Modeling Spatial-Chromatic Distribution for CBIR NTUT CSIE D.W. Lin 2004.3.19

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

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

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

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

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

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

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

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

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.

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

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

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

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/(2.8-0.1) = 0.084 Equal-width-interval MED For uniform distribution

Algorithm for refining modeling Eta = 0.8183 Eta = 0.9563

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

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

References J. Cheng, N.C. Beaulieu, “Maximum-likelihood based estimation of the Nakagami m parameter,” IEEE Communications Letters, Vol. 5, No. 3, pp. 101-103, 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. 2003.

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. 674-677, 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. 305-313, Nov. 1995 T. Jaakkola, M. Meila, and T. Jebara, “Maximum entropy discrimination,” In Advance in Neural Information Processing Systems 12 MIT Press, 1999