SERIE B INFORMATIK Approximate Matching of Polygonal Shapes
نویسندگان
چکیده
For two given simple polygons P Q the problem is to determine a rigid motion I of Q giving the best possible match between P and Q i e minimizing the Hausdor distance between P and I Q Faster algorithms as the one for the general problem are obtained for special cases namely that I is restricted to translations or even to translations only in one speci ed direction It turns out that determining pseudo optimal solutions i e ones that di er from the optimum by just a constant factor can be done much more e ciently than determining optimal solutions In the most general case the algorithm for the pseudo optimal solution is based on the surprising fact that for the optimal possible match between P and an image I Q of Q the distance between the centroids of the edges of the convex hulls of P and I Q is a constant multiple of the Hausdor distance between P and I Q It is also shown that the Hausdor distance between two polygons can be determined in time O n log n where n is the total number of vertices Freie Universit at Berlin Fachbereich Mathematik und Informatik Institut f ur Informatik Takustr D Berlin e mail alt tcs fu berlin de bloemer tcs fu berlin de This research was supported by the Deutsche Forschungsgemeinschaft under Grant Al Schwer punktprogramm Datenstrukturen und e ziente Algorithmen and by the ESPRIT Basic Research Action No ALCOM II
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