Anoop Cherian

Jensen-Bregman LogDet Divergence with Application to Efficient Similarity Search for Covariance Matrices

Covariance matrices have found success in several computer vision applications, including activity recognition, visual surveillance, and diffusion tensor imaging. This is because they provide an easy platform for fusing multiple features compactly. An important task in all of these applications is to compare two covariance matrices using a (dis)similarity function, for which the common choice is the Riemannian metric on the manifold inhabited by these matrices. As this Riemannian manifold is not flat, the dissimilarities should take into account the curvature of the manifold. As a result, such distance computations tend to slow down, especially when the matrix dimensions are large or gradients are required. Further, suitability of the metric to enable efficient nearest neighbor retrieval is an important requirement in the contemporary times of big data analytics. To alleviate these difficulties, this paper proposes a novel dissimilarity measure for covariances, the Jensen-Bregman LogDet Divergence (JBLD). This divergence enjoys several desirable theoretical properties and at the same time is computationally less demanding (compared to standard measures). Utilizing the fact that the square root of JBLD is a metric, we address the problem of efficient nearest neighbor retrieval on large covariance datasets via a metric tree data structure. To this end, we propose a K-Means clustering algorithm on JBLD. We demonstrate the superior performance of JBLD on covariance datasets from several computer vision applications.

Efficient similarity search for covariance matrices via the Jensen-Bregman LogDet Divergence

Covariance matrices provide compact, informative feature descriptors for use in several computer vision applications, such as people-appearance tracking, diffusion-tensor imaging, activity recognition, among others. A key task in many of these applications is to compare different covariance matrices using a (dis)similarity function. A natural choice here is the Riemannian metric corresponding to the manifold inhabited by covariance matrices. But computations involving this metric are expensive, especially for large matrices and even more so, in gradient-based algorithms. To alleviate these difficulties, we advocate a novel dissimilarity measure for covariance matrices: the Jensen-Bregman LogDet Divergence. This divergence enjoys several useful theoretical properties, but its greatest benefits are: (i) lower computational costs (compared to standard approaches); and (ii) amenability for use in nearest-neighbor retrieval. We show numerous experiments to substantiate these claims.

Action recognition using global spatio-temporal features derived from sparse representations

Abstract Recognizing actions is one of the important challenges in computer vision with respect to video data, with applications to surveillance, diagnostics of mental disorders, and video retrieval. Compared to other data modalities such as documents and images, processing video data demands orders of magnitude higher computational and storage resources. One way to alleviate this difficulty is to focus the computations to informative (salient) regions of the video. In this paper, we propose a novel global spatio-temporal self-similarity measure to score saliency using the ideas of dictionary learning and sparse coding. In contrast to existing methods that use local spatio-temporal feature detectors along with descriptors (such as HOG, HOG3D, and HOF), dictionary learning helps consider the saliency in a global setting (on the entire video) in a computationally efficient way. We consider only a small percentage of the most salient (least self-similar) regions found using our algorithm, over which spatio-temporal descriptors such as HOG and region covariance descriptors are computed. The ensemble of such block descriptors in a bag-of-features framework provides a holistic description of the motion sequence which can be used in a classification setting. Experiments on several benchmark datasets in video based action classification demonstrate that our approach performs competitively to the state of the art.

Compact covariance descriptors in 3D point clouds for object recognition

One of the most important tasks for mobile robots is to sense their environment. Further tasks might include the recognition of objects in the surrounding environment. Three dimensional range finders have become the sensors of choice for mapping the environment of a robot. Recognizing objects in point clouds provided by such sensors is a difficult task. The main contribution of this paper is the introduction of a new covariance based point cloud descriptor for such object recognition. Covariance based descriptors have been very successful in image processing. One of the main advantages of these descriptors is their relatively small size. The comparisons between different covariance matrices can also be made very efficient. Experiments with real world and synthetic data will show the superior performance of the covariance descriptors on point clouds compared to state-of-the-art methods.

Riemannian Sparse Coding for Positive Definite Matrices

Inspired by the great success of sparse coding for vector valued data, our goal is to represent symmetric positive definite (SPD) data matrices as sparse linear combinations of atoms from a dictionary, where each atom itself is an SPD matrix. Since SPD matrices follow a non-Euclidean (in fact a Riemannian) geometry, existing sparse coding techniques for Euclidean data cannot be directly extended. Prior works have approached this problem by defining a sparse coding loss function using either extrinsic similarity measures (such as the log-Euclidean distance) or kernelized variants of statistical measures (such as the Stein divergence, Jeffrey’s divergence, etc.). In contrast, we propose to use the intrinsic Riemannian distance on the manifold of SPD matrices. Our main contribution is a novel mathematical model for sparse coding of SPD matrices; we also present a computationally simple algorithm for optimizing our model. Experiments on several computer vision datasets showcase superior classification and retrieval performance compared with state-of-the-art approaches.

