We present a method for extracting depth information from a rectified image pair. We train a convolutional neural network to predict how well two image patches match and use it to compute the stereo matching cost. The cost is refined by cross-based cost aggregation and semiglobal matching, followed by a left-right consistency check to eliminate errors in the occluded regions. Our stereo method achieves an error rate of 2.61 on the KITTI stereo dataset and is currently (August 2014) the top performing method on this dataset.
used sum of squared distances to compute an initial matching cost. They trained a model to predict the probability distribution over three classes: the initial disparity is correct, the initial disparity is incorrect due to fattening of a foreground object, and the initial disparity is incorrect due to other reasons. The predicted probabilities were used to adjust the initial matching cost. later extend their work by combining predictions obtained by computing normalized cross-correlation over different window sizes and centers. initialized the matching cost with AD-Census @cite_8 and used multiclass linear discriminant analysis to learn a mapping from the computed matching cost to the final disparity.
@cite_8
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Stereo matching algorithms usually consist of four steps, including matching cost calculation, matching cost aggregation, disparity calculation, and disparity refinement. Existing CNN-based methods only adopt CNN to solve parts of the four steps, or use different networks to deal with different steps, making them difficult to obtain the overall optimal solution. In this paper, we propose a network architecture to incorporate all steps of stereo matching. The network consists of three parts. The first part calculates the multi-scale shared features. The second part performs matching cost calculation, matching cost aggregation and disparity calculation to estimate the initial disparity using shared features. The initial disparity and the shared features are used to calculate the prior and posterior feature constancy. The initial disparity, the prior and posterior feature constancy are then fed to a sub-network to refine the initial disparity through a Bayesian inference process. The proposed method has been evaluated on the Scene Flow and KITTI datasets. It achieves the state-of-the-art performance on the KITTI 2012 and KITTI 2015 benchmarks while maintaining a very fast running time. We present an improved three-step pipeline for the stereo matching problem and introduce multiple novelties at each stage. We propose a new highway network architecture for computing the matching cost at each possible disparity, based on multilevel weighted residual shortcuts, trained with a hybrid loss that supports multilevel comparison of image patches. A novel post-processing step is then introduced, which employs a second deep convolutional neural network for pooling global information from multiple disparities. This network outputs both the image disparity map, which replaces the conventional "winner takes all" strategy, and a confidence in the prediction. The confidence score is achieved by training the network with a new technique that we call the reflective loss. Lastly, the learned confidence is employed in order to better detect outliers in the refinement step. The proposed pipeline achieves state of the art accuracy on the largest and most competitive stereo benchmarks, and the learned confidence is shown to outperform all existing alternatives. Stereo matching algorithms usually consist of four steps, including matching cost calculation, matching cost aggregation, disparity calculation, and disparity refinement. Existing CNN-based methods only adopt CNN to solve parts of the four steps, or use different networks to deal with different steps, making them difficult to obtain the overall optimal solution. In this paper, we propose a network architecture to incorporate all steps of stereo matching. The network consists of three parts. The first part calculates the multi-scale shared features. The second part performs matching cost calculation, matching cost aggregation and disparity calculation to estimate the initial disparity using shared features. The initial disparity and the shared features are used to calculate the feature constancy that measures correctness of the correspondence between two input images. The initial disparity and the feature constancy are then fed to a sub-network to refine the initial disparity. The proposed method has been evaluated on the Scene Flow and KITTI datasets. It achieves the state-of-the-art performance on the KITTI 2012 and KITTI 2015 benchmarks while maintaining a very fast running time. We present a method for extracting depth information from a rectified image pair. Our approach focuses on the first stage of many stereo algorithms: the matching cost computation. We approach the problem by learning a similarity measure on small image patches using a convolutional neural network. Training is carried out in a supervised manner by constructing a binary classification data set with examples of similar and dissimilar pairs of patches. We examine two network architectures for this task: one tuned for speed, the other for accuracy. The output of the convolutional neural network is used to initialize the stereo matching cost. A series of post-processing steps follow: cross-based cost aggregation, semiglobal matching, a