The world is composed of objects, the ground, and the sky. Visual perception of objects requires solving two fundamental challenges: 1) segmenting visual input into discrete units and 2) tracking identities of these units despite appearance changes due to object deformation, changing perspective, and dynamic occlusion. Current computer vision approaches to segmentation and tracking that approach human performance all require learning, raising the question, Can objects be segmented and tracked without learning? Here, we show that the mathematical structure of light rays reflected from environment surfaces yields a natural representation of persistent surfaces, and this surface representation provides a solution to both the segmentation and tracking problems. We describe how to generate this surface representation from continuous visual input and demonstrate that our approach can segment and invariantly track objects in cluttered synthetic video despite severe appearance changes, without requiring learning.

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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.

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