The problem of data augmentation in feature space is considered. A new architecture, denoted the FeATure TransfEr Network (FATTEN), is proposed for the modeling of feature trajectories induced by variations of object pose. This architecture exploits a parametrization of the pose manifold in terms of pose and appearance. This leads to a deep encoder decoder network architecture, where the encoder factors into an appearance and a pose predictor. Unlike previous attempts at trajectory transfer, FATTEN can be efficiently trained end-to-end, with no need to train separate feature transfer functions. This is realized by supplying the decoder with information about a target pose and the use of a multi-task loss that penalizes category- and pose-mismatches. In result, FATTEN discourages discontinuous or non-smooth trajectories that fail to capture the structure of the pose manifold, and generalizes well on object recognition tasks involving large pose variation. Experimental results on the artificial ModelNet database show that it can successfully learn to map source features to target features of a desired pose, while preserving class identity. Most notably, by using feature space transfer for data augmentation (w.r.t. pose and depth) on SUN-RGBD objects, we demonstrate considerable performance improvements on one few-shot object recognition in a transfer learning setup, compared to current state-of-the-art methods.
Since objects describe smooth trajectories in image space, as a function of viewing angle, it has long been known that such trajectories span a 3D manifold in image space, parameterized by the viewing angle. Hence, many of the manifold modeling methods proposed in the literature @cite_33 @cite_39 @cite_8 could, in principle, be used to develop trajectory transfer algorithms. However, many of these methods are transductive, , they do not produce a function that can make predictions for images outside of the training set, and do not leverage recent advances in deep learning. While deep learning could be used to explicitly model pose manifolds, it is difficult to rely on CNNs pre-trained on ImageNet for this purpose. This is because these networks attempt to collapse the manifold into a space where class discrimination is linear. On the other hand, the feature trajectories in response to pose variability are readily available. These trajectories are also much easier to model. For example, if the CNN is successful in mapping the pose manifold of a given object into a single point, , exhibits total pose invariance for that object, the problem is already solved and trajectory leaning is trivial for that object.
@cite_8 @cite_33 @cite_39
2053186076 2097308346
The problem of data augmentation in feature space is considered. A new architecture, denoted the FeATure TransfEr Network (FATTEN), is proposed for the modeling of feature trajectories induced by variations of object pose. This architecture exploits a parametrization of the pose manifold in terms of pose and appearance. This leads to a deep encoder decoder network architecture, where the encoder factors into an appearance and a pose predictor. Unlike previous attempts at trajectory transfer, FATTEN can be efficiently trained end-to-end, with no need to train separate feature transfer functions. This is realized by supplying the decoder with information about a target pose and the use of a multi-task loss that penalizes category- and pose-mismatches. In result, FATTEN discourages discontinuous or non-smooth trajectories that fail to capture the structure of the pose manifold, and generalizes well on object recognition tasks involving large pose variation. Experimental results on the artificial ModelNet database show that it can successfully learn to map source features to target features of a desired pose, while preserving class identity. Most notably, by using feature space transfer for data augmentation (w.r.t. pose and depth) on SUN-RGBD objects, we demonstrate considerable performance improvements on one few-shot object recognition in a transfer learning setup, compared to current state-of-the-art methods. We address the problem of fine-grain head pose angle estimation from a single 2D face image as a continuous regression problem. Currently the state of the art, and a promising line of research, on head pose estimation seems to be that of nonlinear manifold embedding techniques, which learn an "optimal" low-dimensional manifold that models the nonlinear and continuous variation of face appearance with pose angle. Furthermore, supervised manifold learning techniques attempt to achieve this robustly in the presence of latent variables in the training set (especially identity, illumination, and facial expression), by incorporating head pose angle information accompanying the training samples. Most of these techniques are designed with the classification scenario in mind, however, and are not directly applicable to the regression scenario where continuous numeric values (pose angles), rather than class labels (discrete poses), are available. In this paper, we propose to deal with the regression case in a principled way. We present a taxonomy of methods for incorporating continuous pose angle information into one or more stages of the manifold learning process, and discuss its implementation for Neighborhood Preserving Embedding (NPE) and Locality Preserving Projection (LPP). Experiments