## Cascaded Linear Shift-Invariant Processors in Optical Pattern Recognition

Applied Optics, Vol. 40, Issue 23, pp. 3843-3849 (2001)

http://dx.doi.org/10.1364/AO.40.003843

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### Abstract

We study a cascade of linear shift-invariant processing modules (correlators), each augmented with a nonlinear threshold as a means to increase the performance of high-speed optical pattern recognition. This configuration is a special class of multilayer, feed-forward neural networks and has been proposed in the literature as a relatively fast best-guess classifier. However, it seems that, although cascaded correlation has been proposed in a number of specific pattern recognition problems, the importance of the configuration has been largely overlooked. We prove that the cascaded architecture is the exact structure that must be adopted if a multilayer feed-forward neural network is trained to produce a shift-invariant output. In contrast with more generalized multilayer networks, the approach is easily implemented in practice with optical techniques and is therefore ideally suited to the high-speed analysis of large images. We have trained a digital model of the system using a modified backpropagation algorithm with optimization using simulated annealing techniques. The resulting cascade has been applied to a defect recognition problem in the canning industry as a benchmark for comparison against a standard linear correlation filter, the minimum average correlation energy (MACE) filter. We show that the nonlinear performance of the cascade is a significant improvement over that of the linear MACE filter in this case.

© 2001 Optical Society of America

**OCIS Codes**

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(070.4560) Fourier optics and signal processing : Data processing by optical means

(070.5010) Fourier optics and signal processing : Pattern recognition

(100.1160) Image processing : Analog optical image processing

**Citation**

Stuart Reed and Jeremy Coupland, "Cascaded Linear Shift-Invariant Processors in Optical Pattern Recognition," Appl. Opt. **40**, 3843-3849 (2001)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-23-3843

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