Image surface predicates and the neural encoding of two-dimensional signal variations

Empirical evidence from both psychology and physiology stresses the importance of inherently two-dimensional signals and corresponding operations in vision. Examples of this are the existence of "bug-detectors" , hypercomplex and dot-responsive cells, the occurence of contour illusions, and interactions of patterns with clearly separated orientations. These phenomena can not be described, and have been largely ignored, by common theories of size and orientation selective channels. The reason for this is shown to be located at the heart of the theory of linear systems: their one-dimensional eigenfunctions and the "or"-like character of the superposition principle. Consequently, a nonlinear theory is needed. We present a first approach towards a general framework for the description of 2D-signals and 2D-cells in biological vision.