Simultaneous Localization and Mapping using RGB-D cameras has been a fertile research topic in the latest decade, due to the suitability of such sensors for indoor robotics. In this paper we propose a direct RGB-D SLAM algorithm with state-of-the-art accuracy and robustness at a los cost. Our experiments in the RGB-D TUM dataset [34] effectively show a better accuracy and robustness in CPU real time than direct RGB-D SLAM systems that make use of the GPU. The key ingredients of our approach are mainly two. Firstly, the combination of a semi-dense photometric and dense geometric error for the pose tracking (see Figure 1), which we demonstrate to be the most accurate alternative. And secondly, a model of the multi-view constraints and their errors in the mapping and tracking threads, which adds extra information over other approaches. We release the open-source implementation of our approach 1 . The reader is referred to a video with our results 2 for a more illustrative visualization of its performance.
@cite_2 shows and compares three different alignment strategies for direct tracking, namely the forward-compositional, the inverse-compositional and the efficient second-order minimization approach. In this paper we use the inverse composition, as it is the most efficient of the three.
@cite_2
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We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal @math rank- @math symmetric positive definite matrices. This special type of metric allows for a highly efficient evaluation of the proximal mapping. The key to this efficiency is a general proximal calculus in the new metric. By using duality, formulas are derived that relate the proximal mapping in a rank- @math modified metric to the original metric. We also describe efficient implementations of the proximity calculation for a large class of functions; the implementations exploit the piece-wise linear nature of the dual problem. Then, we apply these results to acceleration of composite convex minimization problems, which leads to elegant quasi-Newton methods for which we prove convergence. The algorithm is tested on several numerical examples and compared to a comprehensive list of alternatives in the literature. Our quasi-Newton splitting algorithm with the prescribed metric compares favorably against state-of-the-art. The algorithm has extensive applications including signal processing, sparse recovery, machine learning and classification to name a few. Sparse representation has been applied to visual tracking by finding the best candidate with minimal reconstruction error using target templates. However most sparse representation based trackers only consider the holistic representation and do not make full use of the sparse coefficients to discriminate between the target and the background, and hence may fail with more possibility when there is similar object or occlusion in the scene. In this paper we develop a simple yet robust tracking method based on the structural local sparse appearance model. This representation exploits both partial information and spatial information of the target based on a novel alignment-pooling method. The similarity obtained by pooling across the local patches helps not only locate the target more accurately but also handle occlusion. In addition, we employ a template update strategy which combines incremental subspace learning and sparse representation. This strategy adapts the template to the appearance change of the target with less possibility of drifting and reduces the influence of the occluded target template as well. Both qualitative and quantitative evaluations on challenging benchmark image sequences demonstrate that the proposed tracking algorithm performs favorably against several state-of-the-art methods. There has been a paradigm shifting trend towards feature-less methods due to their elegant formulation, accuracy and ever increasing computational power. In this work, we present a direct edge alignment approach for 6-DOF tracking. We argue that photo-consistency based methods are plagued by a much smaller convergence basin and are extremely sensitive to noise, changing illumination and fast motion. We propose to use the Distance Transform in the energy formulation which can significantly extend the influence of the edges for tracking. We address the problem of non-differentiability of our cost function and of the previous methods by use of a sub-gradient method. Through extensive experiments we show that the proposed method gives comparable performance to the previous method under nominal conditions and is able to run at 30 Hz in single threaded mode. In addition, under large motion we demonstrate our method outperforms previous methods using the same runtime configuration for our method. In this paper we propose a robust visual tracking method by casting tracking as a sparse approximation problem in a particle filter framework. In this framework, occlusion, corruption and other challenging issues are addressed seamlessly through a set of trivial templates. Specifically, to find the tracking target at a new frame, each target candidate is sparsely represented in the space spanned by target templates and trivial templates. The sparsity is achieved by solving an l 1 -regularized least squares problem. Then the candidate with the smallest projection error is taken as the tracking target. After that, tracking is continued using a Bayesian state inference framework in which a particle filter is used for propagating sample distributions over time. Two additional components further improve the robustness of our approach: 1) the nonnegativity constraints that help filter out clutter that is similar to tracked targets in reversed intensity patterns, and 2) a dynamic template update scheme that keeps track of the most representative templates throughout the tracking procedure. We test the proposed approach on five challenging sequences involving heavy occlusions, drastic illumination changes, and large pose variations. The proposed approach shows excellent performance in comparison with three previously proposed trackers. This paper presents a hierarchical composition