Operations on Images Using Quad Trees

Authors:
Gregory M. Hunter;Kenneth Steiglitz
Affiliations:
MEMBER, IEEE, Decisions and Designs, Inc., McLean, VA 22101.;MEMBER, IEEE, Department of Electrical Engineering and Computer Science, Princeton University, Princeton, NJ 08540.
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1979

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Abstract

A quad tree for representing a picture is a tree in which successively deeper levels represent successively finer subdivisions of picture area. An algorithm is given for superposing N quad trees in time proportional to the total number of nodes in the trees. Warnock-type algorithms are then presented for building the quad tree for the picture of the boundary of a polygon, and for coloring the interior of such a polygon. These algorithms take O(v + p + q) time, where v is the number of polygon vertices, p is the polygon perimeter, and q is a resolution parameter. When the resolution q is fixed, these algorithms are asymptotically optimal.