Optimal binary differencing filters: Design, logic complexity, precision analysis, and application to digital document processing

For given binary image and degradation processes, an optimal mean-absolute-error translation-invariant filter can be designed via the representation of such filters as a union of morphological hit-or-miss transforms. The present paper investigates a different optimization methodology by representing translation-invariant filters as differencing filters. Rather than employing structuring templates to build the entire output image, as is done with direct hit-or-miss representation, differencing filters only employ templates that locate value flips (black-to-white or white-to-black). Differencing filters play a central role in several digital document processing tasks and the paper considers their optimal design. The paper compares the logic designs of differencing and direct hit-or-miss representations, the combinational logic costs of the two representations, and the estimation precision of optimization approaches based on each. Both combinational logic cost and precision are relative to image models. It is also shown how differencing filters are statistically designed and applied in the digital document setting for image restoration and resolution conversion. (C) 1996 SPIE and IS&T.