left-right consistency check, subpixel enhancement, a median filter, and a bilateral filter. We evaluate our method on the KITTI 2012, KITTI 2015, and Middlebury stereo data sets and show that it outperforms other approaches on all three data sets. We present a method for extracting depth information from a rectified image pair. Our approach focuses on the first stage of many stereo algorithms: the matching cost computation. We approach the problem by learning a similarity measure on small image patches using a convolutional neural network. Training is carried out in a supervised manner by constructing a binary classification data set with examples of similar and dissimilar pairs of patches. We examine two network architectures for this task: one tuned for speed, the other for accuracy. The output of the convolutional neural network is used to initialize the stereo matching cost. A series of post-processing steps follow: cross-based cost aggregation, semiglobal matching, a left-right consistency check, subpixel enhancement, a median filter, and a bilateral filter. We evaluate our method on the KITTI 2012, KITTI 2015, and Middlebury stereo data sets and show that it outperforms other approaches on all three data sets. This paper studies two-class (or binary) classification of elements X in R k that allows for a reject option. Based on n independent copies of the pair of random variables (X,Y ) with X 2 R k and Y 2 0,1 , we consider classifiers f(X) that render three possible outputs: 0, 1 and R. The option R expresses doubt and is to be used for few observations that are hard to classify in an automatic way. Chow (1970) derived the optimal rule minimizing the risk P f(X) 6 Y, f(X) 6 R + dP f(X) = R . This risk function subsumes that the cost of making a wrong decision equals 1 and that of utilizing the reject option is d. We show that the classification problem hinges on the behavior of the regression function (x) = E(Y |X = x) near d and 1 d. (Here d 2 [0,1 2] as the other cases turn out to be trivial.) Classification rules can be categorized into plug-in estimators and empirical risk minimizers. Both types are considered here and we prove that the rates of convergence of the risk of any estimate depends on P | (X) d| + P | (X) (1 d)| and on the quality of the estimate for or an appropriate measure of the size of the class of classifiers, in case of plug-in rules and empirical risk minimizers, respectively. We extend the mathematical framework even further by dierentiating between costs associated with the two possible errors: predicting f(X) = 0 whilst Y = 1 and predicting f(X) = 1 whilst Y = 0. Such situations are common in, for instance, medical studies where misclassifying a sick patient as healthy is worse than the opposite. In this paper, we build upon the idea of using robust dense correspondence estimation for exemplar-based image classification and adapt it to the problem of ancient coin classification. We thus account for the lack of available training data and demonstrate that the matching costs are a powerful dissimilarity metric to establish coin classification for training set sizes of one or two images per class. This is accomplished by using a flexible dense correspondence search which is highly insensitive to local spatial differences between coins of the same class and different coin rotations between images. Additionally, we introduce a coarse-to-fine classification scheme to decrease runtime which would be otherwise linear to the number of classes in the training set. For evaluation, a new dataset representing 60 coin classes of the Roman Republican period is used. The proposed system achieves a classification rate of 83.3 and a runtime improvement of 93 through the coarse-to-fine classification. Traditional learning algorithms applied to complex and highly imbalanced training sets may not give satisfactory results when distinguishing between examples of the classes. The tendency is to yield classification models that are biased towards the overrepresented (majority) class. This paper investigates this class imbalance problem in the context of multilayer perceptron (MLP) neural networks. The consequences of the equal cost (loss) assumption on imbalanced data are formally discussed from a statistical learning theory point of view. A new cost-sensitive algorithm (CSMLP) is presented to improve the discrimination ability of (two-class) MLPs. The CSMLP formulation is based on a joint objective function that uses a single cost parameter to distinguish the importance of class errors. The learning rule extends the Levenberg-Marquadt's rule, ensuring the computational efficiency of the algorithm. In addition, it is theoretically demonstrated that the incorporation of prior information via the cost parameter may lead to balanced decision boundaries in the feature space. Based on the statistical analysis of results on real data, our approach shows a significant improvement of the area under the receiver operating characteristic curve and G-mean measures of regular MLPs. Various 3D reconstruction methods have enabled civil engineers to detect damage on a road surface. To achieve the millimeter accuracy required for road condition assessment, a disparity map with subpixel resolution needs to be used. However, none of the existing stereo matching algorithms are specially suitable for the reconstruction of the road surface. Hence in this paper, we propose a novel dense subpixel disparity estimation algorithm with high