Vinay Venkataraman

Attractor-Shape for Dynamical Analysis of Human Movement: Applications in Stroke Rehabilitation and Action Recognition

In this paper, we propose a novel shape-theoretic framework for dynamical analysis of human movement from 3D data. The key idea we propose is the use of global descriptors of the shape of the dynamical attractor as a feature for modeling actions. We apply this approach to the novel application scenario of estimation of movement quality from a single-marker for future usage in home-based stroke rehabilitation. Using a dataset collected from 15 stroke survivors performing repetitive task therapy, we demonstrate that the proposed method outperforms traditional methods, such as kinematic analysis and use of chaotic invariants, in estimation of movement quality. In addition, we demonstrate that the proposed framework is sufficiently general for the application of action and gesture recognition as well. Our experimental results reflect improved action recognition results on two publicly available 3D human activity databases.

Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.

Dynamical Regularity for Action Analysis.

In this paper, we propose a new approach for quantification of ‘dynamical regularity’ as applied to modeling human actions. We use approximate entropy-based feature representation to model the dynamics in human movement to achieve temporal segmentation in untrimmed motion capture data and fine-grained quality assessment of diving actions in videos. The principle herein is to quantify regularity (frequency of typical patterns) in the dynamical space computed from trajectories of action data. We extend conventional ideas for modeling dynamics in human movement by introducing multivariate and cross approximate entropy features. Our experimental evaluation on theoretical models and two publicly available databases show that the proposed features can achieve state-ofthe-art results on applications such as temporal segmentation and quality assessment of actions.

Interdisciplinary Concepts for Design and Implementation of Mixed Reality Interactive Neurorehabilitation Systems for Stroke

Interactive neurorehabilitation (INR) systems provide therapy that can evaluate and deliver feedback on a patients movement computationally. There are currently many approaches to INR design and implementation, without a clear indication of which methods to utilize best. This article presents key interactive computing, motor learning, and media arts concepts utilized by an interdisciplinary group to develop adaptive, mixed reality INR systems for upper extremity therapy of patients with stroke. Two INR systems are used as examples to show how the concepts can be applied within: (1) a small-scale INR clinical study that achieved integrated improvement of movement quality and functionality through continuously supervised therapy and (2) a pilot study that achieved improvement of clinical scores with minimal supervision. The notion is proposed that some of the successful approaches developed and tested within these systems can form the basis of a scalable design methodology for other INR systems. A coherent approach to INR design is needed to facilitate the use of the systems by physical therapists, increase the number of successful INR studies, and generate rich clinical data that can inform the development of best practices for use of INR in physical therapy.

Persistent homology of attractors for action recognition

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system. We reconstruct the phase-space of time series corresponding to actions using time-delay embedding, and compute the persistent homology of the phase-space reconstruction. In order to better represent the topological properties of the phase-space, we incorporate the temporal adjacency information when computing the homology groups. The persistence of these homology groups encoded using persistence diagrams are used as features for the actions. Our experiments with action recognition using these features demonstrate that the proposed approach outperforms other baseline methods.

A Riemannian Framework for Statistical Analysis of Topological Persistence Diagrams

Topological data analysis is becoming a popular way to study high dimensional feature spaces without any contextual clues or assumptions. This paper concerns itself with one popular topological feature, which is the number of d–dimensional holes in the dataset, also known as the Betti–d number. The persistence of the Betti numbers over various scales is encoded into a persistence diagram (PD), which indicates the birth and death times of these holes as scale varies. A common way to compare PDs is by a pointto-point matching, which is given by the n-Wasserstein metric. However, a big drawback of this approach is the need to solve correspondence between points before computing the distance, for n points, the complexity grows according to O(n3). Instead, we propose to use an entirely new framework built on Riemannian geometry, that models PDs as 2D probability density functions that are represented in the square-root framework on a Hilbert Sphere. The resulting space is much more intuitive with closed form expressions for common operations. The distance metric is 1) correspondence-free and also 2) independent of the number of points in the dataset. The complexity of computing distance between PDs now grows according to O(K2), for a K K discretization of [0, 1]2. This also enables the use of existing machinery in differential geometry towards statistical analysis of PDs such as computing the mean, geodesics, classification etc. We report competitive results with the Wasserstein metric, at a much lower computational load, indicating the favorable properties of the proposed approach.

