Modeling heading and path perception from optic flow in the case of independently moving objects

Humans are usually accurate when estimating heading or path from optic flow, even in the presence of independently moving objects (IMOs) in an otherwise rigid scene. To invoke significant biases in perceived heading, IMOs have to be large and obscure the focus of expansion (FOE) in the image plane, which is the point of approach. For the estimation of path during curvilinear self motion no significant biases were found in the presence of IMOs. What makes humans robust in their estimation of heading or path using optic flow? We derive analytical models of optic flow for linear and curvilinear self-motion using geometric scene models. Heading biases of a linear least squares method, which builds upon these analytical models, are large, larger than those reported for humans. This motivated us to study segmentation cues that are available from optic flow. We derive models of accretion/deletion, expansion/contraction, acceleration/deceleration, local spatial curvature, and local temporal curvature, to be used as cues to segment an IMO from the background. Integrating these segmentation cues into our method of estimating heading or path now explains human psychophysical data and extends, as well as unifies, previous investigations. Our analysis suggests that various cues available from optic flow help to segment IMO sand, thus, make humans 'heading and path perception robust in the presence of such IMOs.