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This book has taken the reader on a journey through various image processing techniques, some of which will be new and some which will be familiar. On the way, we have encountered well-known methods such as the median filter, morphological operators and the hit-or-miss transform. Most other image processing texts start by deriving a filtering operator and mapping it to a finite sliding window. In this book we begin with the sliding window and consider the processing options available from it. The values within the filter window are treated as logical inputs to a Boolean expression. The design process consists of identifying which Boolean expression (out of all those possible) will result in the lowest overall error. For binary images and small windows, the number of input combinations is sufficiently low such that the conditional probability of each output may be estimated accurately from a modest training set. The theory is straightforward and leads to simple methods for the calculation of the optimal filer and its associated error. It is also easy to compare different filters and compute the increase in error for sub-optimal filters. The effects of the filters (in terms of which patterns of pixels are altered and which are left unchanged) can be seen to be consistent for additive and subtractive noise. For simple document-processing problems, the results can be stunning. This contrasts favorably with commonly used approaches of either applying the median filter regardless or heuristic filter design (i.e. guessing) at a pixel-processing level. The filter is defined in terms of an expression in Boolean logic that may be mapped directly to hardware.
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