Learning Log-Determinant Divergences for Positive Definite Matrices.

Representations in the form of Symmetric Positive Definite (SPD) matrices have been popularized in a variety of visual learning applications due to their demonstrated ability to capture rich second-order statistics of visual data. There exist several similarity measures for comparing SPD matrices with documented benefits. However, selecting an appropriate measure for a given problem remains a challenge and in most cases, is the result of a trial-and-error process. In this paper, we propose to learn similarity measures in a data-driven manner. To this end, we capitalize on the αß-log-det divergence, which is a meta-divergence parametrized by scalars α and ß, subsuming a wide family of popular information divergences on SPD matrices for distinct and discrete values of these parameters. Our key idea is to cast these parameters in a continuum and learn them from data. We systematically extend this idea to learn vector-valued parameters, thereby increasing the expressiveness of the underlying non-linear measure. We conjoin the divergence learning problem with several standard tasks in machine learning, including supervised discriminative dictionary learning and unsupervised SPD matrix clustering. We present Riemannian gradient descent schemes for optimizing our formulations efficiently, and show the usefulness of our method on eight standard computer vision tasks.

Image Descriptors for Weakly Annotated Histopathological Breast Cancer Data.

INTRODUCTION: Cancerous Tissue Recognition (CTR) methodologies are continuously integrating advancements at the forefront of machine learning and computer vision, providing a variety of inference schemes for histopathological data. Histopathological data, in most cases, come in the form of high-resolution images, and thus methodologies operating at the patch level are more computationally attractive. Such methodologies capitalize on pixel level annotations (tissue delineations) from expert pathologists, which are then used to derive labels at the patch level. In this work, we envision a digital connected health system that augments the capabilities of the clinicians by providing powerful feature descriptors that may describe malignant regions. MATERIAL AND METHODS: We start with a patch level descriptor, termed Covariance-Kernel Descriptor (CKD), capable of compactly describing tissue architectures associated with carcinomas. To leverage the recognition capability of the CKDs to larger slide regions, we resort to a multiple instance learning framework. In that direction, we derive the Weakly Annotated Image Descriptor (WAID) as the parameters of classifier decision boundaries in a Multiple Instance Learning framework. The WAID is computed on bags of patches corresponding to larger image regions for which binary labels (malignant vs. benign) are provided, thus obviating the necessity for tissue delineations. RESULTS: The CKD was seen to outperform all the considered descriptors, reaching classification accuracy (ACC) of 92.83%. and area under the curve (AUC) of 0.98. The CKD captures higher order correlations between features and was shown to achieve superior performance against a large collection of computer vision features on a private breast cancer dataset. The WAID outperform all other descriptors on the Breast Cancer Histopathological database (BreakHis) where correctly classified malignant (CCM) instances reached 91.27 and 92.00% at the patient and image level, respectively, without resorting to a deep learning scheme achieves state-of-the-art performance. DISCUSSION: Our proposed derivation of the CKD and WAID can help medical experts accomplish their work accurately and faster than the current state-of-the-art.

The Use of Immersive Environments for the Early Detection and Treatment of Neuropsychiatric Disorders.

Neuropsychiatric disorders are highly prevalent conditions with significant individual, societal, and economic impacts. A major challenge in the diagnosis and treatment of these conditions is the lack of sensitive, reliable, objective, quantitative tools to inform diagnosis, and measure symptom severity. Currently available assays rely on self-reports and clinician observations, leading to subjective analysis. As a step toward creating quantitative assays of neuropsychiatric symptoms, we propose an immersive environment to track behaviors relevant to neuropsychiatric symptomatology and to systematically study the effect of environmental contexts on certain behaviors. Moreover, the overarching theme leads to connected tele-psychiatry which can provide effective assessment.

Use of Computer Vision Tools to Identify Behavioral Markers of Pediatric Obsessive-Compulsive Disorder: A Pilot Study.

