-based descriptors on various benchmarks.