A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition (vol 172, pg 181, 1999)

A new sliced orthogonal nonlinear generalized (SONG) decomposition for imag e processing can be useful for image representation. We examine the use of this representation for two-class pattern recognition in the presence of no ise. The SONG correlation is defined and expressed by means of a diagonal m atrix representation. Common linear correlation, binary correlation and mor phological correlation, among others, can be described in terms of the SONG representation. This matrix allows the investigation of some interesting p roperties of auto-correlation and cross-correlation operations. The discrim ination capability and noise robustness of the SONG correlation are investi gated and compared with those of other methods. Experimental results establ ish the stability of the SONG process at Gaussian noise levels high enough for the other methods to break down. Although the pattern recognition metho d is nonlinear, the elementary correlation operations are linear and so I-h e method is suitable for optical implementation. (C) 2000 Elsevier Science B.V. All rights reserved.