A novel approach is presented to neural network computation of three-dimensional rigid motion from noisy two-dimensional image flow. It is shown that the process of 3-D interpretation of image flow can be viewed as a linear signal transform. The elementary signals of this linear transform are the 2-D vector fields of the six infinitesimal generators of the 3-D Euclidean group. This transform can be performed by a neural network. Results are also reported of neural network simulations for the 3-D interpretation of image flow and a comparison of the performance of this approach with that using conventional methods. Computer simulation results verify the Lie-group-based neural network approach to three-dimensional motion perception.