are carried out on a face dataset containing significant identity and illumination variations, and the results show that our regression-based approach far outperforms previous supervised manifold learning methods for head pose estimation. We aim to infer 3D body pose directly from human silhouettes. Given a visual input (silhouette), the objective is to recover the intrinsic body configuration, recover the viewpoint, reconstruct the input and detect any spatial or temporal outliers. In order to recover intrinsic body configuration (pose) from the visual input (silhouette), we explicitly learn view-based representations of activity manifolds as well as learn mapping functions between such central representations and both the visual input space and the 3D body pose space. The body pose can be recovered in a closed form in two steps by projecting the visual input to the learned representations of the activity manifold, i.e., finding the point on the learned manifold representation corresponding to the visual input, followed by interpolating 3D pose. We cast the problem of motion segmentation of feature trajectories as linear manifold finding problems and propose a general framework for motion segmentation under affine projections which utilizes two properties of trajectory data: geometric constraint and locality. The geometric constraint states that the trajectories of the same motion lie in a low dimensional linear manifold and different motions result in different linear manifolds; locality, by which we mean in a transformed space a data and its neighbors tend to lie in the same linear manifold, provides a cue for efficient estimation of these manifolds. Our algorithm estimates a number of linear manifolds, whose dimensions are unknown beforehand, and segment the trajectories accordingly. It first transforms and normalizes the trajectories; secondly, for each trajectory it estimates a local linear manifold through local sampling; then it derives the affinity matrix based on principal subspace angles between these estimated linear manifolds; at last, spectral clustering is applied to the matrix and gives the segmentation result. Our algorithm is general without restriction on the number of linear manifolds and without prior knowledge of the dimensions of the linear manifolds. We demonstrate in our experiments that it can segment a wide range of motions including independent, articulated, rigid, non-rigid, degenerate, non-degenerate or any combination of them. In some highly challenging cases where other state-of-the-art motion segmentation algorithms may fail, our algorithm gives expected results. Contact constraints, such as those between a foot and the ground or a hand and an object, are inherent in many robotic tasks. These constraints define a manifold of feasible states; while well understood mathematically, they pose numerical challenges to many algorithms for planning and controlling whole-body dynamic motions. In this paper, we present an approach to the synthesis and stabilization of complex trajectories for both fully-actuated and underactuated robots subject to contact constraints. We introduce a trajectory optimization algorithm (DIRCON) that extends the direct collocation method, naturally incorporating manifold constraints to produce a nominal trajectory with third-order integration accuracy—a critical feature for achieving reliable tracking control. We adapt the classical time-varying linear quadratic regulator to produce a local cost-to-go in the manifold tangent plane. Finally, we descend the cost-to-go using a quadratic program that incorporates unilateral friction and torque constraints. This approach is demonstrated on three complex walking and climbing locomotion examples in simulation. Object recognition and pose estimation from RGB-D images are important tasks for manipulation robots which can be learned from examples. Creating and annotating datasets for learning is expensive, however. We address this problem with transfer learning from deep convolutional neural networks (CNN) that are pre-trained for image categorization and provide a rich, semantically meaningful feature set. We incorporate depth information, which the CNN was not trained with, by rendering objects from a canonical perspective and colorizing the depth channel according to distance from the object center. We evaluate our approach on the Washington RGB-D Objects dataset, where we find that the generated feature set naturally separates classes and instances well and retains pose manifolds. We outperform state-of-the-art on a number of subtasks and show that our approach can yield superior results when only little training data is available. In this paper, we study a family of semisupervised learning algorithms for “aligning” different data sets that are characterized by the same underlying manifold. The optimizations of these algorithms are based on graphs that provide a discretized approximation to the manifold. Partial alignments of the data sets—obtained from prior knowledge of their manifold structure or from pairwise correspondences of subsets of labeled examples— are completed by integrating supervised signals with unsupervised frameworks for manifold learning. As an illustration of this semisupervised setting, we show how to learn mappings between different data sets of images that are parameterized by the same underlying modes of