from Color Management to Omnidirectional...
Transcript of from Color Management to Omnidirectional...
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Efficient Regression for Computational Imaging:
from Color Management to Omnidirectional Superresolution
Maya R. Gupta
Eric Garcia
Raman Arora
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Regression
2
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Regression
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Regression
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Linear Regression: fast, not good enough
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Problem: Device Dependent Colors Depend on Device
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Color Management For each device, characterize the mapping between the native
color space and a device independent color space.
8/5/2009 7
CIELab (Lab)
ICC Profile
ICC Profile
ICC Profile
ICC Profile
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Color Management • For each device, characterize the mapping between the native
color space and a device independent color space.
8/5/2009 8
CIELab (Lab)
ICC Profile
ICC Profile
ICC Profile
ICC Profile
CIELab is a widely used device-independent color space that is
perceptually uniform (i.e. Euclidean distance approximates human
judgement of color dissimilarity)
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Color Management • For each device, characterize the mapping between the native
color space and a device independent color space.
8/5/2009 9
CIELab (Lab)
ICC Profile
ICC Profile
ICC Profile
ICC Profile
Mapping from RGB -> CIELab and CIELab -> CMYK can be highly
nonlinear
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Gamut mapping: linear transforms not adequate
Skin
tones Skin
tones
Original gamut
Extended gamut
Original Gamut Linear regression Nonlinear regression
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Creating Custom Color Enhancements
original transformed by artist to “sunset”
2 hrs. work in Photoshop
Ex: simulating illumination effects
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Example Convert an image to how it would look in Cinecolor based on 16 sample color pairs
www.widescreenmuseum.org
Original cinecolor
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Color management: speed by LUT
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Color management: speed by LUT
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Color management: speed by LUT
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Color management: speed by LUT
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Color management: speed by LUT
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Color management: speed by LUT
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Color management: speed by LUT
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Linear Interpolation is linear in the outputs
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Linear Interpolation is linear in the outputs
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Linear Interpolation is linear in the outputs
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Lattice Regression Choose the lattice outputs to minimize the post-linear
interpolation empirical risk on the data:
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Lattice Regression Choose the lattice outputs to minimize the post-linear
interpolation empirical risk on the data:
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Lattice Regression Choose the lattice outputs to minimize the post-linear
interpolation empirical risk on the data:
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Effect of Different Lattice Regression Regularizers
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Effect of Different Lattice Regression Regularizers
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Lattice Regression Closed Form Solution
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Sparse: No more than 7dm non-zero entries (of m2) with cubic interpolation.
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Example Color Management Results
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Example Color Management Results
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9/15/2010 31
Omnidirectional Super-resolution:
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Omnidirectional Superres Related Work
State of the Art:
Arican and Frossard 2008-2009 (ICPR 2008 Best Paper Award)
• Interpolation with spherical harmonics
• Alignment with an iterative conjugate gradient approach.
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Lattice Regression Approach Finding the correct registration of the low-resolution images is
challenging non-convex optimization problem.
Evaluate a candidate registration:
use lattice regression on image subset -> high-res spherical grid
sum interpolation error for all left-out low res image data
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Lattice Regression Approach Finding the correct registration of the low-resolution images is
challenging non-convex optimization problem.
Evaluate a candidate registration:
use lattice regression on image subset -> high-res spherical grid
sum interpolation error for all left-out low res image data
Finding the optimal joint registration is a 3(N-1)-d opt. problem
We use FIPS to find the global optimum.
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9/15/2010 36
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Visual Homing
START
.
. .
HOME
. .
.
.
Lattice Regression Better For Visual Homing
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Some Conclusions
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Some Conclusions
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Some Conclusions
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Some Conclusions
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For details, see: • “Optimized Regression for Efficient Function Evaluation,” Eric K. Garcia,
Raman Arora, and Maya R. Gupta, (in review – draft upon request).
• “Lattice Regression”, Eric K. Garcia, Maya R. Gupta, Neural Information Processing Systems (NIPS) 2009.
• “Building Accurate and Smooth ICC Profiles by Lattice Regression,” Eric K. Garcia, Maya R. Gupta, 17th IS&T Color Imaging Conference 2009.
• "Adaptive Local Linear Regression with Application to Printer Color Management," Maya R. Gupta, Eric K. Garcia, and Erika Chin, IEEE Trans. on Image Processing , vol. 17, no. 6, 936-945, 2008.
• "Learning Custom Color Transformations with Adaptive Neighborhoods," Maya R. Gupta, Eric K. Garcia, and Andrey Stroilov, Journal of Electronic Imaging, vol. 17, no. 3, 2008.
• "Gamut Expansion for Video and Image Sets," Hyrum Anderson, Eric K. Garcia, and Maya R. Gupta, Computational Color Imaging Workshop, 2007.
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Color is an event
light source
human
cones respond:
human
perceives
color
L = long wave = red
M = medium wave = green
S = short wave = blue
reflection
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What does it mean to see black?
light source
human
cones respond
???
human
perceives
color
L = long wave = red
M = medium wave = green
S = short wave = blue
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What does it mean to see white?
light source
human
cones respond
???
human
perceives
color
L = long wave = red
M = medium wave = green
S = short wave = blue
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What does it mean to see white? images from: www.omatrix.com/uscolors.html
You can see “white” given
light made up of 2-spectra
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Color Science Crash Course
• What we see can be represented by three primaries.
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Stiles-Burch 10° color matching
functions averaged across 37
observers . Adapted from (Wyszecki
& Stiles, 1982) by handprint.com.
monochromatic
light at some
wavelength
match
mixture of three
primary colors
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Color Distances
• CIELab • Based on spectral
measurements of color, integrated over CMF envelopes.
• Euclidean distance between two colors approximates the perceptual difference noticed by a human observer.
• Distance metrics created to correct for perceptual non- uniformities in the space:
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image source: www.handprint.com
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2-D and 3-D Simulation
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d=2
d=3
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Color printer
8 bit RGB color patch printed
color patch Human eye
Measure CIEL*a*b*
Color management for printers
Goal: Print a given CIEL*a*b* value. Problem: What RGB value to input?
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Inverse Device Characterization
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CIELab
Step 1 Sample the device
Step 2 Build an inverse look-up-table
Regression
Look-up-table
Output Measure
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Gaussian Process Regression • Models data as being drawn from a Gaussian Process
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(L large, σ2 small) (L small, σ2 small) (L large, σ2 large)
• A leading method in geostatistics (2-d regression) also known as Kriging.
• Generally considered a state-of-the-art method by machine learning folks
• Parameters: Covariance Function (length scale L), Noise Power σ2.
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Gaussian Process Regression • Models data as being drawn from a Gaussian Process
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(L large, σ2 small) (L small, σ2 small) (L large, σ2 large)
• A leading method in geostatistics (2-d regression) also known as Kriging.
• Generally considered a state-of-the-art method by machine learning folks
• Parameters: Covariance Function (length scale L), Noise Power σ2.
• Given Covariance form, parameters can be learned by maximizing marginal likelihood. (i.e. automatically from data).
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2-D Simulation
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Gaussian Process Regression (Direct) Gaussian Process Regression (to nodes of lattice) Lattice Regression (GPR bias) Lattice Regression (Bilinear bias)
50 Training Samples 1000 Training Samples
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3-D Simulation
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Gaussian Process Regression (Direct) Gaussian Process Regression (to nodes of lattice) Lattice Regression (GPR bias) Lattice Regression (Bilinear bias)
50 Training Samples 1000 Training Samples