approach for multi-view object tracking. The key idea is to adaptively exploit multiple cues in both 2D and 3D, e.g., ground occupancy consistency, appearance similarity, motion coherence etc., which are mutually complementary while tracking the humans of interests over time. While feature online selection has been extensively studied in the past literature, it remains unclear how to effectively schedule these cues for the tracking purpose especially when encountering various challenges, e.g. occlusions, conjunctions, and appearance variations. To do so, we propose a hierarchical composition model and re-formulate multi-view multi-object tracking as a problem of compositional structure optimization. We setup a set of composition criteria, each of which corresponds to one particular cue. The hierarchical composition process is pursued by exploiting different criteria, which impose constraints between a graph node and its offsprings in the hierarchy. We learn the composition criteria using MLE on annotated data and efficiently construct the hierarchical graph by an iterative greedy pursuit algorithm. In the experiments, we demonstrate superior performance of our approach on three public datasets, one of which is newly created by us to test various challenges in multi-view multi-object tracking. Recently sparse representation has been applied to visual tracker by modeling the target appearance using a sparse approximation over a template set, which leads to the so-called L1 trackers as it needs to solve an l 1 norm related minimization problem for many times. While these L1 trackers showed impressive tracking accuracies, they are very computationally demanding and the speed bottleneck is the solver to l 1 norm minimizations. This paper aims at developing an L1 tracker that not only runs in real time but also enjoys better robustness than other L1 trackers. In our proposed L1 tracker, a new l 1 norm related minimization model is proposed to improve the tracking accuracy by adding an l 1 norm regularization on the coefficients associated with the trivial templates. Moreover, based on the accelerated proximal gradient approach, a very fast numerical solver is developed to solve the resulting l 1 norm related minimization problem with guaranteed quadratic convergence. The great running time efficiency and tracking accuracy of the proposed tracker is validated with a comprehensive evaluation involving eight challenging sequences and five alternative state-of-the-art trackers. In this paper we propose a robust visual tracking method by casting tracking as a sparse approximation problem in a particle filter framework. In this framework, occlusion, corruption and other challenging issues are addressed seamlessly through a set of trivial templates. Specifically, to find the tracking target at a new frame, each target candidate is sparsely represented in the space spanned by target templates and trivial templates. The sparsity is achieved by solving an � 1-regularized least squares problem. Then the candidate with the smallest projection error is taken as the tracking target. After that, tracking is continued using a Bayesian state inference framework in which a particle filter is used for propagating sample distributions over time. Two additional components further improve the robustness of our approach: 1) the nonnegativity constraints that help filter out clutter that is similar to tracked targets in reversed intensity patterns, and 2) a dynamic template update scheme that keeps track of the most representative templates throughout the tracking procedure. We test the proposed approach on five challenging sequences involving heavy occlusions, drastic illumination changes, and large pose variations. The proposed approach shows excellent performance in comparison with three previously proposed trackers. Combining multiple observation views has proven beneficial for tracking. In this paper, we cast tracking as a novel multi-task multi-view sparse learning problem and exploit the cues from multiple views including various types of visual features, such as intensity, color, and edge, where each feature observation can be sparsely represented by a linear combination of atoms from an adaptive feature dictionary. The proposed method is integrated in a particle filter framework where every view in each particle is regarded as an individual task. We jointly consider the underlying relationship between tasks across different views and different particles, and tackle it in a unified robust multi-task formulation. In addition, to capture the frequently emerging outlier tasks, we decompose the representation matrix to two collaborative components which enable a more robust and accurate approximation. We show that the proposed formulation can be efficiently solved using the Accelerated Proximal Gradient method with a small number of closed-form updates. The presented tracker is implemented using four types of features and is tested on numerous benchmark video sequences. Both the qualitative and quantitative results demonstrate the superior performance of the proposed approach compared to several state-of-the-art trackers. 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. Abstract Time-optimal motion planning is one of the most essential problems in robotic theories. The presented direct transcription approach uses convex optimisation method to obtain a minimum-time control for robot manipulators. One subset of motion planning is the waiter motion problem that consists of moving a tablet from one place to another as fast as possible, avoiding the slip of the object that is placed upon it. In this paper the direct transcription method is presented in order to solve the waiter problem. This path tracking problem is also approximated by sequential two dimensional second-order cone programs (SOCP) using nonlinear change of variables. The computational benefit of the sequential method compared to the direct transcription approach is presented. The waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm. The task of tracking multiple targets is often addressed with the so-called tracking-by-detection paradigm, where the first step