COLOR CONSTANCY IN THE COMPRESSED DOMAIN Jayanta Mukhopadhyay Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur, 721302, India jay@cse.iitkgp.ernet.in Sanjit K. Mitra Ming Hsieh Dept. of Electrical Engineering University of Southern California Los Angeles, CA 90089, USA skmitra@usc.edu

Problem of Color Constancy Three factors of image formation: Objects present in the scene. Spectral Energy of Light Sources. Spectral Sensitivity of sensors. Spectral Response of a Sensor Spectral Power Distribution Surface Reflectance Spectrum

Same Scene Captured under Different Illumination Can we transfer colors from one illumination to another one?

Computation of Color Constancy Deriving an illumination independent representation. - Estimation of SPD of Light Source. Color Correction - Diagonal Correction. E(λ) <R, G, B> To perform this computation with DCT coefficients.

Different Spatial Domain Approaches Gray World Assumption (Buchsbaum (1980), Gershon et al. (1988)) <R, G, B> ≡ <Ravg, Gavg, Bavg> White World Assumption (Land (1977)) <R, G, B> ≡ <Rmax, Gmax, Bmax>

Select from a set of Canonical Illuminants Observe distribution of points in 2-D Chromatic Space. Assign SPD of the nearest illuminant. Gamut Mapping Approach (Forsyth (1990), Finlayson (1996)) - Existence of chromatic points. Color by Correlation (Finlayson et. al. (2001)) - Relative strength over the distribution. Nearest Neighbor Approach (Proposed) - Mean and Covariance Matrix. - Use of Mahalanobis Distance.

Processing in the Compressed Domain Consists of non-overlapping DCT blocks (of 8 x 8). Use DC coefficients of each block. The color space used is Y-Cb-Cr instead of RGB. Chromatic Space for Statistical Techniques is the Cb-Cr space.

Different Algorithms under consideration

List of Illuminants

Images Captured at Different Illumination Source: http://www.cs.sfu.ca/ colour/data.

Performance Metrics Estimated SPD: E=<RE,GE,BE> True SPD: T= <RT,GT,BT>

Average Δθ

Average Δrg

Average ΔRGB

Average ΔL

Time and Storage Complexities nl: number of illuminants. nc: size of the 2-D chromaticity space n: number of image pixels f: Fraction of chromaticity space covered. aM+bA  a number of Multiplications and b number of Additions.

Time and Storage Complexities

Equivalent No. of Additions per pixel (1 M= 3 A) n=512, nc=32, nl=12, f=1

Color Correction: An Example Image captured with (solux-4100) Target Ref. Image (syl-50mr16q) COR-DCT MXW-DCT-Y COR

Color Restoration Original Enhanced w/o Color Correction Enhanced with

Conclusion Color-constancy computation in the compressed domain : - requires less time and storage. - comparable quality of results. Both NN and NN-DCT perform well compared to other existing statistical approaches. Color constancy computation is useful in restoration of colors.

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