# Lecture-14 - Good Features to Track 1 Good Features to...

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1 Good Features to Track

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2 Good Features to Track • Corners • Moravec’s Interest Operator Corners = Q y Q y x Q y x Q x f f f f f f C 2 2 = 2 1 0 0 λ C
3 Corners For perfectly uniform region If Q contains an ideal step ed if Q contains a corner of black square on white background 0 2 1 = = λ λ 0 , 0 1 2 > = 0 2 1 ! λ≥ Algorithm Corners • Compute the image gradient over entire image f. • For each image point p: – form the matrix C over (2N+1)X(2N+1) neighborhood Q of p; – compute the smallest eigenvalue of C; – if eigenvalue is above some threshold, save the coordinates of p into a list L.

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4 Algorithm Corners • Sort L in decreasing order of eigenvalues. • Scanning the sorted list top to bottom: for each current point, p, delete all other points on the list which belong to the neighborhood of p. Results
5 Results

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6 Moravec’s Interest Operator Algorithm • Compute four directional variances in horizontal, vertical, diagonal and anti- diagonal directions for each 4 by 4 window. • If the minimum of four directional variances is a local maximum in a 12 by 12 overlapping neighborhood, then that widow (point) is interesting.
7

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8 ∑∑ == + + + + + = 3 0 2 0 2 )) , 1 ( ) , ( ( ji h j y i x P j y i x P V + + + + + = 2 0 3 0 2 )) 1 , ( ) , ( ( v j y i x P j y i x P V + + + + + + = 2 0 2 0 2 )) 1 , 1 ( ) , ( ( d j y i x P j y i x P V + + + + + = 2 0 3 1 2 )) 1 , 1 ( ) , ( ( a j y i x P j y i x P V )) , ( ), , ( ), , ( ), , ( min( ) , ( y x V y x V y x V y x V y x V a d v h = = therwise local y x ifV y x I 0 0 max ) , ( 1 ) , (
9 Feature-based Matching

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10 Feature-based Matching • The input is formed by f1 and f2, two frames of an image sequence, and a set of corresponding feature points in two frames. • Let Q1, Q2 and Q’ be three NXN image regions. • Let “d” be the unknown displacement vector between f1 and f2 of a feature point “p”, on which Q1 is centered. Algorithm • (1) Set d=0, center Q1 on p1. • (2) Estimate the displacement “d0” of “p”, center of “Q1”, using Lucas and Kanade method. Let d=d+d0 . • (3) Let Q’ bet the patch obtained by warping Q1 according to “d0”. – Compute Sum of Square (SSD) difference between new patch Q’ and corresponding patch Q2 in frame f2.
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Lecture-14 - Good Features to Track 1 Good Features to...

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