The problem of identifying the 3D pose of a known object from a given 2D image has important applications in Computer Vision. Our proposed method of registering a 3D model of a known object on a given 2D photo of the object has numerous advantages over existing methods. It does not require prior training, knowledge of the camera parameters, explicit point correspondences or matching features between the image and model. Unlike techniques that estimate a partial 3D pose (as in an overhead view of traffic or machine parts on a conveyor belt), our method estimates the complete 3D pose of the object. It works on a single static image from a given view under varying and unknown lighting conditions. For this purpose we derive a novel illumination-invariant distance measure between the 2D photo and projected 3D model, which is then minimised to find the best pose parameters. Results for vehicle pose detection in real photographs are presented.
Distance metrics can be used to represent a distance between two data sets, and hence give a measure of their similarity. Therefore, distance metrics can be used to measure similarity between different 2D images, as well as 2D images and 2D projections of a 3D model. A basic distance metric would be the or the 2-norm @math . However, this has the disadvantage of being dependent on the scale of measurement. We use the @cite_29 for our work, which is a scale-invariant distance measure. It is used by @cite_15 for clustering. It is also used by Deriche and Faugeras @cite_25 to match line segments in a sequence of time varying images.
@cite_29 @cite_25 @cite_15
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In this paper, we introduce a set of novel distance metrics that use model based representations for trajectories. We determine the similarity of trajectories using the conformity of the corresponding HMM models. These metrics enable the comparison of tracjectories without any limitations of the conventional measures. They accurately identify the coordinate, orientation, and speed affinity. The proposed HMM based distance metrics can be used not only for ground truth comparisons but for clustering as well. Our experiments prove that they have superior discriminative properties. We wish to match sets of images to sets of images where both sets are undergoing various distortions such as viewpoint and lighting changes. To this end we have developed a joint manifold distance (JMD) which measures the distance between two subspaces, where each subspace is invariant to a desired group of transformations, for example affine warping of the image plane. The JMD may be seen as generalizing invariant distance metrics such as tangent distance in two important ways. First, formally representing priors on the image distribution avoids certain difficulties, which in previous work have required ad-hoc correction. The second contribution is the observation that previous distances have been computed using what amounted to "home-grown" nonlinear optimizers, and that more reliable results can be obtained by using generic optimizers which have been developed in the numerical analysis community, and which automatically set the parameters which home-grown methods must set by art. The JMD is used in this work to cluster faces in video. Sets of faces detected in contiguous frames define the subspaces, and distance between the subspaces is computed using JMD. In this way the principal cast of a movie can be 'discovered' as the principal clusters. We demonstrate the method on a feature-length movie. A good distance metric is crucial for unsupervised learning from high-dimensional data. To learn a metric without any constraint or class label information, most unsupervised metric learning algorithms appeal to projecting observed data onto a low-dimensional manifold, where geometric relationships such as local or global pairwise distances are preserved. However, the projection may not necessarily improve the separability of the data, which is the desirable outcome of clustering. In this paper, we propose a novel unsupervised adaptive metric learning algorithm, called AML, which performs clustering and distance metric learning simultaneously. AML projects the data onto a low-dimensional manifold, where the separability of the data is maximized. We show that the joint clustering and distance metric learning can be formulated as a trace maximization problem, which can be solved via an iterative procedure in the EM framework. Experimental results on a collection of benchmark data sets demonstrated the effectiveness of the proposed algorithm. We showed in this work how the Hassanat distance metric enhances the performance of the nearest neighb our classifiers. The results demonstrate the superiority of this distanc e metric over the traditional and most-used distanc es, such as Manhattan distance and Euclidian distance. Moreover, we prove d that the Hassanat distance metric is invariant to data scale, noise and outliers. Throughout this work, it is clearly notab le that both ENN and IINC performed very well with the distance investigated, as their accuracy increased significantly by 3.3 a nd 3.1 respectively, with no significant advantage of the ENN over the IINC in terms of accuracy. Correspondingly, it can be no ted from our results that there is no optimal algor ithm that can solve all reallife problems perfectly; this is supported by the n o-free-lunch theorem. Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been difficult for these to compete with modern classification algorithms in performance and even in feature extraction. In this work, we propose a novel approach explicitly designed to address a number of subtle yet important issues which have stymied earlier DML algorithms. It maintains an explicit model of the distributions of the different classes in representation space. It then employs this knowledge to adaptively assess similarity, and achieve local discrimination by penalizing class distribution overlap. We demonstrate the effectiveness of this idea on several tasks. Our approach achieves state-of-the-art classification results on a number of fine-grained visual recognition datasets, surpassing the standard softmax classifier and outperforming triplet loss by a relative margin of 30-40 . In terms of computational performance, it alleviates training inefficiencies in the traditional triplet loss, reaching the same error in 5-30 times fewer iterations. Beyond classification, we further validate the saliency of the learnt representations via their attribute concentration and hierarchy recovery properties, achieving 10-25 relative gains on the softmax classifier and 25-50 on triplet loss in these tasks. In recent years, the effect of the curse of high dimensionality has been studied in great detail on several problems such as clustering, nearest neighbor search, and indexing. In high dimensional space the data becomes sparse, and traditional indexing and algorithmic techniques fail from a efficiency and or effectiveness perspective. Recent research results show that in high dimensional space, the concept of proximity, distance or nearest neighbor may not even be qualitatively meaningful. In this paper, we view the dimensionality curse from the point of view of the distance metrics which are used to measure the similarity between objects. We specifically examine the behavior of the commonly used Lk norm and show that the problem of meaningfulness in high dimensionality is sensitive to the value of k. For example, this means that the Manhattan distance metric (L1 norm) is consistently more preferable than the Euclidean distance metric (L2 norm) for high dimensional data mining applications. Using the intuition derived from our analysis, we introduce and examine a natural extension of the Lk norm to fractional distance metrics. We show that the fractional distance metric provides more meaningful results both from the theoretical and empirical perspective. The results show that fractional distance metrics can significantly improve the effectiveness of standard clustering algorithms such as the k-means algorithm. Distance metric plays a key role in grouping superpixels to produce object proposals for object detection. We observe that existing distance metrics work primarily for low complexity cases. In this paper, we develop a novel distance metric for grouping two superpixels in high-complexity scenarios. Combining them, a complexity-adaptive distance measure is produced that achieves improved grouping in different levels of complexity. Our extensive experimentation shows that our method can achieve good results in the PASCAL VOC 2012 dataset surpassing the latest state-of-the-art methods. Abstract: Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been difficult for these to compete with modern classification algorithms in performance and even in feature extraction. In this work, we propose a novel approach explicitly designed to address a number of subtle yet important issues which have stymied earlier DML algorithms. It maintains an explicit model of the distributions of the different classes in representation space. It then employs this knowledge to adaptively assess similarity, and achieve local discrimination by penalizing class distribution overlap. We demonstrate the effectiveness of this idea on several tasks. Our approach achieves state-of-the-art classification results on a number of fine-grained visual recognition datasets, surpassing the standard softmax classifier and outperforming triplet loss by a relative margin of 30-40 . In terms of computational performance, it alleviates training inefficiencies in the traditional triplet loss, reaching the same error in 5-30 times fewer iterations. Beyond classification, we further validate the saliency of the learnt representations via their attribute concentration and hierarchy recovery properties, achieving 10-25 relative gains on the softmax classifier and 25-50 on triplet loss in these tasks. Along with the arrival of multimedia time, multimedia data has replaced textual data to transfer information in various fields. As an important form of multimedia data, images have been widely utilized by many applications, such as face recognition and image classification. Therefore, how to accurately annotate each image from a large set of images is of vital importance but challenging. To perform these tasks well, it is crucial to extract suitable features to character the visual contents of images and learn an appropriate distance metric to measure similarities between all images. Unfortunately, existing feature operators, such as histogram of gradient, local binary pattern, and color histogram, care more about the visual character of images and lack the ability to distinguish semantic information. Similarities between those features cannot reflect the real category correlations due to the well-known semantic gap. In order to solve this problem, this paper proposes a regularized distance metric framework called semantic discriminative metric learning (SDML). SDML combines geometric mean with normalized