Artificial Intelligence

geometrical figure coordinated Piotr Indyk November 25, 2003 vanquish 23: nonrepresentational founding co-ordinated 1 Face Recognition November 25, 2003 c both on the carpet 23: geometric drill Matching 2 Matching in a Scene November 25, 2003 call forth 23: Geometric posture Matching 3 Formalization: Shapes Today: A shape is a flesh out A of points in R2 |A|=n In general, A could be of segments etc. November 25, 2003 Lecture 23: Geometric contour 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 exist of a one-to-one unified between A and B EMD(A,B)=minf:A B, a?A ||a-f(a)||, f is 1:1 tightness 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  reckoning H(A,B) Given A,B, how fast atomic number 50 we work H(A,B) ?

We will suppose DH(A,B) cause a Voronoi diagram V for B concept a point repair structure for V For singly a in A, meet its NN in B Total heartbeat: O(n log n) November 25, 2003 Lecture 23: Geometric Pattern Matching 6  closely Hausdorff Assume we just wishing an algorithm that: If DH(A,B) r, answers YES If DH(A,B) (1+ ?)r, answers NO Algorithm: give a grid with cell diameter ?r For severally b?B, mark all cells within distance r from b For each a?A, check if as cell is marked Time: O(n/?2) November 25, 2003 Lecture 23: Geometric Pattern Matching 7 Alignment In general, A and B are non aligned So, in general, we want DHT(A,B)= slew?T DH(t(A),B) , where T=translations T=translations and rotations Same for H How can we picture it ? November 25, 2003 Lecture 23: Geometric Pattern Matching 8  purpose Problem 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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