Issues and methods

Let us now suppose that we have isolated a character by some acceptable process, possibly only tentatively, and that we now wish to proceed to the recognition/classification stage. The intervening step is to measure some properties or characteristics or features of the character, so we will be able to compare and contrast the results of doing the same measurements on other characters. There are several well established methods which will shortly be described, but there are a few issues to be contemplated before going into a list of them.

If I suggest a suite of measurement operations, certain properties may or may not hold for my selection. For example, it is conceivable that my measurements would be quite unaffected by simply shifting the character by one pixel to the right. More generally, I might choose to make measurements that would be the same no matter where the character is on the page. In this case we say that the measurement process is invariant under shifts. Similarly, if a measurement process were invariant under scaling, it would yield a set of numbers which would be the same for any two characters which had one simply a scaled up version of the other, and if it were invariant under rotations, it would not matter how much you rotated a character, the measuring process would give the same output. These ideas derive from the continuous case, and have to be modified a bit for the case of pixel arrays, but clearly there is some vague and approximate notion of invariance in the discrete case.

Even if the measuring process were not shift invariant, it would certainly simplify recognition if the resulting vector of numbers did not change beyond recognition if the character were moved one pixel to the left. Since we may very well want to know where the character is, complete shift invariance is undesirable, but it would be useful to have the measurement process partitioned into a part which tells you where the character is, another part which tells you how big it is, another part where the numbers tell you if it has been rotated, another part perhaps telling you if it has been transformed in some other standard way, such as a change of font, and finally a component which would be the same no matter how much the character had been scaled or rotated or where it was. It is not too much to hope that some of these properties would be found to hold for a well chosen suite of measurements. Conversely, a suite of measurements which had every number changed completely by shifting the character one pixel sideways is going to be less appealing.

So it is possible to think a little bit about what constitutes a sensible sort of system of measurements rather than to jump on the first such system that occurs to you. This can save a good deal of time in the longer run.