Spectral-based Image Reproduction Workflow From Capture to Print Philipp Urban
Why Color Management?
The Ultimate Goal No difference They are Any Camera similar Data Processing Still no Any Printer difference
Digital Counts (239,32,78) (245,21,87) RGB Each Device is Different Surface Reflectance
Each Device is Different (48,-91,60) Control Values Printed output in ( C, M, Y, K)= CIELAB, D50 (98, 3, 99,1) (46,-46,-5)
Typical Metameric Workflow (ICC) ICC Camera Profile Profile Connection Space ICC Printer Profile Goal
Success Story of Metameric Reproduction File Formats Measurement Equipment Devices OS Color Management Software Applications
Limitations of the Metameric ICC-Based Reproduction
Limitations of a Typical Metameric Workflow (ICC) Information Reduction ⇒ Camera Metamerism r g b Bayer Multiple Reflectance Observer + Illuminant Mismatch with PCS ⇒ Information Loss ≠ ≠ X r X r Camera PCS Observer’s Real Observer’s ↔ ↔ Sensitivities CMFs CMFs Y g Y r (CIE 1931) ≠ ≠ Z b Z r Acquisition PCS Viewing Transformation between color spaces Illuminant Illuminant Illuminant is neither well-defined nor unique (CIE D50)
Limitations of a Typical Metameric Workflow (ICC) Illuminant Metamerism Ideally: In General: Match for single Mismatch for same Observer Observer and and Illuminant different Illuminant Original Reproduction Original Reproduction Observer Metamerism Ideally: In General: Match for single Mismatch for Observer different Observer and and Illuminant same Illuminant Original Reproduction Original Reproduction
Typical Metameric Workflow Camera Printer Profile Profile Connection Profile Space ICC ICC (ICC)
What Needs to be Changed?
What Needs to be Changed? c 1 Increase the number 1 : of camera channels ⇒ reduce loss of information c m (m » 3) c 1 Estimate the reflectance 2 : spectrum instead of a c m tristimulus for a specific Signal observer and illuminant Processing X 1 Y 1 or Z 1 c 1 Estimate tristimuli for X 1 2a : Y 1 multiple illuminants Z 1 c m Signal X 1 Y 1 Processing Z 1
What Needs to be Changed? C M Increase the number of Y colorants (inks) 3 K ⇒ R maximize spectral G printer gamut B V C M Separate colors based on Y or 4 spectral or multi-illuminant K R information X 1 Signal G Y 1 ⇒ minimize metamerism B Z 1 Processing V X 1 Y 1 Z 1 X 1 Y 1 Z 1
The Spectral End-to-End Reproduction Workflow
Spectral End-to-End Reproduction Workflow Multi-Channel Response Camera Response Processing Normalization Linearization using white ref. (model based) Multispectral-Camera Original Spectral estimation target/model-based High Dimensional Space (e.g. spectral space) Spectral Printing Spectral Separation (model inversion) Multi-Ink-Printer Ink limitation Spectral Gamut Mapping Multi-Ink-Control Reproduction
Where is a Spectral Workflow useful? Where are the Applications?
