A Complete Set of Translation Invariants Based on the Cyclic Correlation Property of the Generalized Circular Transforms

Nonlinear spatial transforms are established in feature extraction and pattern recognition. This paper describes a method for calculating the cyclic crosscorrelation with the help of generalized circular transforms. Based on the crosscorrelation property, a nonlinear translation invariant autocorrelation and a complete set of simplified translation invariants, called -spectrum, can G̃ be deduced. Moreover, the generalized circular transforms can now be interpreted as signal dependent transforms. In addition we will demonstrate how the G̃ -spectrum can significantly extend the pattern separability properties for transforms with low computeral complexity.