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Invariant Image Improvement by sRGB Colour Space Sharpening

1Graham D. Finlayson, 2Mark S. Drew, and 2Cheng Lu1School of Information Systems, University of East Anglia

Norwich (U.K.) graham@cmp.uea.ac.uk2School of Computing Science, Simon Fraser University

Vancouver (CANADA) {mark,clu}@cs.sfu.ca

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What is an invariant image?

We would like to obtain a greyscale image which removes illuminant effects.

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Shadows stem from what illumination effects?

Changes of illuminant in both intensity and colour• Intensity – can be removed in chromaticity space

• Colour – ? shadows still exist in the chromaticity image!

Region Lit by Sky-light only

)/(},,{ BGRBGR

Region Lit by Sunlight and

Sky-light

)/(},,{ BGRBGR

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Model of illuminantsIllumination is restricted to the Planckian locus

• represent illuminants by their equivalent Planckian black-body illuminants

Wien’s approximation:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

r/(r+g+b)

g/(

r+g

+b

)

Illuminant Chromaticities

Most typical illuminants lie on,

or close to, the Planckian locus

T

c

ecIE 2

51)(

5

)(S

)(E )()( SE

Image Formation

Camera responses depend on 3 factors: light (E), surface (S),

and sensor (Q) is Lambertian shading

,)()()( dQSE kk

BGRk ,,

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Q2()

Sen s

i tiv

i ty

Q1() Q3()

=

Delta functions “select” single wavelengths:

R R1 qQ

Using Delta-Function Sensitivities

RRRRR SEqdESq

GGqQ 2

BBqQ 3

RRR SEqR

GGG SEqG

BBB SEqB

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For delta-function sensors and Planckian illumination we have:

Back to the image formation equation

T

c

kkkkkecIqS 2

51)(

Surface Light

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Band-ratio chromaticity

R

G

B

Plane G=1

Perspective projection onto G=1

,2..1,/ kpkk

Let us define a set of 2D band-ratio chromaticities:

p is one of the channels,(Green, say) [or Geometric Mean]

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Let’s take log’s:

Band-ratios remove shading and intensity

Teess pkpkkk /)()/log()log('

with ,)(51 kkkk qScs kk ce /2

Gives a straight line:

)(

)())/log(()/log(

1

21

'12

'2

p

ppp ee

eessss

Shading and intensity are gone.

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Calibration: find invariant direction

Log-ratio chromaticities for 6 surfaces under 14 different Planckian

illuminants, HP912 camera

Macbeth ColorChecker:

24 patches

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Deriving the Illumination Invariant

This axis is invariant to shading + illuminant

intensity/colour

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Algorithm, cont’d:

eI k''

Form greyscale I’ in log-space:

)'exp(II exponentiate:

Finlayson et al.,ECCV2002

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Problems in Practice

What if camera sensors are not narrowband?

Find a sensor transform M that sharpens camera sensors

• Equivalent to transforming RGB to a new colour space

Kodak DCS420 camera

sensors

3 x 3

colors

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Problem 2: Nonlinearity We generally have nonlinear image data.

Linearise images prior to invariant image formation

Forming invariant image from nonlinear images

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Approach : solve for sharpened sRGB space

sRGB – standard RGB• Color Management strategy proposed by Microsoft and HP• A device independent color space – small cost for storage

and transfer• Transform CIE tristimulus values so as to suit to current

monitors

XYZ sRGB

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sRGB-to-XYZ conversionTwo steps:

• Nonlinear sRGB to linear RGB – Gamma correction

• Transformation to CIE XYZ tristimulus with a D65 white point

– Using a 3 by 3 matrix M

The problem of nonlinearity• solved ! (well enough)

The problem of non-narrowband sensors • XYZ D65 color matching functions are quite

sharp, but can be sharper.

)(S

)(SM

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Spectral sharpening for XYZ D65

∴ Apply database spectral sharpening • mapping two sets of patch images formed with the camera

under two different lights, with a 3 x 3 matrix P

• For diagonal color constancy, compute eigenvectors T of P

• The sharpened XYZ color matching functions under D65 have narrower curves.

.)( 1 TDdiagTP

5065 DD XYZPXYZ

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Linear sRGB color space sharpening

Concatenating the conversion to the XYZ tristimulus values by the spectral sharpening transform T: a sharpened sRGB space.

Performing the invariant image finding routine in this new sharpened linear color space:

)( TMS

RGB → sRGB → XYZ →XYZ#

S M T

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One more trickLogarithms of colour ratios in finding the invariant involves a singularity

Modify by making use of a generalised logarithm function:

)1()( /1 xxg

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Some examples