Multi-scale conditional transition map: Modeling spatial-temporal dynamics of human movements with local and long-term correlations

This paper presents a novel approach to modeling the dynamics of human movements with a grid-based representation. The model we propose, termed as Multi-scale Conditional Transition Map (MCTMap), is an inhomogeneous HMM process that describes transitions of human location state in spatial and temporal space. Unlike existing work, our method is able to capture both local correlations and long-term dependencies on faraway initiating events. This enables the learned model to incorporate more information and to generate an informative representation of human existence probabilities across the grid map and along the temporal axis for intelligent interaction of the robot, such as avoiding or meeting the human. Our model consists of two levels. For each grid cell, we formulate the local dynamics using a variant of the left-to-right HMM, and thus explicitly model the exiting direction from the current cell. The dependency of this process on the entry direction is captured by employing the Input-Output HMM (IOHMM). On the higher level, we introduce the place where the whole trajectory originated into the IOHMM framework forming a hierarchical input structure to capture long-term dependencies. The capabilities of our method are verified by experimental results from 10 hours of data collected in an office corridor environment.