A modified binary synthetic discriminant function filter designed to recognize objects over a range of rotated views has been verified on a laboratory optical correlator. A binary synthetic discriminant function filter has been previously described that will produce a specified correlation response for a set of training images. [See D. A. Jared and D. J. Ennis, "Inclusion of Filter Modulation in Synthetic-Discriminant-Function Construction," Appl. Opt. 28, 232–239 (1989).] In the filter design, the modulation characteristics of the device onto which the filter is mapped are included in the synthesis equations. The system of nonlinear equations is then solved using an iteration procedure based on the Newton-Raphson algorithm. The development of the filter-SDF (fSDF) method was driven by the practical concern to make currently available spatial light modulators with limited modulation capabilities functional for distortion invariant pattern recognition. This technique is used to synthesize filters for a binary magnetooptic spatial light modulator (MOSLM), the Sight-MOD produced by Semetex. Two MOSLMs are used in the laboratory correlator, one in the filter plane and one in the input plane. We demonstrate that a single filter produces equal correlation peaks for a sample object (a Shuttle Orbiter in these tests) over in-plane and out-of-plane rotation ranges up to 75°. The correlator is able to track dynamically the shuttle as it moves along a curved path across the input field. Views of the object in between those in the training set are also recognized when training images are sufficiently close in angle (~5° apart).
Max B. Reid, Paul W. Ma, John D. Downie, and Ellen Ochoa, "Experimental verification of modified synthetic discriminant function filters for rotation invariance," Appl. Opt. 29, 1209-1214 (1990)