A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition

A new sliced orthogonal nonlinear generalized (SONG) decomposition for image processing can be useful for image representation. We examine the use of this representation for two-class pattern recognition in the presence of noise. The SONG correlation is defined and expressed by means of a diagonal matrix representation. Common linear correlation, binary correlation and morphological correlation, among others, can be described in terms of the SONG representation. This matrix allows the investigation of some interesting properties of auto-correlation and cross-correlation operations. The discrimination capability and noise robustness of the SONG correlation are investigated and compared with those of other methods. Experimental results establish the stability of the SONG process at Gaussian noise levels high enough for the other methods to break down. Although the pattern recognition method is nonlinear, the elementary correlation operations are linear and so the method is suitable for optical implementation. © 1999 Elsevier Science B.V. All rights reserved.