variability (e.g., pose and viewing angle). The curse of dimensionality in these problems is overcome by exploiting the low dimensional structure of image manifolds. This paper is focused on studying the view-manifold structure in the feature spaces implied by the different layers of Convolutional Neural Networks (CNN). There are several questions that this paper aims to answer: Does the learned CNN representation achieve viewpoint invariance? How does it achieve viewpoint invariance? Is it achieved by collapsing the view manifolds, or separating them while preserving them? At which layer is view invariance achieved? How can the structure of the view manifold at each layer of a deep convolutional neural network be quantified experimentally? How does fine-tuning of a pre-trained CNN on a multi-view dataset affect the representation at each layer of the network? In order to answer these questions we propose a methodology to quantify the deformation and degeneracy of view manifolds in CNN layers. We apply this methodology and report interesting results in this paper that answer the aforementioned questions. Many motion segmentation algorithms based on manifold clustering rely on a accurate rank estimation of the trajectory matrix and on a meaningful affinity measure between the estimated manifolds. While it is known that rank estimation is a difficult task, we also point out the problems that can be induced by an affinity measure that neglects the distribution of the principal angles. In this paper we suggest a new interpretation of the rank of the trajectory matrix and a new affinity measure. The rank estimation is performed by analysing which rank leads to a configuration where small and large angles are best separated. The affinity measure is a new function automatically parametrized so that it is able to adapt to the actual configuration of the principal angles. Our technique has one of lowest misclassification rates on the Hopkins155 database and has good performances also on synthetic sequences with up to 5 motions and variable noise level. We propose a novel algorithm for segmenting multiple motions of different types from point correspondences in multiple affine or perspective views. Since point trajectories associated with different motions live in different manifolds, traditional approaches deal with only one manifold type: linear subspaces for affine views, and homographic, bilinear and trilinear varieties for two and three perspective views. As real motion sequences contain motions of different types, we cast motion segmentation as a problem of clustering manifolds of different types. Rather than explicitly modeling each manifold as a linear, bilinear or multilinear variety, we use nonlinear dimensionality reduction to learn a low-dimensional representation of the union of all manifolds. We show that for a union of separated manifolds, the LLE algorithm computes a matrix whose null space contains vectors giving the segmentation of the data. An analysis of the variance of these vectors allows us to distinguish them from other vectors in the null space. This leads to a new algorithm for clustering both linear and nonlinear manifolds. Although this algorithm is theoretically designed for separated manifolds, our experiments demonstrate its performance on real data where this assumption does not hold. We test our algorithm on the Hopkins 155 motion segmentation database and achieve an average classification error of 4.8 , which compares favorably against state-of-the art multiframe motion segmentation methods. A multi-view image sequence provides a much richer capacity for object recognition than from a single image. However, most existing solutions to multi-view recognition typically adopt hand-crafted, model-based geometric methods, which do not readily embrace recent trends in deep learning. We propose to bring Convolutional Neural Networks to generic multi-view recognition, by decomposing an image sequence into a set of image pairs, classifying each pair independently, and then learning an object classifier by weighting the contribution of each pair. This allows for recognition over arbitrary camera trajectories, without requiring explicit training over the potentially infinite number of camera paths and lengths. Building these pairwise relationships then naturally extends to the next-best-view problem in an active recognition framework. To achieve this, we train a second Convolutional Neural Network to map directly from an observed image to next viewpoint. Finally, we incorporate this into a trajectory optimisation task, whereby the best recognition confidence is sought for a given trajectory length. We present state-of-the-art results in both guided and unguided multi-view recognition on the ModelNet dataset, and show how our method can be used with depth images, greyscale images, or both. Person re-identification is challenging due to the large variations of pose, illumination, occlusion and camera view. Owing to these variations, the pedestrian data is distributed as highly-curved manifolds in the feature space, despite the current convolutional neural networks (CNN)’s capability of feature extraction. However, the distribution is unknown, so it is difficult to use the geodesic distance when comparing two samples. In practice, the current deep embedding methods use the Euclidean distance for the training and test. On