computational efficiency and robustness. This is achieved by first transforming the perspective view of the target frame into the reference view, which not only increases the accuracy of the block matching for the road surface but also improves the processing speed. The disparities are then estimated iteratively using our previously published algorithm, where the search range is propagated from three estimated neighboring disparities. Since the search range is obtained from the previous iteration, errors may occur when the propagated search range is not sufficient. Therefore, a correlation maxima verification is performed to rectify this issue, and the subpixel resolution is achieved by conducting a parabola interpolation enhancement. Furthermore, a novel disparity global refinement approach developed from the Markov random fields and fast bilateral stereo is introduced to further improve the accuracy of the estimated disparity map, where disparities are updated iteratively by minimizing the energy function that is related to their interpolated correlation polynomials. The algorithm is implemented in C language with a near real-time performance. The experimental results illustrate that the absolute error of the reconstruction varies from 0.1 to 3 mm. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. We study digital-goods auctions for items in unlimited supply introduced by Goldberg, Hartline and Wright. Since no deterministic algorithms are competitive for this class of auctions, one of the central research issues is how to obtain a nice probabilistic distribution over truthful algorithms. In this paper, we introduce a rather systematic approach to this goal: Consider for example the Sampling Cost Share (SCS) auction. It is well known that SCS works well if the the current bid vector produces many winners against F(2), the standard benchmark algorithm for competitive analysis. In fact, its competitive ratio is approaching to 2.0 as k (= the number of F(2) winners) grows. On the other hand, its competitive ratio becomes as bad as 4.0 for k = 2. Our new approach is to develop a sequence of similar cost-share type algorithms, DCSk, which work well for small k. Now we choose a sufficiently large constant N and run DCS1, DCS2, ..., DCSN and SCS with probabilities p1, p2, ..., pN and q, respectively. It should be noted that we can use LP to obtain optimal p1, p2,..., pN and q. By this averaging method, we can improve the competitive ratio of SCS from 4.0 to 3.531 and that of the currently best Aggregated γ3 algorithm due to Hartline and McGrew from 3.243 to 3.119. Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1 epsilon) competitive ratio in the standard adversarial online model, much effort has gone into developing useful online models that incorporate some stochasticity in the arrival process. One such popular model is the "known I.I.D. model" where different customer-types arrive online from a known distribution. We develop algorithms with improved competitive ratios for some basic variants of this model with integral arrival rates, including: (a) the case of general weighted edges, where we improve the best-known ratio of 0.667 due to [Haeupler, Mirrokni and Zadimoghaddam WINE 2011] to 0.705; and (b) the vertex-weighted case, where we improve the 0.7250 ratio of [Jaillet and Lu Math. Oper. Res 2013] to 0.7299. We also consider two extensions, one is "known I.I.D." with non-integral arrival rate and stochastic rewards; the other is "known I.I.D." b-matching with non-integral arrival rate and stochastic rewards. We present a simple non-adaptive algorithm which works well simultaneously on the two extensions. One of the key ingredients of our improvement is the following (offline) approach to bipartite-matching polytopes with additional constraints. We first add several valid constraints in order to get a good fractional solution f; however, these give us less control over the structure of f. We next remove all these additional constraints and randomly move from f to a feasible point on the matching polytope with all coordinates being from the set 0, 1 k, 2 k,..., 1 for a chosen integer k. The structure of this solution is inspired by [Jaillet and Lu Math. Oper. Res 2013] and is a tractable structure for algorithm design and analysis. The appropriate random move preserves many of the removed constraints (approximately [exactly] with high probability [in expectation]). This underlies some of our improvements, and, we hope, could be of independent interest. Automated data-driven decision making systems are increasingly being used to assist, or even replace humans in many settings. These systems function by learning from historical decisions, often taken by humans. In order to maximize the utility of these systems (or, classifiers), their training involves minimizing the errors (or, misclassifications) over the given historical data. However, it is quite possible that the optimally trained classifier makes decisions for people belonging to different social groups with different misclassification rates (e.g., misclassification rates for females are higher than for males), thereby placing these groups at an unfair disadvantage. To account for and avoid such unfairness, in this paper, we introduce a new notion of unfairness, disparate mistreatment, which is defined in terms of misclassification rates. We then propose intuitive measures of disparate mistreatment for decision boundary-based classifiers, which can be