Lucid Representations

Cover Lucid Representations
Lucid Representations
Ernest Davis
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The compu- tations may no longer be easy, either for the computer to perform, or for the programmer to work out. If the policy is to be followed consistently, the semantics of the representation must be carefully ^Unless quad-tree or sparse array representations are used. But then the enforcement of the consistency conditions becomes trickier.
defined; that is, it is necessary to establish a convention as to which representations can approxi- mate which real shapes [Davis, 90]. For example, in
...figure 2, if we say that a square is marked as belonging to an object if the object at all overlaps the square, then the distance between A and B is between three and five units. If we say that a square is marked as belonging to an object if the object overlaps at least half the area of the square, then the distance between A and B is between two and four units.
Moreover, it may still emerge, after the semantics have been fixed, that there are shapes that cannot even be approximated. For example, a natural rule for viewing a region in an occupancy array as an approximation is to posit that the real region may partially fill boundary cells, but must completely fill internal cells.


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