Chapter 17
Invariants and Perspective
Invariants are important for achieving recognition in both 2-D and 3-D. The basic idea is to identify any parameters that do not vary between different instances of the same object. Unfortunately, perspective projection makes the issue far harder in the general 3-D case. This chapter explores the problem and demonstrates a number of useful techniques. At the same time it explores the problems of perspective projection, with some interesting outcomes.
Look out for:
• how a ratio of distances between features along the same straight line can act as a convenient invariant under weak perspective projection.
• how a ratio of ratios (or “cross-ratio”) can act as a convenient invariant under full perspective projection. ...
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