easily incorporated into their formulation as convex-concave constraints. Experiments on synthetic as well as real world datasets show that our methodology is effective at avoiding disparate mistreatment, often at a small cost in terms of accuracy. Uncertainty arises in classification problems when the input pattern is not perfect or measurement error is unavoidable. In many applications, it would be beneficial to obtain an estimate of the uncertainty associated with a new observation and its membership within a particular class. Although statistical classification techniques base decision boundaries according to the probability distributions of the patterns belonging to each class, they are poor at supplying uncertainty information for new observations. Previous research has documented a multiarchitecture, monotonic function neural network model for the representation of uncertainty associated with a new observation for two-class classification. This paper proposes a modification to the monotonic function model to estimate the uncertainty associated with a new observation for multiclass classification. The model, therefore, overcomes a limitation of traditional classifiers that base decisions on sharp classification boundaries. As such, it is believed that this method will have advantages for applications such as biometric recognition in which the estimation of classification uncertainty is an important issue. This approach is based on the transformation of the input pattern vector relative to each classification class. Separate, monotonic, single-output neural networks are then used to represent the "degree-of-similarity" between each input pattern vector and each class. An algorithm for the implementation of this approach is proposed and tested with publicly available face-recognition data sets. The results indicate that the suggested approach provides similar classification performance to conventional principle component analysis (PCA) and linear discriminant analysis (LDA) techniques for multiclass pattern recognition problems as well as providing uncertainty information caused by misclassification The problem of learning from imbalanced data sets, while not the same problem as learning when misclassication costs are unequal and unknown, can be handled in a similar manner. That is, in both contexts, we can use techniques from roc analysis to help with classier design. We present results from two studies in which we dealt with skewed data sets and unequal, but unknown costs of error. We also compare for one domain these results to those obtained by over-sampling and under-sampling the data set. The operations of sampling, moving the decision threshold, and adjusting the cost matrix produced sets of classiers that fell on the same roc curve. It sometimes happens (for instance in case control studies) that a classifier is trained on a data set that does not reflect the true a priori probabilities of the target classes on real-world data. This may have a negative effect on the classification accuracy obtained on the real-world data set, especially when the classifier's decisions are based on the a posteriori probabilities of class membership. Indeed, in this case, the trained classifier provides estimates of the a posteriori probabilities that are not valid for this real-world data set (they rely on the a priori probabilities of the training set). Applying the classifier as is (without correcting its outputs with respect to these new conditions) on this new data set may thus be suboptimal. In this note, we present a simple iterative procedure for adjusting the outputs of the trained classifier with respect to these new a priori probabilities without having to refit the model, even when these probabilities are not known in advance. As a by-product, estimates of the new a priori probabilities are also obtained. This iterative algorithm is a straightforward instance of the expectation-maximization (EM) algorithm and is shown to maximize the likelihood of the new data. Thereafter, we discuss a statistical test that can be applied to decide if the a priori class probabilities have changed from the training set to the real-world data. The procedure is illustrated on different classification problems involving a multilayer neural network, and comparisons with a standard procedure for a priori probability estimation are provided. Our original method, based on the EM algorithm, is shown to be superior to the standard one for a priori probability estimation. Experimental results also indicate that the classifier with adjusted outputs always performs better than the original one in terms of classification accuracy, when the a priori probability conditions differ from the training set to the real-world data. The gain in classification accuracy can be significant. In recent years, automated data-driven decision-making systems have enjoyed a tremendous success in a variety of fields (e.g., to make product recommendations, or to guide the production of entertainment). More recently, these algorithms are increasingly being used to assist socially sensitive decision-making (e.g., to decide who to admit into a degree program or to prioritize individuals for public housing). Yet, these automated tools may result in discriminative decision-making in the sense that they may treat individuals unfairly or unequally based on membership to a category or a minority, resulting in disparate treatment or disparate impact and violating both moral and