Brain dynamics based automated epileptic seizure detection.

We developed and tested a seizure detection algorithm based on two measures of nonlinear and linear dynamics, that is, the adaptive short-term maximum Lyapunov exponent (ASTLmax) and the adaptive Teager energy (ATE). The algorithm was tested on long-term (0.5-11.7 days) continuous EEG recordings from five patients (3 with intracranial and 2 with scalp EEG) with a total of 56 seizures, producing a mean sensitivity of 91% and mean specificity of 0.14 false positives per hour. The developed seizure detection algorithm is data-adaptive, training-free, and patient-independent.

Decision Support for Stroke Rehabilitation Therapy via Describable Attribute-based Decision Trees

This paper proposes a computational framework for movement quality assessment using a decision tree model that can potentially assist a physical therapist in a telereha-bilitation context. Using a dataset of key kinematic attributes collected from eight stroke survivors, we demonstrate that the framework can be reliably used for movement quality assessment of a reach-to-grasp cone task, an activity commonly used in upper extremity stroke rehabilitation therapy. The proposed framework is capable of providing movement quality scores that are highly correlated to the ratings provided by therapists, who used a custom rating rubric created by rehabilitation experts. Our hypothesis is that a decision tree model could be easily utilized by therapists as a potential assistive tool, especially in evaluating movement quality on a large-scale dataset collected during unsupervised rehabilitation (e.g., training at the home), thereby reducing the time and cost of rehabilitation treatment.

A Generalized Lyapunov Feature for Dynamical Systems on Riemannian Manifolds

Dynamic phenomena such as human activities, dynamic scenes, and moving crowds are commonly observed through visual sensors, resulting in feature trajectories sampled in time. Such phenomena can be accurately modeled by taking the temporal variations and changes into account. For problems where the trajectories are sufficiently different, elastic metrics can provide distances that are invariant to speed, but for more complex problems such as fine grained activity classification, one needs to exploit higher order dynamical properties. For features in the Euclidean space, applications such as crowd monitoring, dynamic scene recognition and human movement quality analysis have found a lot of success this way. In this paper we propose the largest Riemannian Lyapunov exponent (L-RLE), which is the first generalization of the largest Lyapunov exponent to Riemannian manifolds. The largest Lyapunov exponent is a classic measure to quantify the amount of chaos within signals in the Euclidean space, and allows us to exploit higher order dynamics for various applications. We show the effectiveness of the L-RLE on two manifolds the Grassmann and the SO(3) lie group. By modeling human actions as dynamic processes evolving on Riemannian manifolds, we show that L-RLE can measure the amount of chaos within each action accurately. We show that our measure is a good generalization of largest Euclidean Lyapunov exponent (L-ELE), and is less susceptible to arbitrary distortions.

Attractor-shape descriptors for balance impairment assessment in Parkinson's disease

In this paper, we propose a computational framework using high-dimensional shape descriptors of reconstructed attractors of center-of-pressure (CoP) tracings collected from subjects with Parkinsons disease while performing dynamical posture shifts, to quantitatively assess balance impairment. Using a dataset collected from 60 subjects, we demonstrated that the proposed method outperforms traditional methods, such as dynamical shift indices and use of chaotic invariants, in assessment of balance impairment.In this paper, we propose a computational framework using high-dimensional shape descriptors of reconstructed attractors of center-of-pressure (CoP) tracings collected from subjects with Parkinsons disease while performing dynamical posture shifts, to quantitatively assess balance impairment. Using a dataset collected from 60 subjects, we demonstrated that the proposed method outperforms traditional methods, such as dynamical shift indices and use of chaotic invariants, in assessment of balance impairment.