OBJECTIVES: The clinical presentation of pediatric obsessive-compulsive disorder (OCD) is heterogeneous, which is a stumbling block to understanding pathophysiology and to developing new treatments. A major shift in psychiatry, embodied in the Research Domain Criteria (RDoC) initiative of National Institute of Mental Health, recognizes the pitfalls of categorizing mental illnesses using diagnostic criteria. Instead, RDoC encourages researchers to use a dimensional approach, focusing on narrower domains of psychopathology to characterize brain-behavior relationships. Our aim in this multidisciplinary pilot study was to use computer vision tools to record OCD behaviors and to cross-validate these behavioral markers with standard clinical measures. METHODS: Eighteen youths with OCD and 21 healthy controls completed tasks in an innovation laboratory (free arrangement of objects, hand washing, arrangement of objects on contrasting carpets). Tasks were video-recorded. Videos were coded by blind raters for OCD-related behaviors. Children's Yale-Brown Obsessive Compulsive Scale (CY-BOCS) and other scales were administered. We compared video-recorded measures of behavior in OCD versus healthy controls and correlated video measures and clinical measures of OCD. RESULTS: Behavioral measures on the videos were significantly correlated with specific CY-BOCS dimension scores. During the free arrangement task, more time spent ordering objects and more moves of objects were both significantly associated with higher CY-BOCS ordering/repeating dimension scores. Longer duration of hand washing was significantly correlated with higher scores on CY-BOCS ordering/repeating and forbidden thoughts dimensions. During arrangement of objects on contrasting carpets, more moves and more adjustment of objects were significantly associated with higher CY-BOCS ordering/repeating dimension scores. CONCLUSION: Preliminary data suggest that measurement of behavior using video recording is a valid approach for quantifying OCD psychopathology. This methodology could serve as a new tool for investigating OCD using an RDoC approach. This objective, novel behavioral measurement technique may benefit both researchers and clinicians in assessing pediatric OCD and in identifying new behavioral markers of OCD. Clinical Trial Registry: Development of an Instrument That Monitors Behaviors Associated With OCD. NCT02866422. http://clinicaltrials.gov.

Bayesian Nonparametric Clustering for Positive Definite Matrices.

Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.

Tensor Dictionary Learning for Positive Definite Matrices.

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.

Efficient nearest neighbors via robust sparse hashing.

This paper presents a new nearest neighbor (NN) retrieval framework: robust sparse hashing (RSH). Our approach is inspired by the success of dictionary learning for sparse coding. Our key idea is to sparse code the data using a learned dictionary, and then to generate hash codes out of these sparse codes for accurate and fast NN retrieval. But, direct application of sparse coding to NN retrieval poses a technical difficulty: when data are noisy or uncertain (which is the case with most real-world data sets), for a query point, an exact match of the hash code generated from the sparse code seldom happens, thereby breaking the NN retrieval. Borrowing ideas from robust optimization theory, we circumvent this difficulty via our novel robust dictionary learning and sparse coding framework called RSH, by learning dictionaries on the robustified counterparts of the perturbed data points. The algorithm is applied to NN retrieval on both simulated and real-world data. Our results demonstrate that RSH holds significant promise for efficient NN retrieval against the state of the art.

Computer vision tools for low-cost and noninvasive measurement of autism-related behaviors in infants.

The early detection of developmental disorders is key to child outcome, allowing interventions to be initiated which promote development and improve prognosis. Research on autism spectrum disorder (ASD) suggests that behavioral signs can be observed late in the first year of life. Many of these studies involve extensive frame-by-frame video observation and analysis of a child's natural behavior. Although nonintrusive, these methods are extremely time-intensive and require a high level of observer training; thus, they are burdensome for clinical and large population research purposes. This work is a first milestone in a long-term project on non-invasive early observation of children in order to aid in risk detection and research of neurodevelopmental disorders. We focus on providing low-cost computer vision tools to measure and identify ASD behavioral signs based on components of the Autism Observation Scale for Infants (AOSI). In particular, we develop algorithms to measure responses to general ASD risk assessment tasks and activities outlined by the AOSI which assess visual attention by tracking facial features. We show results, including comparisons with expert and nonexpert clinicians, which demonstrate that the proposed computer vision tools can capture critical behavioral observations and potentially augment the clinician's behavioral observations obtained from real in-clinic assessments.

Tensor sparse coding for positive definite matrices.

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.

Robust foreground detection in video using pixel layers.

A framework for robust foreground detection that works under difficult conditions such as dynamic background and moderately moving camera is presented in this paper. The proposed method includes two main components: coarse scene representation as the union of pixel layers, and foreground detection in video by propagating these layers using a maximum-likelihood assignment. We first cluster into "layers" those pixels that share similar statistics. The entire scene is then modeled as the union of such non-parametric layer-models. An in-coming pixel is detected as foreground if it does not adhere to these adaptive models of the background. A principled way of computing thresholds is used to achieve robust detection performance with a pre-specified number of false alarms. Correlation between pixels in the spatial vicinity is exploited to deal with camera motion without precise registration or optical flow. The proposed technique adapts to changes in the scene, and allows to automatically convert persistent foreground objects to background and re-convert them to foreground when they become interesting. This simple framework addresses the important problem of robust foreground and unusual region detection, at about 10 frames per second on a standard laptop computer. The presentation of the proposed approach is complemented by results on challenging real data and comparisons with other standard techniques.