ethical standards. This may happen when the training dataset is itself biased (e.g., if individuals belonging to a particular group have historically been discriminated upon). However, it may also happen when the training dataset is unbiased, if the errors made by the system affect individuals belonging to a category or minority differently (e.g., if misclassification rates for Blacks are higher than for Whites). In this paper, we unify the definitions of unfairness across classification and regression. We propose a versatile mixed-integer optimization framework for learning optimal and fair decision trees and variants thereof to prevent disparate treatment and or disparate impact as appropriate. This translates to a flexible schema for designing fair and interpretable policies suitable for socially sensitive decision-making. We conduct extensive computational studies that show that our framework improves the state-of-the-art in the field (which typically relies on heuristics) to yield non-discriminative decisions at lower cost to overall accuracy. Given dissimilarity data on pairs of objects in a set, we study the problem of fitting a tree metric to this data so as to minimize additive error (i.e. some measure of the difference between the tree metric and the given data). This problem arises in constructing an M-level hierarchical clustering of objects (or an ultrametric on objects) so as to match the given dissimilarity data - a basic problem in statistics. Viewed in this way, the problem is a generalization of the correlation clustering problem (which corresponds to M = 1). We give a very simple randomized combinatorial algorithm for the M-level hierarchical clustering problem that achieves an approximation ratio of M+2. This is a generalization of a previous factor 3 algorithm for correlation clustering on complete graphs. The problem of fitting tree metrics also arises in phylogeny where the objective is to learn the evolution tree by fitting a tree to dissimilarity data on taxa. The quality of the fit is measured by taking the l sub p norm of the difference between the tree metric constructed and the given data. Previous results obtained a factor 3 approximation for finding the closest tree tree metric under the l spl infin norm. No nontrivial approximation for general l sub p norms was known before. We present a novel LP formulation for this problem and obtain an O((log n log log n) sup 1 p ) approximation using this. Enroute, we obtain an O((log n log log n) sup 1 p ) approximation for the closest ultrametric under the l sub p norm. Our techniques are based on representing and viewing an ultrametric as a hierarchy of clusterings, and may be useful in other contexts. A commonly encountered problem in MLP (multi-layer perceptron) classification problems is related to the prior probabilities of the individual classes - if the number of training examples that correspond to each class varies significantly between the classes, then it may be harder for the network to learn the rarer classes in some cases. Such practical experience does not match theoretical results which show that MLPs approximate Bayesian a posteriori probabilities (independent of the prior class probabilities). Our investigation of the problem shows that the difference between the theoretical and practical results lies with the assumptions made in the theory (accurate estimation of Bayesian a posteriori probabilities requires the network to be large enough, training to converge to a global minimum, infinite training data, and the a priori class probabilities of the test set to be correctly represented in the training set). Specifically, the problem can often be traced to the fact that efficient MLP training mechanisms lead to sub-optimal solutions for most practical problems. In this chapter, we demonstrate the problem, discuss possible methods for alleviating it, and introduce new heuristics which are shown to perform well on a sample ECG classification problem. The heuristics may also be used as a simple means of adjusting for unequal misclassification costs. Metric learning methods, for person re-identification, estimate a scaling for distances in a vector space that is optimized for picking out observations of the same individual. This paper presents a novel approach to the pedestrian re-identification problem that uses metric learning to improve the state-of-the-art performance on standard public datasets. Very high dimensional features are extracted from the source color image. A first processing stage performs unsupervised PCA dimensionality reduction, constrained to maintain the redundancy in color-space representation. A second stage further reduces the dimensionality, using a Local Fisher Discriminant Analysis defined by a training set. A regularization step is introduced to avoid singular matrices during this stage. The experiments conducted on three publicly available datasets confirm that the proposed method outperforms the state-of-the-art performance, including all other known metric learning methods. Further-more, the method is an effective way to process observations comprising multiple shots, and is non-iterative: the computation times are relatively modest. Finally, a novel statistic is derived to characterize the Match Characteristic: the normalized entropy reduction can be used to define the 'Proportion of Uncertainty Removed' (PUR). This measure is invariant to test set size and provides an intuitive indication of performance.