Non-rigid Shape Definition
A more flexible definition of shape takes into consideration the fact that realistic shapes are often deformable, e.g. a person in different postures, a tree bending in the wind or a hand with different finger positions. By allowing also isometric (or near-isometric) deformations like bending, the intrinsic geometry of the object will stay the same, while sub-parts might be located at very different positions in space. This definition uses the fact that, geodesics (curves measured along the surface of the object) stay the same, independent of the isometric embedding. This means that the distance from a finger to a toe of a person measured along the body is always the same, independent of posture. By only considering geodesic distances or other isometric properties as done in spectral shape analysis, it is possible to retrieve all cats in a database of animals independent of the pose.
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Famous quotes containing the words non-rigid, shape and/or definition:
“Let’s call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don’t require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.”
—Saul Kripke (b. 1940)
“After that it came to my door. Now it lives here.
And of course: it is a soft sound, soft as a seal’s ear,
that was caught between a shape and a shape and then returned to me.”
—Anne Sexton (1928–1974)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)