The natural difficulty is the effect of noise. This can change the result, as shown in Figure 6.16.
This can certainly be ameliorated by using the earlier morphological operators (Section 3.6)
to clean the image, but this can obscure the shape when the noise is severe. The major point
is that this noise shows that the effect of a small change in the object can be quite severe on
the resulting distance transform. As such, it has little tolerance of occlusion or change to its
perimeter.
(a) Noisy rectangle (b) Distance transform
Figure 6.16 Distance transformation on noisy images
The natural extension from distance transforms is to the medial axis transform (Blum, 1967),
which determines the skeleton that consists of the locus of all the centres of maximum disks in the
analysed region/shape. This has found use in feature extraction and description, so approaches
have considered improvement in speed (Lee, 1982). One more recent study (Katz and Pizer,
2003) noted the practically difficulty experienced in noisy imagery: ‘It is well documented how