Motion and Appearance Nonparametric Joint Entropy for Video Segmentation

This paper deals with video segmentation based on motion and spatial information. Classically, the motion term is based on a motion compensation error (MCE) between two consecutive frames. Defining a motion-based energy as the integral of a function of the MCE over the object domain implicitly results in making an assumption on the MCE distribution: Gaussian for the square function and, more generally, parametric distributions for functions used in robust estimation. However, these assumptions are not necessarily appropriate. Instead, we propose to define the energy as a function of (an estimation of) the MCE distribution. This function was chosen to be a continuous version of the Ahmad-Lin entropy approximation, the purpose being to be more robust to outliers inherently present in the MCE. Since a motion-only constraint can fail with homogeneous objects, the motion-based energy is enriched with spatial information using a joint entropy formulation. The resulting energy is minimized iteratively using active contours. This approach provides a general framework which consists in defining a statistical energy as a function of a multivariate distribution, independently of the features associated with the object of interest. The link between the energy and the features observed or computed on the video sequence is then made through a nonparametric, kernel-based distribution estimation. It allows for example to keep the same energy definition while using different features or different assumptions on the features.