divergences and separates images from different classes simultaneously. The learned distance metric can treat all images from different classes equally. And distinctions between similar classes with entirely different semantic contents are emphasized by SDML. This procedure ensures the consistency between dissimilarities and semantic distinctions and avoids inaccuracy similarities incurred by unbalanced locations of samples. Various experiments on benchmark image datasets show the excellent performance of the novel method. The distance metric is the corner stone of nearest neighbor (NN)-based methods, and therefore, of nearest prototype (NP) algorithms. That is because they classify depending on the similarity of the data. When the data is characterized by a set of features which may contribute to the classification task in different levels, feature weighting or selection is required, sometimes in a local sense. However, local weighting is typically restricted to NN approaches. In this paper, we introduce local feature weighting (LFW) in NP classification. LFW provides each prototype its own weight vector, opposite to typical global weighting methods found in the NP literature, where all the prototypes share the same one. Providing each prototype its own weight vector has a novel effect in the borders of the Voronoi regions generated: They become nonlinear. We have integrated LFW with a previously developed evolutionary nearest prototype classifier (ENPC). The experiments performed both in artificial and real data sets demonstrate that the resulting algorithm that we call LFW in nearest prototype classification (LFW-NPC) avoids overfitting on training data in domains where the features may have different contribution to the classification task in different areas of the feature space. This generalization capability is also reflected in automatically obtaining an accurate and reduced set of prototypes. We present the Word Mover's Distance (WMD), a novel distance function between text documents. Our work is based on recent results in word embeddings that learn semantically meaningful representations for words from local cooccurrences in sentences. The WMD distance measures the dissimilarity between two text documents as the minimum amount of distance that the embedded words of one document need to "travel" to reach the embedded words of another document. We show that this distance metric can be cast as an instance of the Earth Mover's Distance, a well studied transportation problem for which several highly efficient solvers have been developed. Our metric has no hyperparameters and is straight-forward to implement. Further, we demonstrate on eight real world document classification data sets, in comparison with seven state-of-the-art baselines, that the WMD metric leads to unprecedented low k-nearest neighbor document classification error rates. Image distance (similarity) is a fundamental and important problem in image processing. However, traditional visual features based image distance metrics usually fail to capture human cognition. This paper presents a novel Social embedding Image Distance Learning (SIDL) approach to embed the similarity of collective social and behavioral information into visual space. The social similarity is estimated according to multiple social factors. Then a metric learning method is especially designed to learn the distance of visual features from the estimated social similarity. In this manner, we can evaluate the cognitive image distance based on the visual content of images. Comprehensive experiments are designed to investigate the effectiveness of SIDL, as well as the performance in the image recommendation and reranking tasks. The experimental results show that the proposed approach makes a marked improvement compared to the state-of-the-art image distance metrics. An interesting observation is given to show that the learned image distance can better reflect human cognition. Estimating 3D pose similarity is a fundamental problem on 3D motion data. Most previous work calculates L2-like distance of joint orientations or coordinates, which does not sufficiently reflect the pose similarity of human perception. In this paper, we present a new pose distance metric. First, we propose a new rich pose feature set called Geometric Pose Descriptor (GPD). GPD is more effective in encoding pose similarity by utilizing features on geometric relations among body parts, as well as temporal information such as velocities and accelerations. Based on GPD, we propose a semisupervised distance metric learning algorithm called Regularized Distance Metric Learning with Sparse Representation (RDSR), which integrates information from both unsupervised data relationship and labels. We apply the proposed pose distance metric to applications of motion transition decision and content-based pose retrieval. Quantitative evaluations demonstrate that our method achieves better results with only a small amount of human labels, showing that the proposed pose distance metric is a promising building block for various 3D-motion related applications. Metric learning aims at finding a distance that approximates a task-specific notion of semantic similarity. Typically, a Mahalanobis distance is learned from pairs of data labeled as being semantically similar or not. In this paper, we learn such metrics in a weakly supervised setting where "bags" of instances are labeled with "bags" of labels. We formulate the problem as a multiple instance learning (MIL) problem over pairs of bags. If two bags