Image Processing Reference
In-Depth Information
Chapter 10
This topic has taken the reader on a journey through various image processing tech-
niques, 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 topic
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 mod-
est 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 ap-
plying 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.
The difficulty with this design approach comes when we wish to make the win-
dow size larger for more complex problems. For each extra location in the filter
window, the number of input combinations doubles. Any window much larger than
3 pixels results in too many input combinations to estimate when using a train-
ing set containing a few images.
In any design approach based on training, it is essential that the size of the train-
ing set is matched to the complexity of the problem. If the search space is too large,
constraints must be applied in order to limit the complexity of the problem. The
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