Translational Decomposition of Flow Fields

We introduce a low-level description of image motion called the local translational decomposition (LTD). This description associates with image features or small image areas, a three-dimensional unit vector describing the direction of motion of the corresponding environmental feature or small surface area. The local translational decomposition is derived by applying a procedure for processing purely translational motion to small overlapping image areas. This intermediate representation of motion considerably simpli es the inference of motion parameters for ego-motion and can support qualitative inferences for nonrigid motions. We rst show how to compute the LTD from optic ow elds and then show how the LTD is used to recover the parameters of rigid body motions. We present three cases for which the recovery of motion parameters is particularly robust: motion constrained to a determined plane (the normal to the plane is known); motion constrained to an undetermined plane (the normal to the plane is not known); arbitrary motion relative to locally planar surfaces. We then discuss techniques for computing the local translational decomposition directly from real image sequences without the initial extraction of optic ow and other areas for future work.