Abstract
Shapes play an important role in many human activities, but are rarely
seen in their natural form as raw and unanalyzed. Rather, shapes come
analyzed, structured in terms of their certain parts, forming shape
decompositions. Different kinds of shape decompositions are developed, the
most interesting among which are the decompositions that could be used as
shape approximations. Two kinds of such decompositions, discrete
and bounded, are examined in greater detail. Computations with
shapes conducted in the framework of shape grammars and related shape
algebras have been standard for over 3 decades. Similar computations are
possible with analyzed shapes or shape decompositions. Different algebras
to compute with shape decompositions are developed and compared to the
shape algebras. The measure of their agreement determines how well the
shapes are approximated by their decompositions.
Publisher
Cambridge University Press (CUP)
Subject
Artificial Intelligence,Industrial and Manufacturing Engineering
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