The Study Of Second Order Statistics Of Natural Images

This thesis is based on the work presented in the paper Provenzi et al.,2016[1],and is its continuation.The paper studied the second order statistics of natural image.More specifically,it studied around covariance of pixels.In a big statistical picture,every pixel in RGB image domain is modeled as random variable,with correlation to each other.What principal component analysis teaches us is,through analyzing covariance of a set of random variables,we can find out a common orthogonal basis for all of the original random variable,which are,in fact,the eigenvectors of the covariance matrix.This provides us a possible cdecomposition of natural image.The paper Provenzi et al.,2016[1]has found out the explicit form of the eigenvectors,with assuming the covariance matrices of all possible pixel pairs in RGB image commute.The paper has also done the experiments,and found out that the covariance matrices almost commute for raw RGB image.Starting from this point,this paper wants to find a good transformation for raw RGB image,after which,the covariance matrices exhibit better commutativity.I mainly focused on one transformation= Michaelis-Menten(also known as Naka-Rushton)equation,Iu?/(Iu?+mu?),which models the photochemical transduct,ion from radiance to action potential performed by retinal photoreceptors and plays a major role in the adaptation mechanisms of human vision.And I adapted two techniques,analysis of covariance and joint diagonalization,to quantify the commutativity of the covariance matrices.Also,I proposed a composite measurement,penalized F-statistic,to take noise into account in order not to select trivial solution,which is piece wise constant transformation.With the help of this penalized F-statistic,I found out that the transformation increases the commutativity more around ?= 0.2 and 0.3.