New approach of higher order textural parameters for image classification using statistical methods

Many researchers have demonstrated that textural data increase the precision of image classification when they are combined with grey level information. However, textural parameters of order two take too long computation time. The problem is more complex when one must compute higher order textural parameters, which however can considerably improve the precision of a classification. In this work, we propose a new formulation for the calculation of statistical textural parameters. The principle consists in reducing the calculation of a n-summation of type $$ \sum^{L-1}_{i_{0}=0}\sum^{L-1}_{i_{1}=0}\sum^{L-1}_{i_{2}=0} \cdots\sum^{L-1}_{i_{n-1}=0}\psi[i_{0},i_{1},\cdots,i_{(n-1)},P_{i_{0},i_{1},\cdots i_{n-1}}] $$ generally used in the evaluation of textural parameters, to a double summation of type \( \sum\nolimits_{p=0}^{Wx}\sum\nolimits_{q=0}^{Wy}X(p,q)\) where L is the dynamic of grey levels (number of quantification levels) in the image, ( \( P_{i_{0},i_{1},\cdots i_{n-1}}\) ) is the occurrence frequency matrix (co-occurrence matrix in the case of order two parameters) and W x (respectively W y ) is the width (respectively the height) of the image window. This method produces the same results as the classical method, but it’s about L n-1 times faster than the classical method and a gain of L n of memory space is obtained, where n is the order of the textural parameter.