Artificial Intelligence

geometrical figure coordinated Piotr Indyk November 25, 2003 trounce 23: geometrical design interconnected 1 Face Recognition November 25, 2003 strap 23: nonrepresentational drill Matching 2 Matching in a Scene November 25, 2003 blab out 23: Geometric Pattern Matching 3 formalisation: Shapes Today: A shape is a particularise A of burdens in R2 |A|=n In general, A could be of segments etc. November 25, 2003 Lecture 23: Geometric Pattern Matching 4 Formalization: (Dis)similarity Hausdorff distance DH(A,B)=maxa?A minb?B ||a-b|| H(A,B)=max[ DH(A,B), DH(B,A) ] Earth-Mover Distance Minimum make up of a one-to-one matching between A and B EMD(A,B)=minf:A B, a?A ||a-f(a)||, f is 1:1 Bottleneck matching BM(A,B)= minf:A November 25, 2003 B, max a?A ||a-f(a)||, f is 1:1 5 Lecture 23: Geometric Pattern Matching  figuring H(A,B) Given A,B, how spry can we work H(A,B) ?

We will compute DH(A,B) cause a Voronoi diagram V for B Construct a point location structure for V For severally a in A, find its NN in B Total cadence: O(n logarithm n) November 25, 2003 Lecture 23: Geometric Pattern Matching 6  nigh Hausdorff Assume we just want an algorithm that: If DH(A,B) r, answers YES If DH(A,B) (1+ ?)r, answers NO Algorithm: implement a grid with cell diameter ?r For each b?B, mark all cells inside distance r from b For each a?A, quit if as cell is marked Time: O(n/?2) November 25, 2003 Lecture 23: Geometric Pattern Matching 7  co-occurrence In general, A and B are not line up So, in general, we want! DHT(A,B)=mint?T DH(t(A),B) , where T=translations T=translations and rotations Same for H How can we compute it ? November 25, 2003 Lecture 23: Geometric Pattern Matching 8 Decision fuss Again, focus on if DHT(A,B) r For a?A, define T(a)={ t: ?b?B ||t(a)-b|| r } DHT(A,B) r iff a?A T(a) is non-empty November 25, 2003...If you want to get a full essay, order it on our website: OrderCustomPaper.com

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