Dynamical Regularity for Action Analysis

An activity can be seen as a resultant of coordinated movement of body joints and their respective interdependencies to achieve a goal-directed task. This idea is further supported by Johansson’s demonstrations that visual perception of the entire human body motion can be represented by a few bright spots which holistically describe the motion of important joints. Traditional dynamical modeling approaches usually operate on the level of individual joints of the human body, lacking any information about the interdependencies between joints. We propose a novel approach for dynamical modeling by extending conventional ideas to quantify the interdependencies between body joints. Towards this end, we propose a new approach – approximate entropy-based feature representation to model the dynamics in human movement by quantifying dynamical regularity. In this paper, we utilize the algorithmic framework of [3] for estimating approximate entropy from time series data and extend it to model the dynamics in human activities for applications such as temporal segmentation and fine-grained quality assessment of actions. Approximate entropy is a statistical tool proposed by Pincus [3, 4] for quantification of regularity of time series data and system complexity, based on the log-likelihood of repetitions of patterns of length m being close within a defined tolerance window that will exhibit similar characteristics as patterns of length (m+1) [2, 3]. It assigns a non-negative number to time series data, with lower values for predictable (ordered) signals and higher values for signals with increased irregularity (or randomness). It is defined using three parameters: embedding dimension (m), radius (r), and time delay (τ). Here, m represents the length of pattern (also called as embedding vector) in the data which is checked for repeatability, τ is selected so that the components of the embedding vector are sufficiently independent, and r is used for the estimation of local probabilities. Given N data samples {x1,x2, . . . ,xN}, we can define embedding vector x(i) as,