Comparing and Combining Time Series Trajectories Using Dynamic Time Warping

This research proposes the application of dynamic time warping (DTW) algorithm to analyse multivariate data from virtual reality training simulators, to assess the skill level of trainees. We present results of DTW algorithm applied to trajectory data from a virtual reality haptic training simulator for epidural needle insertion. The proposed application of DTW algorithm serves two purposes, to enable (i) two trajectories to be compared as a similarity measure and also enables (ii) two or more trajectories to be combined together to produce a typical or representative average trajectory using a novel hierarchical DTW process. Our experiments included 100 expert and 100 novice simulator recordings. The data consists of multivariate time series data-streams including multi-dimensional trajectories combined with force and pressure measurements. Our results show that our proposed application of DTW provides a useful time-independent method for (i) comparing two trajectories by providing a similarity measure and (ii) combining two or more trajectories into one, showing higher performance compared to conventional methods such as linear mean. These results demonstrate that DTW can be useful within virtual reality training simulators to provide a component in an automated scoring and assessment feedback system

Automatic Analysis of Facial Expressions Based on Deep Covariance Trajectories

In this paper, we propose a new approach for facial expression recognition using deep covariance descriptors. The solution is based on the idea of encoding local and global Deep Convolutional Neural Network (DCNN) features extracted from still images, in compact local and global covariance descriptors. The space geometry of the covariance matrices is that of Symmetric Positive Definite (SPD) matrices. By conducting the classification of static facial expressions using Support Vector Machine (SVM) with a valid Gaussian kernel on the SPD manifold, we show that deep covariance descriptors are more effective than the standard classification with fully connected layers and softmax. Besides, we propose a completely new and original solution to model the temporal dynamic of facial expressions as deep trajectories on the SPD manifold. As an extension of the classification pipeline of covariance descriptors, we apply SVM with valid positive definite kernels derived from global alignment for deep covariance trajectories classification. By performing extensive experiments on the Oulu-CASIA, CK+, and SFEW datasets, we show that both the proposed static and dynamic approaches achieve state-of-the-art performance for facial expression recognition outperforming many recent approaches.Comment: A preliminary version of this work appeared in "Otberdout N, Kacem A, Daoudi M, Ballihi L, Berretti S. Deep Covariance Descriptors for Facial Expression Recognition, in British Machine Vision Conference 2018, BMVC 2018, Northumbria University, Newcastle, UK, September 3-6, 2018. ; 2018 :159." arXiv admin note: substantial text overlap with arXiv:1805.0386

Visualization to compare karate motion captures

Multi-dimensional time series from motion capture (MoCap) provide a rich source of data for human motion analysis, yet they are difficult to process and compare. We address MoCap data related to Karate katas, containing predefined sequences of movements, executed independently by several subjects with different timing and speed. We propose a combination of signal processing and data visualization techniques to analyze the misalignment between data from different subjects. We present a web app that implements this proposal, providing a visual comparison of time series, based on Dynamic Time Warping.XVII Workshop de Computación Gráfica.Red de Universidades con Carreras en Informátic

Times series averaging from a probabilistic interpretation of time-elastic kernel

At the light of regularized dynamic time warping kernels, this paper reconsider the concept of time elastic centroid (TEC) for a set of time series. From this perspective, we show first how TEC can easily be addressed as a preimage problem. Unfortunately this preimage problem is ill-posed, may suffer from over-fitting especially for long time series and getting a sub-optimal solution involves heavy computational costs. We then derive two new algorithms based on a probabilistic interpretation of kernel alignment matrices that expresses in terms of probabilistic distributions over sets of alignment paths. The first algorithm is an iterative agglomerative heuristics inspired from the state of the art DTW barycenter averaging (DBA) algorithm proposed specifically for the Dynamic Time Warping measure. The second proposed algorithm achieves a classical averaging of the aligned samples but also implements an averaging of the time of occurrences of the aligned samples. It exploits a straightforward progressive agglomerative heuristics. An experimentation that compares for 45 time series datasets classification error rates obtained by first near neighbors classifiers exploiting a single medoid or centroid estimate to represent each categories show that: i) centroids based approaches significantly outperform medoids based approaches, ii) on the considered experience, the two proposed algorithms outperform the state of the art DBA algorithm, and iii) the second proposed algorithm that implements an averaging jointly in the sample space and along the time axes emerges as the most significantly robust time elastic averaging heuristic with an interesting noise reduction capability. Index Terms-Time series averaging Time elastic kernel Dynamic Time Warping Time series clustering and classification