the other hand, the manifold learning methods suggest to use the Euclidean distance in the local range, combining with the graphical relationship between samples, for approximating the geodesic distance. From this point of view, selecting suitable positive (i.e. intra-class) training samples within a local range is critical for training the CNN embedding, especially when the data has large intra-class variations. In this paper, we propose a novel moderate positive sample mining method to train robust CNN for person re-identification, dealing with the problem of large variation. In addition, we improve the learning by a metric weight constraint, so that the learned metric has a better generalization ability. Experiments show that these two strategies are effective in learning robust deep metrics for person re-identification, and accordingly our deep model significantly outperforms the state-of-the-art methods on several benchmarks of person re-identification. Therefore, the study presented in this paper may be useful in inspiring new designs of deep models for person re-identification. In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the benefit to bring naturally a second desirable quantity when comparing shapes — the spatial covariance — in addition to the conventional affine-shape representation. We derived then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the underlying manifold. Specifically, our approach involves three steps: (1) landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of fixed-rank to build time-parameterized trajectories; (2) a temporal warping is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; (3) finally, a pairwise proximity function SVM is used to classify them, incorporating the (dis-)similarity measure into the kernel function. We show that such representation and metric achieve competitive results in applications as action recognition and emotion recognition from 3D skelet al data, and facial expression recognition from videos. Experiments have been conducted on several publicly available up-to-date benchmarks. Suitable shape representations as well as their temporal evolution, termed trajectories, often lie to non-linear manifolds. This puts an additional constraint (i.e., non-linearity) in using conventional machine learning techniques for the purpose of classification, event detection, prediction, etc. This paper accommodates the well-known Sparse Coding and Dictionary Learning to the Kendall's shape space and illustrates effective coding of 3D skelet al sequences for action recognition. Grounding on the Riemannian geometry of the shape space, an intrinsic sparse coding and dictionary learning formulation is proposed for static skelet al shapes to overcome the inherent non-linearity of the manifold. As a main result, initial trajectories give rise to sparse code functions with suitable computational properties, including sparsity and vector space representation. To achieve action recognition, two different classification schemes were adopted. A bi-directional LSTM is directly performed on sparse code functions, while a linear SVM is applied after representing sparse code functions using Fourier temporal pyramid. Experiments conducted on three publicly available datasets show the superiority of the proposed approach compared to existing Riemannian representations and its competitiveness with respect to other recently-proposed approaches. When the benefits of invariance are maintained from the Kendall's shape representation, our approach not only overcomes the problem of non-linearity but also yields to discriminative sparse code functions. We describe a novel method for simultaneously detecting faces and estimating their pose in real time. The method employs a convolutional network to map images of faces to points on a low-dimensional manifold parametrized by pose, and images of non-faces to points far away from that manifold. Given an image, detecting a face and estimating its pose is viewed as minimizing an energy function with respect to the face non-face binary variable and the continuous pose parameters. The system is trained to minimize a loss function that drives correct combinations of labels and pose to be associated with lower energy values than incorrect ones. The system is designed to handle very large range of poses without retraining. The performance of the system was tested on three standard data sets---for frontal views, rotated faces, and profiles---is comparable to previous systems that are designed to handle a single one of these data sets. We show that a system trained simuiltaneously for detection and pose estimation is more accurate on both tasks than similar systems trained for each task separately. Motion models have been proved to be a crucial part in the visual tracking process. In recent trackers, particle filter and sliding windows-based motion models have been widely used. Treating motion models as a sequence prediction problem, we can estimate the motion of objects using their trajectories. Moreover, it is possible to transfer the learned knowledge from annotated trajectories to new objects. Inspired by recent advance in deep learning for visual feature extraction and sequence prediction, we propose a trajectory predictor to learn prior knowledge from annotated trajectories and transfer it to predict the motion of target objects. In this predictor, convolutional