Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

Computer vision as an entire field has a wide and diverse range of applications. The specific application for this project was in the realm of dance, notably ballet and choreography. This project was proof-of-concept for a choreography assistance tool used to recognize and record dance movements demonstrated by a choreographer. Keeping the commercial arena in mind, the Kinect from Microsoft was chosen as the imaging hardware, and a pilot set chosen to verify recognition feasibility. Before implementing a classifier, all training and test data was transformed to a more applicable representation scheme to only pass the important aspects to the classifier to distinguish moves for the pilot set. In addition, several classification algorithms using the Nearest Neighbor (NN) and Support Vector Machine (SVM) methods were tested and compared from a single dictionary as well as on several different subjects. The results were promising given the framework of the project, and several new expansions of this work are proposed.

Object recognition algorithms often focus on determining the class of a detected object in a scene. Two significant phases are usually involved in object recognition. The first phase is the object representation phase, in which the most suitable features that provide the best discriminative power under constraints such as lighting, resolution, scale, and view variations are chosen to describe the objects. The second phase is to use this representation space to develop models for each object class using discriminative classifiers. In this paper, we focus on composite objects, i.e., objects with two or more simpler classes that are interconnected in a complicated manner. One classic example of such a scenario is a bicyclist. A bicyclist consists of a bicycle and a human who rides the bicycle. When we are faced with the task of classifying bicyclists and pedestrians, it is counterintuitive and often hard to come up with a discriminative classifier to distinguish the two classes. We explore global image analysis based on bag of visual words to compare the results with local image analysis, in which we attempt to distinguish the individual parts of the composite object. We also propose a unified naive Bayes framework and a combined histogram feature method for combining the individual classifiers for enhanced performance.

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.

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.

Action classification is an important component of human-computer interaction. Trajectory classification is an effective way of performing action recognition with significant success reported in the literature. We compare two different representation schemes, raw multivariate time-series data and the covariance descriptors of the trajectories, and apply sparse representation techniques for classifying the various actions. The features are sparse coded using the Orthogonal Matching Pursuit algorithm, and the gestures and actions are classified based on the reconstruction residuals. We demonstrate the performance of our approach on standardized datasets such as the Australian Sign Language (AusLan) and UCF Motion Capture datasets, collected using high-quality motion capture systems, as well as motion capture data obtained from a Microsoft Kinect sensor.

Early intervention in mental disorders can dramatically increase an individual's quality of life. Additionally, when symptoms of mental illness appear in childhood or adolescence, they represent the later stages of a process that began years earlier. One goal of psychiatric research is to identify risk-markers: genetic, neural, behavioral and/or social deviations that indicate elevated risk of a particular mental disorder. Ideally, screening of risk-markers should occur in a community setting, and not a clinical setting which may be time-consuming and resource-intensive. Given this situation, a system for automatically detecting risk-markers in children would be highly valuable. In this paper, we describe such a system that has been installed at the Shirley G. Moore Lab School, a research pre-school at the University of Minnesota. This system consists of multiple RGB+D sensors and is able to detect children and adults in the classroom, tracking them as they move around the room. We use the tracking results to extract high-level information about the behavior and social interaction of children, that can then be used to screen for early signs of mental disorders.

In developmental disorders such as autism and schizophrenia, observing behavioral precursors in very early childhood can allow for early intervention and can improve patient outcomes. While such precursors open the possibility of broad and large-scale screening, until now they have been identified only through experts' painstaking examinations and their manual annotations of limited, unprocessed video footage. Here we introduce a system to automate and assist in such procedures. Employing multiple inexpensive real-time rgb+depth (rgb+d) sensors recording from multiple viewpoints, our non-invasive system - now installed at the Shirley G. Moore Lab School, a research preschool - is being developed to monitor and reconstruct the play and interactions of preschoolers. The system's role is to help in assessing the growing volumes of its on-site recordings and to provide the data needed to uncover additional neuromotor behavioral markers via techniques such as data mining.

Sparse models have proven to be extremely successful in image processing and computer vision, and most efforts have been focused on sparse representation of vectors. The success of sparse modeling and the popularity of region covariances have inspired the development of sparse coding approaches for positive definite matrices. While in earlier work [1], the dictionary was pre-determined, it is clearly advantageous to learn a concise dictionary adaptively from the data at hand. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between the sparse coding and dictionary update stages, and two different atom update methods are described. The online versions of the dictionary update techniques are also outlined. Experimental results demonstrate that the proposed learning methods yield better dictionaries for positive definite sparse coding. The learned dictionaries are applied to texture and face data, leading to improved classification accuracy and strong detection performance, respectively.

Background subtraction is a fundamental task in many computer vision applications, such as robotics and automated surveillance systems. The performance of high-level visions tasks such as object detection and tracking is dependent on effective foreground detection techniques. In this paper, we propose a novel background modeling algorithm that represents the background as a linear combination of dictionary atoms and the foreground as a sparse error, when one uses the respective set of dictionary atoms as basis elements to linearly approximate/reconstruct a new image. The dictionary atoms represent variations of the background model, and are learned from the training frames. The sparse foreground estimation during the training and performance phases is formulated as a Lasso [1] problem, while the dictionary update step in the training phase is motivated from the K-SVD algorithm [2]. Our proposed method works well in the presence of foreground in the training frames, and also gives the foreground masks for the training frames as a by-product of the batch training phase. Experimental validation is provided on standard datasets with ground truth information, and the receiver operating characteristic (ROC) curves are shown.

Cameras are becoming a common tool for automated vision purposes due to their low cost. In an era of growing security concerns, camera surveillance systems have become not only important but also necessary. Algorithms for several tasks such as detecting abandoned objects and tracking people have already been successfully developed. While tracking people is relatively easy, counting people in groups is much more challenging. The mutual occlusions between people in a group make it difficult to provide an exact count. The aim of this work is to present a method of estimating the number of people in group scenarios. Several considerations for counting people are illustrated in this paper, and experimental results of the method are described and discussed.