share at least one label, we label the pair positive, and negative otherwise. We propose to learn a metric using those labeled pairs of bags, leading to MildML, for multiple instance logistic discriminant metric learning. MildML iterates between updates of the metric and selection of putative positive pairs of examples from positive pairs of bags. To evaluate our approach, we introduce a large and challenging data set, Labeled Yahoo! News, which we have manually annotated and contains 31147 detected faces of 5873 different people in 20071 images. We group the faces detected in an image into a bag, and group the names detected in the caption into a corresponding set of labels. When the labels come from manual annotation, we find that MildML using the bag-level annotation performs as well as fully supervised metric learning using instance-level annotation. We also consider performance in the case of automatically extracted labels for the bags, where some of the bag labels do not correspond to any example in the bag. In this case MildML works substantially better than relying on noisy instance-level annotations derived from the bag-level annotation by resolving face-name associations in images with their captions. Detecting poorly textured objects and estimating their 3D pose reliably is still a very challenging problem. We introduce a simple but powerful approach to computing descriptors for object views that efficiently capture both the object identity and 3D pose. By contrast with previous manifold-based approaches, we can rely on the Euclidean distance to evaluate the similarity between descriptors, and therefore use scalable Nearest Neighbor search methods to efficiently handle a large number of objects under a large range of poses. To achieve this, we train a Convolutional Neural Network to compute these descriptors by enforcing simple similarity and dissimilarity constraints between the descriptors. We show that our constraints nicely untangle the images from different objects and different views into clusters that are not only well-separated but also structured as the corresponding sets of poses: The Euclidean distance between descriptors is large when the descriptors are from different objects, and directly related to the distance between the poses when the descriptors are from the same object. These important properties allow us to outperform state-of-the-art object views representations on challenging RGB and RGB-D data. 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. The matching of two-dimensional shapes is an important problem with applications in domains as diverse as biometrics, industry, medicine and anthropology. The distance measure used must be invariant to many distortions, including scale, offset, noise, partial occlusion, etc. Most of these distortions are relatively easy to handle, either in the representation of the data or in the similarity measure used. However rotation invariance seems to be uniquely difficult. Current approaches typically try to achieve rotation invariance in the representation of the data, at the expense of discrimination ability, or in the distance measure, at the expense of efficiency. In this work we show that we can take the slow but accurate approaches and dramatically speed them up. On real world problems our technique can take current approaches and make them four orders of magnitude faster, without false dismissals. Moreover, our technique can be used with any of the dozens of existing shape representations and with all the most popular distance measures including Euclidean distance, Dynamic Time Warping and Longest Common Subsequence. The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner. Instance-based learning techniques typically handle continuous and linear input values well, but often do not handle nominal input attributes appropriately. The Value Difference Metric (VDM) was designed to find reasonable distance values between nominal attribute values, but it largely ignores continuous attributes, requiring discretization to map continuous values into nominal values. This paper proposes three new heterogeneous distance functions, called the Heterogeneous Value Difference Metric (HVDM), the Interpolated Value Difference Metric (IVDM), and the Windowed Value Difference Metric (WVDM). These new distance functions are designed to handle applications with nominal attributes, continuous attributes, or both. In experiments on 48 applications the new distance metrics achieve higher classification accuracy on average than three previous distance functions on those datasets that have both nominal and continuous attributes. We introduce a novel measure called e-four-pointscondition (e-4PC), which assigns a value e ∈ [0,1] to every metric space quantifying how close the metric is to a tree metric. Data-sets taken from real Internet measurements indicate remarkable closeness of Internet latencies to tree metrics based on this condition. We study embeddings of e-4PC metric spaces into trees and prove tight upper and lower bounds. Specifically, we show that there are constants c1 and c2 such that, (1) every metric (X,d) which satisfies the e-4PC can be embedded into a tree with distortion (1+e)c1log|X|, and (2) for every e ∈: [0,1] and any number of nodes, there is a metric space (X,d) satisfying the e-4PC that does not embed into a tree with distortion less than (1+e)c2log|X|. In addition, we prove a lower bound on approximate distance labelings of e-4PC metrics, and give tight bounds for tree embeddings with additive error guarantees.