Image Processing Reference

In-Depth Information

Chapter 10

Conclusions

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

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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