This paper presents the results of combining (i) theoretical analysis regarding connections between the orientation selectivity and the elongation of receptive fields for the affine Gaussian derivative model with (ii) biological measurements of orientation selectivity in the primary visual cortex to investigate if (iii) the receptive fields can be regarded as spanning a variability in the degree of elongation.

From an in-depth theoretical analysis of idealized models for the receptive fields of simple and complex cells in the primary visual cortex, we established that the orientation selectivity becomes more narrow with increasing elongation of the receptivefields. Combined with previously established biological results, concerning broad vs. sharp orientation tuning of visual neurons in the primary visual cortex, as well as previous experimental results concerning distributions of the resultant of the orientation selectivity curves for simple and complex cells, we show that these results are consistent with the receptive fields spanning a variability over the degree of elongation of the receptive fields. We also show that our principled theoretical model for visual receptive fields leads to qualitatively similar types of deviations from a uniform histogram of the resultant descriptor of the orientation selectivity curves for simple cells, as can be observed in the results from biological experiments.

To firmly determine if the underlying working hypothesis, regarding the receptive fields spanning a variability in the degree of elongation, would truly hold for the receptive fields in the primary visual cortex of higher mammals, we formulate a set of testable predictions, that can be used for investigate this property experimentally, and, if applicable, then also characterize if such a variability would, in a structured way, be related to the pinwheel structure in the visual cortex.