Variations
There are many ways of representing the shape of an object. The shape of an object can be considered as a member of an equivalence class formed by taking the set of all sets of k points in n dimensions, that is Rkn and factoring out the set of all translations, rotations and scalings. A particular representation of shape is found by choosing a particular representation of the equivalence class. This will give a manifold of dimension kn-4. Procrustes is one method of doing this with particular statistical justification.
Bookstein obtains a representation of shape by fixing the position of two points called the bases line. One point will be fixed at the origin and the other at (1,0) the remaining points form the Bookstein coordinates.
It is also common to consider shape and scale that is with translational and rotational components removed.
Read more about this topic: Procrustes Analysis
Famous quotes containing the word variations:
“I may be able to spot arrowheads on the desert but a refrigerator is a jungle in which I am easily lost. My wife, however, will unerringly point out that the cheese or the leftover roast is hiding right in front of my eyes. Hundreds of such experiences convince me that men and women often inhabit quite different visual worlds. These are differences which cannot be attributed to variations in visual acuity. Man and women simply have learned to use their eyes in very different ways.”
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