Praktikum zur Analyse von Formen - Abstandsmaße -. Helmut Alt Freie Universität Berlin. Distance functions, Matching. Distance functions d on patterns and shapes measuring their similarity
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Freie Universität Berlin
d(A,B) = max ( max min ||a-b||, max min ||a-b||)
a A b B b B a A
dF(a,b) = inf max ||a(f(t))-b(g(t))||
f,g : [0,1 ] [0,1] t [0,1]
where f and g range over continuous non-decreasing
aFree Space Diagram
path in the free space from (0,0) to (1,1)
aFinding a monotone path in O(mn) time
Regions on the boundaries of the
cells that can be reached by a
monotone path from lower left
Find these by traversing cells from
bottom to top and from left to right.
This algorithm solves the decision problem in O(nm) time.
For the computation problem:
Binary search on e in O(nmk), where k = # of correct bits
Parametric search gives an O(nm log (nm)) algorithm