Hongjing Lu, Tungyou Lin, Alan Lee, Luminita Vese, Alan L. Yuille
It has been speculated that the human motion system combines noisy measurements with prior expectations in an optimal, or rational, manner. The basic goal of our work is to discover experimentally which prior distribution is used. More specifically, we seek to infer the functional form of the motion prior from the performance of human subjects on motion estimation tasks. We restricted ourselves to priors which combine three terms for motion slowness, first-order smoothness, and second-order smoothness. We focused on two functional forms for prior distributions: L2-norm and L1-norm regularization corresponding to the Gaussian and Laplace distributions respectively. In our first experimental session we estimate the weights of the three terms for each functional form to maximize the fit to human performance. We then measured human performance for motion tasks and found that we obtained better fit for the L1-norm (Laplace) than for the L2-norm (Gaussian). We note that the L1-norm is also a better fit to the statistics of motion in natural environments. In addition, we found large weights for the second-order smoothness term, indicating the importance of high-order smoothness compared to slowness and lower-order smoothness. To validate our results further, we used the best fit models using the L1-norm to predict human performance in a second session with different experimental setups. Our results showed excellent agreement between human performance and model prediction -- ranging from 3\% to 8\% for five human subjects over ten experimental conditions -- and give further support that the human visual system uses an L1-norm (Laplace) prior.