1. Color Management Using Device Models And Look-Up Tables
Edward J. Delp
School of Electrical and Computer Engineering
Purdue University
West Lafayette, Indiana

2. Outline Introduction Color Management Current Practices
Motivation For The Proposed Method
Constructing A Transformation Based on Device Models
Color Management Using Look-Up Tables
Conclusions And Future Work

3. Typical Delivery Of Visual Data
Refinement (êr)
W is set of visual stimuli, Z is set of digital images/video in common 24bit RGB.
A digital image is only a collection of numbers.
“Refinement” aims to improve the “look”. Analogous operation for motion pictures is color grading during post production.
e є W Λ(.) i є Z Ψ(.) ê є W
(visual data) (capture) (digital image) (display) (delivered data)

4. Need For Color Managementê1 ê2 ê3 êr
1. Color boundaries are only sumbolic.
The artist would want: ê1 = ê2 = ê3 = êr

5. Current Approaches To Color Management
Solutions for still digital images
Capture and display device profiles
Color management module (CMM)
Solutions for professionally screened digital video
Target display environment (cinema theatre projection) is known
Artists need to view content in similar environment during post-production
Custom-built display devices
We focus on profile based solutions
Custom displays are tech solutions (unlike engineering solutions) – expensive and not flexible.
CMM is part of OS. Applications which support profiles request service from CMM.

6. Color Management Using Profiles
Device 1 profile
Device 2 profile
Gamut
mapping
RGB1 image
PCS
PCS
RGB2 image
CMM
Profile connection space (PCS) is typically CIE XYZ or CIE LAB
CMM is part of the operating system

7. Motivation For An Alternative
All applications do not support profiles
Vendors are going beyond ICC profiles – Vista’ WCS
Complex CMM not suitable for portable devices
Profile format for WCS is a superset of ICC profile format, mostly backward compatible but all features work only on Vista.
Traditionally, CMMs have been simple and rely on several LUTs to perform different tasks. But with greater computing power, more complex CMMs now frequently perform real time math – unsuitable for low-end devices.
Color profile support in Firefox 3.0
(Courtesy: Deb Richardson)

8. Motivation For An Alternative
Consider an analogy with currency exchange
GCIS participant from China
100 CNY  EUR
EUR  NOK
100 CNY  NOK
Multi-step conversions
Lower accuracy, slower
Not suitable for multiple/continuous transactions
Using EUR is like using profiles, we can obtain any other currency but sacrifice the advantage of a direct conversion.
(Conversions courtesy: as on June 6, 2009)

9. Motivation For The Proposed Method
RGB
Device 1
PCS
PCS
RGB
Device 2
Gamut mapping
Achieving visual similarity using profiles
RGB
Device 1
RGB
Device 2
1. One step vs three step solution.
Overall transformation f(.)
Achieving visual similarity using the proposed model-based method

10. Model-Based Color Transformation
Consider two display devices Ψref and Ψuser and a digital visual data i є Z
Construct a function f: Z  Z such that
Ψref( i) ≈ Ψuser( f (i))
where ≈ represents visual similarity
We consider similarity in a perceptual sense
Account for different viewing conditions and chromatic adaptation
Match the color outputs in CIE LAB space
Chromatic adaptation is performed using Von Kries model.

11. Model-Based Color Transformation
i є Z1
j є Z2
During white balancing, we ensure both devices have common white point D65.
Monitor models consist of gray balancing and linear RGB-XYZ transform. Gray balancing by 1D LUTs, linear transform by an optimized 3x3 matrix.
Gamut mapping uses Straight Chroma Clipping technique – retains lightness and hue.
Non-Linear Transformation with White Point Correction (NLXWP)
Monitor data by spectro-radiometric measurements

12. Model-Based Color Transformation
The model NLXWP is represented by f (.)
We use 3D look-up tables (LUT) to make it computationally more viable
Let table look-up be represented by Φ (.)
Input space is 256 × 256 × 256
We construct LUT by evaluating f at:
Then,
where £ represents 3D interpolation

13. Optimal 3D LUT
Given a function f and a size specification G (number of entries) for the LUT
Accuracy of Φ depends on choice of Ω and £
Measure accuracy with respect to f
Formulate it as an optimization problem
Let,
Then over a training set,
Obtain parameters so as to minimize
1. Training set contained 1000 random (R,G,B) values.
2. Eight-point interpolation with weights proportional to square of inverse Euclidean distance in 3D space.

14. Color Management Using 3D LUT
Assumption: There is always an intended reference device for visual content
Digital Cinema (DCI) Reference Projector for motion pictures
With the knowledge of Ψref construct a function f (NLXWP) for any given display Ψuser
Use f to obtain optimal LUT Φ for this device pair
Color correct content using Φ whenever this reference device is specified
Reference device can be specified as metadata in the content.
An artist can decide on a reference when editing the content. His/her display device will then work using a 3D LUT corresponding to the reference. Later, any user viewing the content will also using a LUT for the same reference.

15. Color Management Using 3D LUT
Compare the performance of LUT based color management with ICC profiles
Profiles vary from 0.5 KB to over 0.5 MB in size
Consider average size profiles ~15 KB each for the reference and user device
Comparable largest LUT will be 21 × 21 × 21
Evaluate accuracy of much smaller LUTs
In terms of over a testing set
Assuming NLXWP is accurate
1. 21x21x21 = 9,261 < 10,000 < (2*15KB)/3: 2 profiles of 15KB, memory divided equally between RGB channels.

16. Color Management Using 3D LUT
Testing error statistics in ΔE units
An optimal 12 × 12 × 12 LUT keeps mean error below 2 ΔE using less than 20% of the designated memory
Non-optimal LUT uses tri-linear interpolation and uniform sampling of RGB space

17. Future Work
Have shown that device models and 3D LUT can be used for color management
Compare with ICC profile-based color management system
Accuracy and speed
Expect improvement in both: specific solution is accurate, LUT is faster
Design a collection of LUTs corresponding to different reference devices
User device can select the appropriate LUT
Multiple (likely two) LUTs may be used for each reference corresponding to user device being in illuminated or dark rooms.
We may mention that LUTs should be able to handle small changes in display settings (brightness, etc) by the user. One solution is to make LUTs that work over a range of display settings. Alternatively, give the CMM ability to adjust LUT entries due to these changes.