Gauge invariant framework for trajectories analysis

Hassen Drira (1) , Barbara Tumpach (2) , Mohamed Daoudi (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 LPP - Laboratoire Paul Painlevé - UMR 8524

In this paper we focus on problems that deal with comparison of shapes of trajectories. One motivation comes from action recognition where features extracted from video (or RGB Depth video) frames are naturally represented by elements of nonlinear manifolds, and where temporal evolutions of an action can be modeled by trajectories on those manifolds. How- ever, as mentionned by [11], [14] and [7], the execution rate (velocity) of activities may often vary. It follows that, without the execution invariance, two identical actions can be viewed as very different trajectories. Typical approaches for accounting for variations in execution rate are either directly based on the dynamic time warping (DTW) algorithm or some variation of this algorithm. One promising idea is to formulate the features motion as trajectories. Matikainen et al. [4] present a method for using the trajectories of tracked feature points in a bag of words paradigm for video action recognition. Despite of the promising results obtained, the authors do not take into account the geometric information of the trajectories. More recently, in the case of human skeleton in RGB-Depth images, Devianne et al. [2] propose to formulate the actions recognition as the problem of computing a distance between trajectories generated by the joints moving during the action. An action is a parameterized path on the shape space of the human skeleton. Similar to the ideas of Devianne et al., Su et al. [8] propose a metric which takes into account time-warping on a Riemannian manifold. They propose a metric, which allows the regitration of trajectories and compute statistics of the trajectories. Su et al. [9] apply this framework to the problem of visual speech recognition. All these approachs require a registration of trajectories. In the present paper, we propose a new theoretical framework which uses the shape information of trajectories. The main contributions of this paper are: • The proposed framework is independent of time-re-parameterization of trajectories in $R3$. • A new rate-invariant metric on the shape space of trajectories is proposed. No trajec- tories registration is required. • We demonstrate the use of this framework theory in two computer vision applications. The rest of this paper is organized as follows. Section 2 presents the gauge invariant framework for comparing shapes. Section 3 presents applications of the proposed approach to action recognition.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Hassen Drira, Barbara Tumpach, Mohamed Daoudi. Gauge invariant framework for trajectories analysis. DIFFCV workshop, 2015, Swansea, UK, United Kingdom. ⟨10.5244/C.29.DIFFCV.6⟩. ⟨hal-01534886⟩