Abstract-Moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance. The notion of complex moments is introduced as a simple and straightforward way to derive moment invariants. Through this relation, properties of complex moments are used to characterize moment invariants. Aspects of information loss, suppression, and redundancy encountered in moment invariants are investigated and significant results are derived. The behavior of moment invariants in the presence of additive noise is also described.

This paper provides a brief introduction to forecasting in financial markets with emphasis on commodity futures and foreign exchange. We describe the basic approaches to forecasting, and discuss the noisy nature of financial data. Using neural networks as a learning paradigm, we describe different techniques for choosing the inputs, outputs, and error function. We also describe the learning from hints technique that augments the standard learning from examples method. We demonstrate the use of hints in foreign-exchange trading of the U.S. Dollar versus the British Pound, the German Mark, the Japanese Yen, and the Swiss Franc, over a period of 32 months. The paper does not assume a background in financial markets.

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Abstract-The role of moments in image normalization and invariant pattern recognition is addressed. The classical idea of the principal axes is analyzed and extended to a more general definition. The relationship between moment-based normalization, moment invariants, and circular harmonics is established. Invariance properties of moments, as opposed to their recognition properties, are identified using a new class of normalization procedures. The application of moment-based normalization in pattern recognition is demonstrated by experiment.