Learning color receptive fields and color differential structure

In this paper we study the role of brain plasticity, and investigate the emergence and self-emergence of receptive fields from scalar and color natural images by principal component analysis of image patches. We describe the classical experiment on localized PCA on center-surround weighted patches of natural scalar images. The resulting set turns out to show great similarity to Gaussian spatial derivatives, and exhibits steerability behavior. We then relate the famous experiment by Blakemore of training a cat with only visual horizontal bar information with PCA analysis of images with primarily unidirectional structure. PCA is performed for patches of RGB natural color images. The resulting profiles resemble spatio-spectral operators extracting color differential structure and shape. We discuss how spatio-spectral Gaussian derivative operators along the wavelength dimension can be modeled, originally proposed by Koenderink, and based on Hering's opponent color theory. The discussion puts the PCA findings in the perspective of multi-scale Gaussian differential geometry, multi-orientation sub-Riemannian geometry, and PCA on affinity matrices for contextual models.