Comparison of second and third order statistics based adaptive filters for texture characterization

In the framework of parametric texture modeling, a question arises: are adaptive approaches based on higher order statistics (HOS) more appropriate to characterize texture models than those based on second order statistics (SOS)? In order to give some responses to this question, we have compared two fast adaptive filters for texture characterization: the 2-D FLRLS filter (2-D fast lattice recursive least square) based on SOS only and the 2-D OLRIV filter (2-D overdetermined lattice recursive instrumental variable) based on third order statistics. Extensive experiments to study the characterization performance of each filter are presented and interpreted. They show that the 2-D FLRLS filter provides a very good performance for texture characterization, even with important noise. Furthermore, the third order based algorithm presents higher variance than the second order one. We believe that for 2-D adaptive modeling, there is no advantage to using a HOS based adaptive algorithm for characterizing textures