Dierent signal realizations generated from a given source may not appear the same. Time shifts, frequency shifts, and scales are among the signal variations commonly encountered. Time-frequency distributions (TFDs) covariant to time and frequency shifts and scale changes reect these variations in a predictable manner. Based on such TFDs, representations invariant to these signal distortions are possible. Presented here are two approaches for discriminating between signal classes where within class translation and scale variation occur. The rst method uses an auto-correlation followed by a scale transform to achieve the invariances. The second method treats the TFD as a twodimensional probability density function and applies a transformation that removes the mean and variance to provide the shift and scale invariance. Each method employs discrimination mechanisms to yield powerful results.
We present a method for detection and classification of a spatial pattern in noise contaminated binary images which is based on performing subspace decomposition on a nonnegative definite matrix of higher order moments of the image. We introduce a method which uses normalized power moments or ascending factorial moments as descriptors. While the set of p t h order factorial moments are in one-to-one correspondence with the set of p t h order power moments, the computation of factorial moments is much more numerically stable than the power moments. Indeed, using factorial moments we are able to implement pattern classifiers with over 30% more moment descriptors. We illustrate these techniques for word classification in binary document images.
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