Morphological decomposition of restricted domains: a vector spacesolution
Kanungo, T.
Haralick, R.M.
Dept. of Electr. Eng., Washington Univ., Seattle, WA;
Abstract
Restricted domains, which are a restricted class of 2-D shapes,
are defined. It is proved that any restricted domain can be decomposed
as n-fold dilations of thirteen basis structuring elements and
hence can be represented in a thirteen-dimensional space. This
thirteen-dimensional space is spanned by the thirteen basis structuring
elements comprising of lines, triangles, and a rhombus. It is shown that
there is a linear transformation from this thirteen-dimensional space to
an eight-dimensional space wherein a restricted domain is represented in
terms of its side lengths. Furthermore, the decomposition in general is
not unique, and all the decompositions can be constructed by finding the
homogeneous solutions of the transformation and adding it to a
particular solution. An algorithm for finding all possible
decompositions is provided
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