Basic f - f Т - f ТТ inter-relationship

Slide 17 of 42

If you project this vaguely helical curve downward or to the left you get the parametric curves which we saw in the previous slide. You can also project it this way, but we aren't really going to be using that in our analysis.

So thats pretty, but what good is it. Well, suppose you were given a volume, and suppose you marched through the volume, gradually accumulating information about the global relationship between f, f' and f'' in that volume. And suppose that in that measured relationship you found a curve like this. Then, you could assume that there must have been a boundary somewhere in the given volume. And, asked the question, where's the boundary, you could say "here", at this data value, corresponding to the max in f' or the zero-crossing in f''. So the usefulness of this curve is that it represents the particular relationship between f, f', and f'' that signifies the presence of a boundary in the original volume, and, it provides the context for precisely locating that boundary in the data value domain. Now what we need is a tool for measuring that relationship.