The properties of the different strata are briefly summarized in Table 2.1 . The different geometric strata are presented. The number of degrees of freedom, transformations and the specific invariants are given for each stratum. Figure 2.5 gives an example of an object which is equivalent to a cube under the different geometric ambiguities. Note from the figure that for purposes of visualization at least a metric level should be reached (i.e. is perceived as a cube).

Table 2.1:Number of degrees of freedom, transformations and invariants corresponding to the different geometric strata (the coefficients form orthonormal matrices)

ambiguity

DOF

transformation

invariants

projective

15

cross-ratio

affine

12

relative distances

along direction

parallelism

plane at infinity

metric

7

relative distances

angles

absolute conic

Euclidean

6

absolute distances

Figure 2.5:Shapes which are equivalent to a cube for the different geometric ambiguities