A novel procedure is presented to construct image-domain filters (receptive fields) that directly recover local motion and shape parameters. These receptive fields are derived from training on image deformations that best discriminate between different shape and motion parameters. Beginning with the construction of 1D receptive fields that detect local surface shape and motion parameters within cross sections, we show how the recovered shape and motion model parameters are sufficient to produce local estimates of time to collision. In general, filter pairs (receptive fields) can be synthesized to perform or detect specific image deformations. At the heart of the method is the use of a matrix to represent image deformation correspondence between individual pixels of two views of a surface. The image correspondence matrix can be decomposed using singular value decomposition to yield a pair of corresponding receptive fields that detect image changes due to the deformation of interest.

This paper introduces a monocular optical flow algorithm that has been shown to perform well at nearly real-time frame rates (4 FPS on a 100 MHz SGI Indy workstation), using natural image sequences. The system is completely bottom-up, using pixel region-matching techniques. A coordinated gradient descent method is broken down into two stages: pixel region matching error measures are locally minimized and flow field consistency constraints apply nonlinear adaptive diffusion, causing confident measurements to influence their less confident neighbors. Convergence is usually accomplished with one iteration for an image frame pair. Temporal integration predicts upcoming flow fields. The algorithm is designed for flexibility: large displacements are tracked as easily as sub-pixel displacements, and higher-level information can feed flow field predictions into the measurement process.