Correlation, functional analysis and optical pattern recognition
Correlation integrals have played a central role in optical pattern recognition. The success of correlation, however, has been limited. What is needed is a mathematical operation more complex than correlation. Suitably complex operations are the functionals defined on the Hilbert space of Lebesgue square integrable functions. Correlation is a linear functional of a parameter. In this paper, we develop a representation of functionals in terms of inner products or equivalently correlation functions. We also discuss the role of functionals in neutral networks. Having established a broad relation of correlation to pattern recognition, we discuss the computation of correlation functions using acousto-optics.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 10133905
- Report Number(s):
- SAND--94-0733C; CONF-9406128--1; ON: DE94008431; BR: GB0103012
- Country of Publication:
- United States
- Language:
- English
Similar Records
Digital and optical shape representation and pattern recognition
Pattern recognition, inner products and correlation filters