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Machine Vision, 3rd Edition by E. R. Davies

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Invariants and Their Applications

Invariants are intrinsic to the idea of recognition in both 2-D and 3-D. The basic idea is to identify some parameter or 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.

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.

• how the cross ratio type of invariant can rather cunningly be generalized to ...

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