Highly Accurate Proofing of Offset-Press-Prints Metameric Workflow Spectral Workflow Proof Press Proof Press Viewing conditions ISO Standard Viewing conditions Client Standard satisfied Client satisfied Client not satisfied
Cultural Heritage Van Gogh’s The Starry Night (what are the real colors?) • Reproducing artwork Bring the real color appearance of a van Gogh painting into the living room • Support and document restoration work
Highly Accurate Industrial Color Communication Today Color Communication (swatches, samples…)
Highly Accurate Industrial Color Communication Tomorrow? Color Communication (swatches, samples…)
Multispectral Cameras
Ways to Increase the Number of Camera Channels λ -Separation Illumination Sample Imager Estimation Reflectance x λ Filter Wheel Color Filter Liquid Crystal Direct Image Prism Multiple CCD Array Tunable Filter Sensor +CCD + Filters Combination Combination CFA Filters + CFA + Multiple CCD + Filters
Camera Response Processing
Vector Representation of Spectra Relative power\reflectance S = [50 65 85 80 60 58 55 50 45 40] T
Reflectance Estimation λ -Separation Illumination Sample Imager Estimation Reflectance c 1 : c m Signal Processing Problem is under-determined (ill-posed) General Approach: Utilize as much information as possible
Reflectance Estimation c 1 : c m Signal Processing Training-based Model-based Spatio-Spectral Multipoint spectral Methods Methods Methods Measurement Methods
Reflectance Estimation [Training-based Methods] Camera Characterization Calculate transformation that maps camera responses Capture target to spectral reflectance factor Target Spectral measurements of each sample Spectral estimation of each pixel Spectral Imaging
Training-based Methods General Problem Necessary Condition: Spectral agreement between training colors and original It is unlikely that the spectrum of the red-pigments can be accurately estimated Training Target Original The spectral estimation quality depends strongly on the selected target. Multipoint spectral measurement methods “Target is the Original”
Sensor Response of a Linear Imaging Device Camera Sensitivities Illuminant Reflectance d λ c 1 : X X = c m [s 1 … s m ] T i r c 1 s 11 i 1 … s 1n i n r 1 = L ⋅ r : : : : = Vector representation: c m s m1 i 1 … s mn i n r n L (Lighting Matrix)
Reflectance Estimation [Model-based Methods] Calculate colorimetric transform x = L Use lighting matrix L and additional information to calculate spectral reflectance factor from camera responses c = L ·r The camera model: camera response lighting matrix reflectance (known) (known) (unknown) Solve underdetermined equation with respect to r: f( L ,c) = r The Mathematics
Reflectance Estimation [Model-based Methods] Pseudoinverse Simple mathematical solution Does not minimize the spectral RMS error Sensitive to noise Principle Component Method Additional assumption: Natural reflectances can be described by a n-dimensional space low-dimensional linear model Model parameter (principle components) can be calculated using a spectral database Wiener Inverse Additional assumption: Natural reflectances and noise are normally distributed Density Determine covariance matrices from spectral database λ 1 Optimal linear filter for reflectance estimation λ 2
Reflectance Estimation [Model-based Methods] Spatially Adaptive Wiener Inverse c i-1j c ij c ij-1 c ij+1 Combining noise reducing and reflectance c i+1j estimating Wiener filter Urban et al. 2008 Average spectral RMS error PI PC Wiener σ 2 σ 1 Results: Six channel Sinar camera
Spectral Printing
Are all Natural Spectra Printable? A look at the effective spectral dimension Effective dimension ~ minimal number of characteristic spectra that sufficiently represent the spectral dataset
Are all Natural Spectra Printable? 25 Munsell 1269 paint chips (matt) Natural (Vrhel database) Objects (Vrhel database) 20 Pigments (Vrhel database) Mitsubishi CMY Printer Effective Dimension HP Z3100 CMYKRGB Printer 15 10 5 0 Required Accumulated Energy = 99% Hardeberg 2002
Are all Natural Spectra Printable? Spectral printer gamut All natural reflectances Dimension difference ⇒ Nearly every given spectrum is out-of-gamut ⇒ Spectral Gamut Mapping necessary Colorimetric Gamut Warning Spectral Gamut Warning
Spectral Gamut Mapping • How to calculate the spectral gamut? ? L* b* a* Colorimetric Gamut Spectral Gamut • How to gamut map spectral images? What are the objectives? - Minimizing a spectral distance metric related to human color vision Or - For one illuminant as visual correct as a colorimetric reproduction - For other illuminants superior
Printer Model • What spectral printer model should be used? Control values (e.g. CMYKRGB) Model Reflectance • Printer model needs to be inverted Control values (e.g. CMYKRGB) Reflectance Model Inversion • Problems: area coverage (effective) effective Non-linear theoretical Optical dot gain area coverage (control)
Printer Model Inversion • Model inversion on a Pixel by Pixel Basis ⇒ very fast algorithm and implementation
Ink Limitation Limited mechanical colorant-absorption of media ⇒ ink limitation necessary Secondary and tertiary colors (Chen 2006)
Spectral Printing Workflow Spectral Gamut Mapping Printer Model Inversion Ink Limitation theoretical out-of-gamut in-gamut printable control values spectra spectra control values
Spectral Printer Model
Printer Model What spectral printer model should be used? Control values (e.g. CMYKRGB) Model Reflectance Many different models have been developed: Pure empirical, physical and hybrid models. [see Wyble and Berns 2000 for a comparison] The Cellular Yule Nielsen Spectral Neugebauer (CYNSN) model is widely used (good compromise between simplicity and accuracy)
Spectral Gamut Mapping
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