is to obtain a set of target hypotheses for each frame independently. Tracking can then be regarded as solving two separate, but tightly coupled problems. The first is to carry out data association, i.e., to determine the origin of each of the available observations. The second problem is to reconstruct the actual trajectories that describe the spatio-temporal motion pattern of each individual target. The former is inherently a discrete problem, while the latter should intuitively be modeled in continuous space. Having to deal with an unknown number of targets, complex dependencies, and physical constraints, both are challenging tasks on their own and thus most previous work focuses on one of these subproblems. Here, we present a multi-target tracking approach that explicitly models both tasks as minimization of a unified discrete-continuous energy function. Trajectory properties are captured through global label costs, a recent concept from multi-model fitting, which we introduce to tracking. Specifically, label costs describe physical properties of individual tracks, e.g., linear and angular dynamics, or entry and exit points. We further introduce pairwise label costs to describe mutual interactions between targets in order to avoid collisions. By choosing appropriate forms for the individual energy components, powerful discrete optimization techniques can be leveraged to address data association, while the shapes of individual trajectories are updated by gradient-based continuous energy minimization. The proposed method achieves state-of-the-art results on diverse benchmark sequences. In this paper, we tackle two key aspects of multiple target tracking problem: 1) designing an accurate affinity measure to associate detections and 2) implementing an efficient and accurate (near) online multiple target tracking algorithm. As for the first contribution, we introduce a novel Aggregated Local Flow Descriptor (ALFD) that encodes the relative motion pattern between a pair of temporally distant detections using long term interest point trajectories (IPTs). Leveraging on the IPTs, the ALFD provides a robust affinity measure for estimating the likelihood of matching detections regardless of the application scenarios. As for another contribution, we present a Near-Online Multi-target Tracking (NOMT) algorithm. The tracking problem is formulated as a data-association between targets and detections in a temporal window, that is performed repeatedly at every frame. While being efficient, NOMT achieves robustness via integrating multiple cues including ALFD metric, target dynamics, appearance similarity, and long term trajectory regularization into the model. Our ablative analysis verifies the superiority of the ALFD metric over the other conventional affinity metrics. We run a comprehensive experimental evaluation on two challenging tracking datasets, KITTI [16] and MOT [2] datasets. The NOMT method combined with ALFD metric achieves the best accuracy in both datasets with significant margins (about 10 higher MOTA) over the state-of-the-art. In this paper, we focus on the two key aspects of multiple target tracking problem: 1) designing an accurate affinity measure to associate detections and 2) implementing an efficient and accurate (near) online multiple target tracking algorithm. As the first contribution, we introduce a novel Aggregated Local Flow Descriptor (ALFD) that encodes the relative motion pattern between a pair of temporally distant detections using long term interest point trajectories (IPTs). Leveraging on the IPTs, the ALFD provides a robust affinity measure for estimating the likelihood of matching detections regardless of the application scenarios. As another contribution, we present a Near-Online Multi-target Tracking (NOMT) algorithm. The tracking problem is formulated as a data-association between targets and detections in a temporal window, that is performed repeatedly at every frame. While being efficient, NOMT achieves robustness via integrating multiple cues including ALFD metric, target dynamics, appearance similarity, and long term trajectory regularization into the model. Our ablative analysis verifies the superiority of the ALFD metric over the other conventional affinity metrics. We run a comprehensive experimental evaluation on two challenging tracking datasets, KITTI and MOT datasets. The NOMT method combined with ALFD metric achieves the best accuracy in both datasets with significant margins (about 10 higher MOTA) over the state-of-the-arts. Comon's (1994) well-known scheme for independent component analysis (ICA) is based on the maximal diagonalization, in a least-squares sense, of a higher-order cumulant tensor. In a previous paper, we proved that for fourth-order cumulants, the computation of an elementary Jacobi rotation is equivalent to the computation of the best rank-1 approximation of a fourth-order tensor. In this paper, we show that for third-order tensors, the computation of an elementary Jacobi rotation is again equivalent to a best rank-1 approximation; however, here, it is a matrix that has to be approximated. This favorable computational load makes it attractive to do "something third-order-like" for fourth-order cumulant tensors as well. We show that simultaneous optimal diagonalization of "third-order tensor slices" of the fourth-order cumulant is a suitable strategy. This "simultaneous third-order tensor diagonalization" approach (STOTD) is similar in spirit to the efficient JADE-algorithm. Stochastic Dual Coordinate Descent (SDCD) has become one of the most efficient ways to solve the family of @math -regularized empirical risk minimization problems, including linear SVM, logistic regression, and many others. The vanilla implementation of DCD is quite slow; however, by maintaining primal variables while updating dual variables, the time complexity of SDCD can be significantly reduced. Such a strategy forms the core algorithm in the widely-used LIBLINEAR package. In this paper, we parallelize the SDCD algorithms in LIBLINEAR. In recent research, several synchronized parallel SDCD algorithms have been proposed, however, they fail to achieve good speedup in the shared