A receptive field constitutes a region in the visual field where a visual cell responds to visual stimuli. The subject of this talk is to present a theoretical model for what types of receptive field profiles could be regarded as natural for an idealized vision system, given a set of natural symmetry requirements on the first stages of visual processing that reflect symmetry properties of the outside world. Specifically, it will be shown that a set of families of receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives and closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition and shape estimation. Hence, this so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. Interestingly, there are very close similarities between several of the receptive field profiles obtained from scale-space theory and receptive field profiles recorded from biological vision. In this talk, I will describe the basic structure of some of these necessity results concerning the mathematical foundation and indicate how this theory could be used when studying and modelling biological vision.
Some of the material to be presented will be based on the following recent article in Journal of Mathematical Imaging and Vision
http://www.csc.kth.se/~tony/abstracts/Lin10-GenGaussScSp.html
The talk will be at an overview level and will not go into the formal proofs.
