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Proceedings Paper

Quadratic correlation filters for optical correlators
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Paper Abstract

Linear correlation filters have been implemented in optical correlators and successfully used for a variety of applications. The output of an optical correlator is usually sensed using a square law device (such as a CCD array) which forces the output to be the squared magnitude of the desired correlation. It is however not a traditional practice to factor the effect of the square-law detector in the design of the linear correlation filters. In fact, the input-output relationship of an optical correlator is more accurately modeled as a quadratic operation than a linear operation. Quadratic correlation filters (QCFs) operate directly on the image data without the need for feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required to detect peaks in the outputs of multiple linear filters, but choosing a winner among them is an error prone task. In contrast, all channels in a QCF work together to optimize the same performance metric and produce a combined output that leads to considerable simplification of the post-processing. In this paper, we propose a novel approach to the design of quadratic correlation based on the Fukunaga Koontz transform. Although quadratic filters are known to be optimum when the data is Gaussian, it is expected that they will perform as well as or better than linear filters in general. Preliminary performance results are provided that show that quadratic correlation filters perform better than their linear counterparts.

Paper Details

Date Published: 6 August 2003
PDF: 11 pages
Proc. SPIE 5106, Optical Pattern Recognition XIV, (6 August 2003); doi: 10.1117/12.497581
Show Author Affiliations
Abhijit Mahalanobis, Lockheed Martin (United States)
Robert R. Muise, Lockheed Martin (United States)
Bhagavatula V. K. Vijaya Kumar, Carnegie Mellon Univ. (United States)

Published in SPIE Proceedings Vol. 5106:
Optical Pattern Recognition XIV
David P. Casasent; Tien-Hsin Chao, Editor(s)

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