The Function Space of an Activity

An activity consists of an actor performing a series of actions in a pre-defined temporal order. An action is an individual atomic unit of an activity. Different instances of the same activity may consist of varying relative speeds at which the various actions are executed, in addition to other intra- and inter- person variabilities. Most existing algorithms for activity recognition are not very robust to intra- and inter-personal changes of the same activity, and are extremely sensitive to warping of the temporal axis due to variations in speed profile. In this paper, we provide a systematic approach to learn the nature of such time warps while simultaneously allowing for the variations in descriptors for actions. For each activity we learn an #145;average #146; sequence that we denote as the nominal activity trajectory. We also learn a function space of time warpings for each activity separately. The model can be used to learn individualspecific warping patterns so that it may also be used for activity based person identification. The proposed model leads us to algorithms for learning a model for each activity, clustering activity sequences and activity recognition that are robust to temporal, intra- and inter-person variations. We provide experimental results using two datasets.