geometric constraints

Page numbers are for draft copy at present; they will be replaced with correct numbers when final book is formatted. Chapter numbers are correct and will not change now.

A geometric constraint is a form of constraint of an image that is driven by knowledge of 2D and 3D geometry. For example:

As a general rule if object A is in front of object B and object B is in front of objectC, then A must also be in front of C.
Waltz's algorithm uses the fact that, inter alia, if three edges meet at a Y-like point they are usually either all be outward facing or all inward facing joins.
Shadoes tend to lie on the same side of objects opposite the primary light source.

As is evident from the phrases 'as a general rule', 'usually', 'tend to', theer are often odd examples where the particular camera angle or strangely shaped objects break the 'rules', but they are often strubg heuristics if not inviolable laws.

Used on Chap. 12: page 272

Scene with edges labelled by Waltz' algorithm using on vertex constriants

An 'improper scene', which cannot be labelled by Walz' algorithm as it appears to violate geometric constraints. Note however if the L-shaped faces where suitably curved it would be possible to construct this.