New training method for linear separable threshold Boolean filters

Octavian Valeriu Sarca; Jaakko T. Astola; Edward R. Dougherty

doi:10.1117/12.279647

14 October 1997 New training method for linear separable threshold Boolean filters

Octavian Valeriu Sarca, Jaakko T. Astola, Edward R. Dougherty

Proceedings Volume 3167, Statistical and Stochastic Methods in Image Processing II; (1997) https://doi.org/10.1117/12.279647
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

The key point of the LS-TBF (Linear Separable Threshold Boolean Filter) design is the training of the Linear Separable Boolean Function (LSBF). The standard LS-TBF design method approximates the LSBF with a linear function. This procedure leads to a closed form expression of the filter weights but it does not provide the optimal solution. Other LSBF training algorithms are not really applicable in filter design because they either require too many iterations or do not offer a reasonable stability. This paper introduces a new gradient- type method applicable for LS-TBF design. The proposed algorithm is able to reach the optimal solution in very few iterations. In order to provide high convergence rate together with stability the method uses multiple gain factors at the same time. This way the proposed algorithm simulates a continuous-time implementation of the steepest-descent method. While the known training methods use many iterations the proposed one minimizes the number of iterations but increases the amount of calculations at each step. Consequently the computational effort spent for additional operations like disk access, windowing and thresholding becomes negligible and also the overall effort is very much reduced. Among other advantages the proposed training algorithm is very suitable for parallel implementation.

Citation Download Citation

Octavian Valeriu Sarca, Jaakko T. Astola, and Edward R. Dougherty "New training method for linear separable threshold Boolean filters", Proc. SPIE 3167, Statistical and Stochastic Methods in Image Processing II, (14 October 1997); https://doi.org/10.1117/12.279647

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