Restoration by Increasing Binary Filters
Robert P. Loce, Edward R. Dougherty · 1997
Digital documents can suffer from degradations that render them either aesthetically unpleasing, machine unreadable, or human illegible. The degradations may have been introduced by the scanning process or may have been present on the hardcopy original. Due to the physical processes involved, degradation is often either extensive or antiextensive, and therefore the required restoration is an inverse mapping that must be antiextensive or extensive, respectively. Although increasing filters are a subclass of nonincreasing filters, experience has shown that their performance is comparable for these constrained image mappings. The advantage of using increasing filters is primarily a matter of implementation cost: increasing filters often may be represented by less than a dozen erosions in the minimal erosion expansion, while an equivalent nonincreasing filter may require hundreds or thousands of structuring-element pairs in the general hit-or-miss representation. Moreover, statistical filter design of increasing filters from realizations generally requires far less training data than design of nonincreasing filters. Finally, even when degradation is neither extensive nor antiextensive, increasing filters can sometimes perform well, especially if they are used in an iterative fashion.