0 Two-dimensional color images 2-D color image (QBIC) –Compute a k-element color histogram for...
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Transcript of 0 Two-dimensional color images 2-D color image (QBIC) –Compute a k-element color histogram for...
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Two-dimensional color images
• 2-D color image (QBIC)– Compute a k-element color histogram for each image
• 16×106 → 256•
A: color-to-color similarity matrix
• When A is identity matrix dhist reduces to Euclidean distance• Example of A
k
i
k
jjjiiij
thist
yxyxa
yxAyxyxd
1 1
2
))((
)()(),(
2
– Two obstacles for applying the F-index method• Dimensionality curse
• O(k2): cross-talk problem
– Consider RGB color space• Average color of an image x = (Ravg, Gavg, Bavg)t-
N
Pavg
N
Pavg
N
Pavg
PBN
B
PGN
G
PRN
R
1
1
1
)()1
(
)()1
(
)()1
(
3
– for quick-and-dirty test
– Solve the cross-talk problem• Allow indexing with SAM
• Solve the dimensionality curse problem
• Save CPU time
• Theorem 10.5.1 (Quadratic Distance Bounding)
– (), where 1 is constant, depending on A
)()(),(2 yxyxyxd tavg
21
2 () avghist dd
1
2
221
()
()()
))(),((),(
avg
histavg
feature
d
dd
OFQFKDOQD
4
5
Sub-pattern matching
• Sub-pattern matching
– The problem: given sequences S1, S2, …, Sn, query Q of length Len(Q),
{(Si, k) | D(Q, Si[k:k+Len(Q)-1]) }
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• ST-index
– Sliding window w; a data sequence of length Len(S) is mapped to a trail of Len(S)-w+1 points in the feature space
7
8
9
– Divide the trail into sub-trails, each represented by an MBR
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• A dividing method in [FRM 94]
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– Query processing• Queries of length w
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• Queries of length > w
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– Break the query into p disjoint pieces of length w
– Search for each piece, with tolerance
– ‘OR’ the results and discard false alarms
–
• Can the method be extended to deal with 2-d images?
• Other applications?
– Distance function
– Lower-bounding lemma
p
)),((),( 10 p
sqDVSQD iiPi