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)
“The poet will prevail to be popular in spite of his faults, and in spite of his beauties too. He will hit the nail on the head, and we shall not know the shape of his hammer. He makes us free of his hearth and heart, which is greater than to offer one the freedom of a city.”
—Henry David Thoreau (1817–1862)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)