5.2-image-matching

5.2-image-matching - Matching and Tracking Goal: develop...

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Image-based matching- 1 Zoran Duric Matching and Tracking Goal: develop matching procedures that can recognize and track objects when objects are partially occluded image cannot be segmented by thresholding Key questions: How do we represent the appearance of an object? How do we match these representations against an image?
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Image-based matching- 2 Zoran Duric Solution 1: Image correlation Given: n x n image, M, of an object of interest. This is called a template and is our representation of the appearance of the object. n x n image, N, that possibly contains that object (usually a window of a larger image) Goal: Develop functions that compare M and N and measure the similarity of M and N sum of squared differences: correlation: SSD = [ M ( i , j ) ! N ( i , j )] 2 j = 1 n " i = 1 n " C = M ( i , j ) N ( i , j ) j = 1 n ! i = 1 n ! [ M ( i , j ) 2 N ( i , j ) 2 ] 1/2 j = 1 n ! i = 1 n ! j = 1 n ! i = 1 n !
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Image-based matching- 3 Zoran Duric Image correlation This correlation measure takes on values in the range [0,1] it is 1 if and only if N = cM for some constant c so N can be uniformly brighter or darker than the template, M, and the correlation will still be high. the SSD is sensitive to these differences in overall brightness The first term in the denominator, ΣΣ M 2 depends only on the template, and can be ignored The second term in the denominator, ΣΣ N 2 can be eliminated if we first normalize the grey levels of N so that their total value is the same as that of M - just scale each pixel in N by ΣΣ M/ ΣΣ N practically, this step is sometimes ignored, or M is scaled to have average grey level of the big image from which the unknown images, N, are drawn.
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Image-based matching- 4 Zoran Duric Image correlation Suppose that M(i,j) = cN(i,j) C = M ( i , j ) N ( i , j ) j = 1 n ! i = 1 n ! [ M ( i , j ) 2 N ( i , j ) 2 ] 1/2 j = 1 n ! i = 1 n ! j = 1 n ! i = 1 n ! = cN ( i , j ) N ( i , j ) j = 1 n ! i = 1 n ! [ c 2 N ( i , j ) 2 N ( i , j ) 2 ] 1/2 j = 1 n ! i = 1 n ! j = 1 n ! i = 1 n ! = c N ( i , j ) 2 j = 1 n ! i = 1 n ! c [ N ( i , j ) 2 N ( i , j ) 2 ] 1/2 j = 1 n ! i = 1 n ! j = 1 n ! i = 1 n ! = 1
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Image-based matching- 5 Zoran Duric Image correlation Alternatively, we can rescale both M and N to have unit total intensity N’(i,j) = N(i,j)// ΣΣ N M’(i,j) = M(i,j)/ ΣΣ M Now, we can view these new images, M’ and N’ as unit vectors of length n 2 . The correlation measure ΣΣ M’(i,j)N’(i,j) is the familiar dot product between the two n 2 vectors M’ and N’ recall that the dot product is the cosine of the angle between the two vectors it is equal to 1 when the vectors are the same vector, or the normalized images are identical These are BIG vectors
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Image-based matching- 6 Zoran Duric Reducing the computational cost of correlation matching A number of factors lead to large costs in correlation matching: the image N is much larger than the template M, so we have to perform
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5.2-image-matching - Matching and Tracking Goal: develop...

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