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Orientation selectivity properties for the affine Gaussian derivative and the affine Gabor models for visual receptive fields.
J Comput Neurosci
January 2025
Computational Brain Science Lab, Division of Computational Science and Technology, KTH Royal Institute of Technology, SE-100 44, Stockholm, Sweden.
This paper presents an in-depth theoretical analysis of the orientation selectivity properties of simple cells and complex cells, that can be well modelled by the generalized Gaussian derivative model for visual receptive fields, with the purely spatial component of the receptive fields determined by oriented affine Gaussian derivatives for different orders of spatial differentiation. A detailed mathematical analysis is presented for the three different cases of either: (i) purely spatial receptive fields, (ii) space-time separable spatio-temporal receptive fields and (iii) velocity-adapted spatio-temporal receptive fields. Closed-form theoretical expressions for the orientation selectivity curves for idealized models of simple and complex cells are derived for all these main cases, and it is shown that the orientation selectivity of the receptive fields becomes more narrow, as a scale parameter ratio , defined as the ratio between the scale parameters in the directions perpendicular to vs.
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