Accurate 3D ground plane estimation from a single image

Accurate localization of landmarks in the vicinity of a robot is a first step towards solving the SLAM problem. In this work, we propose algorithms to accurately estimate the 3D location of the landmarks from the robot only from a single image taken from its on board camera. Our approach differs from previous efforts in this domain in that it first reconstructs accurately the 3D environment from a single image, then it defines a coordinate system over the environment, and later it performs the desired localization with respect to this coordinate system using the environments features. The ground plane from the given image is accurately estimated and this precedes segmentation of the image into ground and vertical regions. A Markov Random Field (MRF) based 3D reconstruction is performed to build an approximate depth map of the given image. This map is robust against texture variations due to shadows, terrain differences, etc. A texture segmentation algorithm is also applied to determine the ground plane accurately. Once the ground plane is estimated, we use the respective cameras intrinsic and extrinsic calibration information to calculate accurate 3D information about the features in the scene.

Autonomous altitude estimation of a UAV using a single onboard camera

Autonomous estimation of the altitude of an Unmanned Aerial Vehicle (UAV) is extremely important when dealing with flight maneuvers like landing, steady flight, etc. Vision based techniques for solving this problem have been underutilized. In this paper, we propose a new algorithm to estimate the altitude of a UAV from top-down aerial images taken from a single on-board camera. We use a semi-supervised machine learning approach to solve the problem. The basic idea of our technique is to learn the mapping between the texture information contained in an image to a possible altitude value. We learn an over complete sparse basis set from a corpus of unlabeled images capturing the texture variations. This is followed by regression of this basis set against a training set of altitudes. Finally, a spatio-temporal Markov Random Field is modeled over the altitudes in test images, which is maximized over the posterior distribution using the MAP estimate by solving a quadratic optimization problem with L1 regularity constraints. The method is evaluated in a laboratory setting with a real helicopter and is found to provide promising results with sufficiently fast turnaround time.

Dirichlet process mixture models on symmetric positive definite matrices for appearance clustering in video surveillance applications

Covariance matrices of multivariate data capture feature correlations compactly, and being very robust to noise, they have been used extensively as feature descriptors in many areas in computer vision, like, people appearance tracking, DTI imaging, face recognition, etc. Since these matrices do not adhere to the Euclidean geometry, clustering algorithms using the traditional distance measures cannot be directly extended to them. Prior work in this area has been restricted to using K-means type clustering over the Rieman-nian space using the Riemannian metric. As the applications scale, it is not practical to assume the number of components in a clustering model, failing any soft-clustering algorithm. In this paper, a novel application of the Dirich-let Process Mixture Model framework is proposed towards unsupervised clustering of symmetric positive definite matrices. We approach the problem by extending the existing K-means type clustering algorithms based on the logdet divergence measure and derive the counterpart of it in a Bayesian framework, which leads to the Wishart-Inverse Wishart conjugate pair. Alternative possibilities based on the matrix Frobenius norm and log-Euclidean measures are also proposed. The models are extensively compared using two real-world datasets against the state-of-the-art algorithms and demonstrate superior performance.

Tensor Representations via Kernel Linearization for Action Recognition from 3D Skeletons

In this paper, we explore tensor representations that can compactly capture higher-order relationships between skeleton joints for 3D action recognition. We first define RBF kernels on 3D joint sequences, which are then linearized to form kernel descriptors. The higher-order outer-products of these kernel descriptors form our tensor representations. We present two different kernels for action recognition, namely (i) a sequence compatibility kernel that captures the spatio-temporal compatibility of joints in one sequence against those in the other, and (ii) a dynamics compatibility kernel that explicitly models the action dynamics of a sequence. Tensors formed from these kernels are then used to train an SVM. We present experiments on several benchmark datasets and demonstrate state of the art results, substantiating the effectiveness of our representations.

A multi-sensor visual tracking system for behavior monitoring of at-risk children

Clinical studies confirm that mental illnesses such as autism, Obsessive Compulsive Disorder (OCD), etc. show behavioral abnormalities even at very young ages; the early diagnosis of which can help steer effective treatments. Most often, the behavior of such at-risk children deviate in very subtle ways from that of a normal child; correct diagnosis of which requires prolonged and continuous monitoring of their activities by a clinician, which is a difficult and time intensive task. As a result, the development of automation tools for assisting in such monitoring activities will be an important step towards effective utilization of the diagnostic resources. In this paper, we approach the problem from a computer vision standpoint, and propose a novel system for the automatic monitoring of the behavior of children in their natural environment through the deployment of multiple non-invasive sensors (cameras and depth sensors). We provide details of our system, together with algorithms for the robust tracking of the activities of the children. Our experiments, conducted in the Shirley G. Moore Laboratory School, demonstrate the effectiveness of our methodology.