Invariance in practice

Suppose we have put a box around a putative character. Suppose that the box is of a reasonable size to contain some character, and that the top and bottom edges are parallel and can confidently be declared as horizontal. This is a somewhat courageous commitment because, as inspection of many a photocopy will show, text lines are often curved near the spine of the book, but we proceed in a spirit of optimism.

The first prudent thing to do is to contract the resulting box by making sure the black pixels inside it are touching the edges. A big box with a lot of white space against the right hand edge has more pixels in it than necessary. The next prudent thing to do is to scale it to a standard size and shape. It is prudent because the characters may be deformed and this will normalise them, and also because it is easier to compare like with like. The effect of this on an /o/ will be very different from its effect on an /i/ of course. What constitutes a good size for the standard box will depend to some extent on the font. If the box was a parallelogram which fitted an italicised character, the transformation back may de-italicise it. And it may have rather an odd effect on some characters, making /V/ much to much like /U/ if taken to excess. Some opportunity to experiment with various transformations is given the reader in the exercises.