An Affine Optical Flow Model for Dynamic Surface Reconstruction

In this paper we develop a differential model for simultaneous estimation of geometry and dynamics of a surface patch. To do so we combine a surface patch model in local 3D coordinates, a pinhole camera grid model and a brightness change model analogous to the brightness constancy constraint equation for optical flow. It turns out to be an extension of the well known affine optical flow model to higher dimensional data sets. Each of the translational and affine components of the optical flow is a term consisting of a mixture of surface patch parameters like its depth, slope, velocities etc. We evaluate the model by comparing estimation results using a simple local estimation scheme to available ground-truth. This simple estimation scheme already allows to get results in the same accuracy range one can achieve using range flow, i.e. a model for the estimation of 3D velocities of a surface point given a measured surface geometry. Consequently the new model allows direct estimation of additional surface parameters range flow is not capable of, without loss of accuracy in other parameters. What is more, it allows to design estimators coupling shape and motion estimation which may yield increased accuracy and/or robustness in the future.