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Nonparametric Data Analysis on the Space of Perceived Colors

Moving around in a 3D world, requires the visual system of a living individual to rely on three channels of image recognition, which is done through three types of retinal cones. Newton, Grasmann, Helmholz and Schr$\ddot{o}$dinger laid down the basic assumptions needed to understand colored vision. Such concepts were furthered by Resnikoff, who imagined the space of perceived colors as a 3D homogeneous space. This article is concerned with perceived colors regarded as random objects on a Resnikoff 3D homogeneous space model. Two applications to color differentiation in machine vision are illustrated for the proposed statistical methodology, applied to the Euclidean model for perceived colors.