| Recognition of specific patterns and signatures in images has long been of interest. Powerful techniques exist for detection and classification, but are defeated by commonly observed changes and variations in the pattern. These variations include translation and scale changes. Translation and scaling are well understood in a mathematical sense and transformations exist such that, when applied to an image, the result is invariant to these disturbances. Hence, methods may be designed wherein these effects are absent in the resultant representations. The magnitude of the Mellin transform is a well known method for providing scale invariance in a manner similar to the time shift invariance provided by the magnitude of the Fourier transform. A special case of the Mellin transform, termed the scale transform, has been shown by Cohen to have many desirable properties in treating scale as a physical attribute analogous to frequency. In this dissertation, discrete implementations of the scale transform are developed suitable for computer implementation.; A new technique for pattern recognition invariant to compression and dilation is presented which uses scale and translation invariant representations (STIRs) as one step of a pattern recognition process. A novel feature extraction method then identifies features of the STIRs orthogonal to noise variation. This is followed by a detection approach which exploits these features to detect desired patterns in noise. By explicitly modeling the variation due to noninteger scaling factors and sub-pixel translation, strong discrimination between similar patterns is achieved. Using the orthogonal features of the invariant representations, several methods are shown to classify well. Examples of pattern recognition are presented using time-frequency distributions of marine mammal sounds and image bitmaps of words and characters.; A novel variant of the Mellin transform termed the duoscale transform, is introduced. It is shown to be conducive to the solution of Euler-Cauchy differential equations. The duoscale transform has a duality property of multiplicative convolution similar to the convolution property available with the Fourier transform. Using this property, the concept of scale filtering is developed and examples of filtering by duoscale content are presented. |
