1

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]) }

6

• 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

10

• A dividing method in [FRM 94]

11

– Query processing• Queries of length w

12

• Queries of length > w

13

– 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