Abstract
An algorithm is presented for reconstructing a quadtree from its quadtree medial axis transform (QMAT). It is useful when performing operations for which the QMAT is well suited (e.g., thinning of an image). The algorithm is a postorder tree traversal which propagates the subsumption of each BLACK QMAT node in the eight possible directions. Analysis of the algorithm shows that its average execution time is proportional to the number of leaf nodes in the quadtree. The algorithm also serves to reinforce the appropriateness of the definition of the quadtree skeleton which does not permit a BLACK quadtree node to require more than one element of the quadtree skeleton for its subsumption.
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