First we consider the problem of variations in viewing angle and size. Our template depicts an underground sign from straight on and with a set image size. By deforming this template, according to simple geometric rules, we can predict what the same sign would look like at different distances and viewing angles. To predict the appearance of a more distant sign (or a smaller sign), we just shrink the size of the template. To predict the appearance of a sign viewed at an oblique angle, we rotate and compress the template. In this way, new templates can be produced for Underground signs viewed at any angle and with any image size. A selection of templates depicting signs viewed at different angles is shown in figure 8.5.
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Figure 8.5: Templates for signs viewed at different angles.
This suggests a way of finding the Underground sign in an image. First produce a catalogue of templates depicting an Underground sign viewed at a range of angles and for a range of different image sizes. The catalogue should be comprehensive so that for an arbitrary image of an Underground sign it will include a sign from a similar viewing angle and of a similar image size. Now compare each of the templates from the catalogue, one after the other, with the input image. As before this may be achieved by sliding the templates over the input image, looking at the corresponding grey-levels at each position.
Figure 8.6 shows the grey-levels of a `best-fit' template, produced by manually adjusting the deformation applied to the original template (with the help of a computer) to find a good approximation to the projected shape and size of the Underground sign depicted in figure 8.1. Unfortunately, the grey-levels of this `best-fit' template are still significantly different from those derived from the Underground sign in our input image.
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Figure 8.6: A `best-fit' deformation of the original template.
Although the ability to deform the original template enables us to predict the shape and size of the image of a London Underground sign seen at different viewing angles and distances, it cannot predict the actual grey-levels since these will depend, among other things, on the prevailing lighting conditions. Consequently, it is very unlikely that any of our catalogue of derived templates will match with any sub-array of grey-levels from an input image.
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