memory multi-core setting. In this paper, we propose a family of asynchronous stochastic dual coordinate descent algorithms (ASDCD). Each thread repeatedly selects a random dual variable and conducts coordinate updates using the primal variables that are stored in the shared memory. We analyze the convergence properties when different locking atomic mechanisms are applied. For implementation with atomic operations, we show linear convergence under mild conditions. For implementation without any atomic operations or locking, we present the first backward error analysis for ASDCD under the multi-core environment, showing that the converged solution is the exact solution for a primal problem with perturbed regularizer. Experimental results show that our methods are much faster than previous parallel coordinate descent solvers. Learning of inverse dynamics modeling errors is key for compliant or force control when analytical models are only rough approximations. Thus, designing real time capable function approximation algorithms has been a necessary focus towards the goal of online model learning. However, because these approaches learn a mapping from actual state and acceleration to torque, good tracking is required to observe data points on the desired path. Recently it has been shown how online gradient descent on a simple modeling error offset term to minimize tracking at acceleration level can address this issue. However, to adapt to larger errors a high learning rate of the online learner is required, resulting in reduced compliancy. Thus, here we propose to combine both approaches: The online adapted offset term ensures good tracking such that a nonlinear function approximator is able to learn an error model on the desired trajectory. This, in turn, reduces the load on the adaptive feedback, enabling it to use a lower learning rate. Combined this creates a controller with variable feedback and low gains, and a feedforward model that can account for larger modeling errors. We demonstrate the effectiveness of this framework, in simulation and on a real system. A number of recent works have emphasized the prominent role played by the Kurdyka-źojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of two terms: (i) a differentiable, but not necessarily convex, function and (ii) a function that is not necessarily convex, nor necessarily differentiable. The latter function is expressed as a separable sum of functions of blocks of variables. Such an optimization problem can be addressed with the Forward---Backward algorithm which can be accelerated thanks to the use of variable metrics derived from the Majorize---Minimize principle. We propose to combine the latter acceleration technique with an alternating minimization strategy which relies upon a flexible update rule. We give conditions under which the sequence generated by the resulting Block Coordinate Variable Metric Forward---Backward algorithm converges to a critical point of the objective function. An application example to a nonconvex phase retrieval problem encountered in signal image processing shows the efficiency of the proposed optimization method. This paper addresses the problem of learning similarity-preserving binary codes for efficient retrieval in large-scale image collections. We propose a simple and efficient alternating minimization scheme for finding a rotation of zero-centered data so as to minimize the quantization error of mapping this data to the vertices of a zero-centered binary hypercube. This method, dubbed iterative quantization (ITQ), has connections to multi-class spectral clustering and to the orthogonal Procrustes problem, and it can be used both with unsupervised data embeddings such as PCA and supervised embeddings such as canonical correlation analysis (CCA). Our experiments show that the resulting binary coding schemes decisively outperform several other state-of-the-art methods. In this paper we give an evaluation of different methods for computing frame-to-frame motion estimates for a moving RGB-D sensor, by means of aligning two images using photometric error minimization. These kind of algorithms have recently shown to be very accurate and robust and therefore provide an attractive solution for robot ego-motion estimation and navigation. We demonstrate three different alignment strategies, namely the Forward-Compositional, the Inverse-Compositional and the Efficient Second-Order Minimization approach, in a general robust estimation framework. We further show how estimating global affine illumination changes, in general improves the performance of the algorithms. We compare our results with recently published work, considered as state-of-the art in this field, and show that our solutions are in general more precise and can perform in real-time on standard hardware. We consider the joint optimization of beamformers and linear receivers in a MIMO interference network. Each transmitter transmits a single beam corresponding to a rank-one precoder. When the number of users K is greater than the number of antennas at each terminal N, the maximum degrees of freedom is achieved via spatial interference alignment. Interference alignment is feasible for up to K = 2N−1 users, in which case there is a finite number of solutions to the alignment conditions. This number of solutions increases rapidly with N, and the solutions depend only on the cross-channel coefficients (i. e., they are independent of the direct channels). To maximize the achievable sum rate at high SNRs we therefore wish to select an aligned solution which is best matched to the direct channels. We evaluate the performance of this scheme for large K and N, assuming that the solution is the best out of a random subset of aligned solutions. We then compare numerically this performance with the performance of previously proposed numerical (e. g., forward-backward) techniques for optimizing beams, and a new technique which tracks the local optimum as the SNR is incrementally increased, similar to a homotopy method for improving convergence properties. We observe that the incremental technique typically achieves better performance than the previously proposed methods.