1. Modeling Spatial-Chromatic Distribution for CBIR
NTUT CSIE D.W. Lin

2. Outlines Review Modeling spatial-chromatic distribution
Incorporating shape into color information
Geometry enhanced color histogram
Modeling spatial-chromatic distribution
Nakagami-m distribution
Refining the modeling efficiency
Experiment results at present
Feature works

3. The integration of color and shape
Histogram refinement
Specific-color pixel distribution (single, pair, triple …)
Edge histogram …
Color histogram
Global color histogram
Global color histogram + spatial info.
Partition + local color histogram or color momnets
Dominant color
Extracting the representative colors of image via VQ or clustering (e.g. k-means algorithm)
Spatial info. can be attained
Spatial or frequency

4. Color Correlograms For a nn with m colors image I, The histogram is:
The correlogram is:
The autocorrelogram is:

5. Geometry-enhanced color histogram
For image I1 and I2, the similarity between autocorrelograms with color j and distance k is:
GECH uses first distance moment to decorrelate the spatial information from autocorrelogram

6. Autocorrelogram and GECH
GECH, O(m)
Color moment
distance
Modeled histogram , O(m)
modeling 5 3 1 i
color
Autorrelogram, O(md)

7. Modeling spatial-chromatic distribution
Complexity of feature vector
High dimension for bearing more info.
Nakagami-m distribution
Adequate pixels for a perceptible color region
Clustering phenomenon for meaningful color region (thus the beginning may not be zero)
Variety of distribution curves capture the spatial information well

8. Nakagami-m distribution
Ω=E[R2], second moment
, fading figure

9. Modeling spatial-chromatic distribution – cont.
Parameters estimation for Nakagami-m
based on the maximum-likelihood
Using second order approximation

10. Modeling efficiency Metric: intersection, compared with uniform dist.
Testset
Berkeley14838
Berkeley150
Stanford
th= 3, L2
87.51%(61.91%)
87.74%(60.91%)
Pixel_th = 1%, L2
87.68%(62.11%)
88.55%(61.85%)
Pixel_th = 2%, L2
88.22%(62.81%)
88.98%(62.52%)
Th=3, L1
88.72%(58.20%)
90.95%(57.55%)
90.18%(56.27%)
Th=1%, L1
88.93%(58.37%)
91.14%(57.75%)
91.06%(57.17%)
Th=2%, L1
89.71%(59.06%)
91.74%(58.43%)
91.51%(57.79%)
Metric: intersection, compared with uniform dist.

11. Modeling efficiency – cont.
Testset
Nor
Berkeley
Stanford
Pixel_threshold = 3
72.47% (0.39%)
86.51% (0.73%)
74.64% (0.27%)
Pixel_th = 1%
79.79% (2.8%)
87.32% (1.13%)
82.85% (2.8%)
Pixel_th = 2%
84.51% (7.2%)
89.26% (2.91%)
86.44% (6.1%)
Threshold: percentage of total DC image pixels
Entriey: rule out colors (pixels) in percentage

12. Refining the modeling At the first glance:
Remove the insignificant pixel
Find out the dominant cluster
Segmentation via MED (maximum entropy discrimination)

13. MED Max. entropy discrimination For segmentation
discretization, classification, method(MEM)
Power spectrum estimation
For segmentation
b: SPMF
c: PMF (for max.
entropy)
d: likelihood ratio

14. MED – cont.
20 observed values: 0.1, 0.9, 1.5, 2.0, 2.8, 3.2, 3.3, 3.5, 3.7, 3.8, 4.0, 4.5, 4.9, 5.5, 6.0, 7.3, 8.5, 8.8, 9.1, 9.5
Interval width = 9.5/4
= 2.375
p(I1) = (4/20)/2.375
= 0.084
Elements of Interval
= 20/4 = 5
p(I1) = 0.25/( )
= 0.084
Equal-width-interval
MED
For uniform distribution

15. Algorithm for refining modeling
Eta = Eta =

16. Remarks for the algorithm
Considerations:
Choice of parameters: number of intervals, constraints while merging the neighbor intervals
Sparse data, or scene with texture may be in vain
Concave region

17. Conclusions and feature works
Other features that may satisfy Nagakami-m modeling (avoid biased by correlogram)
Similarity measure: Battachaya distance

18. References
J. Cheng, N.C. Beaulieu, “Maximum-likelihood based estimation of the Nakagami m parameter,” IEEE Communications Letters, Vol. 5, No. 3, pp , 2001
S.-H. Yang and D.-W. Lin, “A geometry-enhanced color histogram,” IEEE Int’l Conf. Information: Research and Education, New Jersey, USA, Aug

19. References - MED
J.B. Jordan and L.C. Ludeman, “Image segmentation using maximum entropy technique,” Intl’ Conf. Acoustics, Speech and Signal Processing (ICASSP’84), Vol. 9, pp , 1984
Hsu , T.S. Chua, and H.K. Pung, “An integrated color-spatial approach to content-based image retrieval,” Proc. Of ACM Multimedia Conf., pp , Nov. 1995
T. Jaakkola, M. Meila, and T. Jebara, “Maximum entropy discrimination,” In Advance in Neural Information Processing Systems 12 MIT Press, 1999