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.

Extrinsic Kernel Ridge Regression Classifier for Planar Kendall Shape Space

Kernel methods have had great success in the statistics and machine learning community. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on manifold due to the non-Euclidean geometry. In this paper, motivated by the extrinsic framework of manifold-valued data analysis, we propose two types of new kernels on planar Kendall shape space $\Sigma_2^k$, called extrinsic Veronese Whitney Gaussian kernel and extrinsic complex Gaussian kernel. We show that our approach can be extended to develop Gaussian like kernels on any embedded manifold. Furthermore, kernel ridge regression classifier (KRRC) is implemented to address the shape classification problem on $\Sigma_2^k$, and their promising performances are illustrated through the real dataset.