neural networks extract the visual features of target objects. Long short-term memory model leverages the annotated trajectory priors as well as sequential visual information, which includes the tracked features and center locations of the target object, to predict the motion. Furthermore, to extend this method to videos in which it is difficult to obtain annotated trajectories, a dynamic weighted motion model that combines the proposed trajectory predictor with a random sampler is proposed. To evaluate the transfer performance of the proposed trajectory predictor, we annotated a real-world vehicle dataset. Experiment results on both this real-world vehicle dataset and an online tracker benchmark dataset indicate that the proposed method outperforms several state-of-the-art trackers. This paper presents a novel discriminative learning method, called manifold discriminant analysis (MDA), to solve the problem of image set classification. By modeling each image set as a manifold, we formulate the problem as classification-oriented multi-manifolds learning. Aiming at maximizing “manifold margin”, MDA seeks to learn an embedding space, where manifolds with different class labels are better separated, and local data compactness within each manifold is enhanced. As a result, new testing manifold can be more reliably classified in the learned embedding space. The proposed method is evaluated on the tasks of object recognition with image sets, including face recognition and object categorization. Comprehensive comparisons and extensive experiments demonstrate the effectiveness of our method. In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the advantage to bring naturally a second desirable quantity when comparing shapes -- the spatial covariance -- in addition to the conventional affine-shape representation. We derive then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the manifold. Specifically, our approach involves three steps: 1) facial landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of rank 2, to build time-parameterized trajectories; 2) a temporal alignment is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; 3) finally, pairwise proximity function SVM (ppfSVM) is used to classify them, incorporating the latter (dis-)similarity measure into the kernel function. We show the effectiveness of the proposed approach on four publicly available benchmarks (CK+, MMI, Oulu-CASIA, and AFEW). The results of the proposed approach are comparable to or better than the state-of-the-art methods when involving only facial landmarks. Adversarial perturbations can pose a serious threat for deploying machine learning systems. Recent works have shown existence of image-agnostic perturbations that can fool classifiers over most natural images. Existing methods present optimization approaches that solve for a fooling objective with an imperceptibility constraint to craft the perturbations. However, for a given classifier, they generate one perturbation at a time, which is a single instance from the manifold of adversarial perturbations. Also, in order to build robust models, it is essential to explore the manifold of adversarial perturbations. In this paper, we propose for the first time, a generative approach to model the distribution of adversarial perturbations. The architecture of the proposed model is inspired from that of GANs and is trained using fooling and diversity objectives. Our trained generator network attempts to capture the distribution of adversarial perturbations for a given classifier and readily generates a wide variety of such perturbations. Our experimental evaluation demonstrates that perturbations crafted by our model (i) achieve state-of-the-art fooling rates, (ii) exhibit wide variety and (iii) deliver excellent cross model generalizability. Our work can be deemed as an important step in the process of inferring about the complex manifolds of adversarial perturbations. In this paper, we address the problem of 3D object instance recognition and pose estimation of localized objects in cluttered environments using convolutional neural networks. Inspired by the descriptor learning approach of , we propose a method that introduces the dynamic margin in the manifold learning triplet loss function. Such a loss function is designed to map images of different objects under different poses to a lower-dimensional, similarity-preserving descriptor space on which efficient nearest neighbor search algorithms can be applied. Introducing the dynamic margin allows for faster training times and better accuracy of the resulting low-dimensional manifolds. Furthermore, we contribute the following: adding in-plane rotations (ignored by the baseline method) to the training, proposing new background noise types that help to better mimic realistic scenarios and improve accuracy with respect to clutter, adding surface normals as another powerful image modality representing an object surface leading to better performance than merely depth, and finally implementing an efficient online batch generation that allows for better variability during the training phase. We perform an exhaustive evaluation to demonstrate the effects of our contributions. Additionally, we assess the performance of the algorithm on the large BigBIRD dataset to demonstrate good scalability properties of the pipeline with respect to the number of models.