Contrast Preserving Decolorization Cewu Lu, Li Xu, Jiaya Jia, The Chinese University of Hong Kong.

Contrast Preserving Decolorization

Cewu Lu, Li Xu, Jiaya Jia, The Chinese University of Hong Kong

Mono printers are still the majority

• Fast• Economic• Environmental friendly

Documents generally have color figures

The printing problem

HP printer


Our Result


Decolorization

Mapping

Single Channel

Applications

Color Blindness

Decolorization could lose contrast Mapping( )

Mapping( ) =

=

Mapping

Decolorization could lose contrast

• Bala and Eschbach 2004

• Neumann et al. 2007

• Smith et al. 2008

Pervious Work (Local methods)

Pervious Work (Local methods)

Naive Mapping

Color Contrast

Result

• Gooch et al. 2004

• Rasche et al. 2005

• Kim et al. 2009

Pervious Work (Global methods)


Color feature preserving optimization mapping function

( )g f c


In most global methods, color order is strictly satisfied

( )g f c

Color order could be ambiguous

Can you tell the order?

brightness( ) < brightness ( ) YUV space

Lightness( ) > Lightness ( ) LAB space


People with different culture and language background have different senses of brightness with respect to color.

E. Ozgen et al., Current Directions in Psychological Science, 2004

K. Zhou et al., National Academy of Sciences, 2010

The order of different colors cannot be defined uniquely by people

B. Wong et al., Nature Methods, 2010


If we enforce the color order constraint, contrast loss could happen

Input Ours[Rasche et al. 2005] [Kim et al. 2009]


Our Contribution

Weak Color Order

Bimodal Contrast-PreservingRelax the color order constraint

Unambiguous color pairs

Global Mapping Polynomial Mapping

The Framework

• Objective Function Bimodal Contrast-Preserving Weak Color Order

• Finite Multivariate Polynomial Mapping Function

• Numerical Solution

Bimodal Contrast-Preserving

• Color pixel , grayscale contrast , color contrast (CIELab distance) • follows a Gaussian distribution with mean

{ , }x y xy x yg g g

xyg xy

xy

2

22

, exp2xy xy

xy

gG


• Color pixel , grayscale contrast , color contrast (CIELab distance) • follows a Gaussian distribution with mean .

{ , }x y xy x yg g g

xyg xy

xy

2

22

, exp2xy xy

xy

gG

xy xyg


• Tradition methods (order preserving):

2

( , )

max sign( , ) ,xyg

x y N

G x y

N : neighborhood pixel set

• Our bimodal contrast-preserving for ambiguous color pairs:

2 2

( , )

max , ,xy xyg

x y N

G G


2

( , )

max sign( , ) ,xyg

x y N

G x y

2 2

( , )

max , ,xy xyg

x y N

G G

xyxy

xy xyg

xyg

sign(x,y) 1=


2

( , )

max sign( , ) ,xyg

x y N

G x y

2 2

( , )

max , ,xy xyg

x y N

G G

xyxy

xyg

xyg

xy

sign(x,y) 1=

Our Work




Weak Color Order

• Unambiguous color pairs: or & &x y x y x yr r g g b b & &x y x y x yr r g g b b

Weak Color Order

• Unambiguous color pairs: or & &x y x y x yr r g g b b & &x y x y x yr r g g b b

,

1.0 unambiguous color pair

0.5 ambiguous color pairx y

• Our model thus becomes

2 2, ,

( , )

max , 1 ,x y xy x y xyg

x y N

G G

Our Work




Multivariate Polynomial Mapping Function

2 2, ,

( , )


x y N

G G

Solve for grayscale image: g

Variables (pixels): 400x250 = 100,000

Example

Too many (easily produce unnatural structures)


2 2, ,

( , )


x y N

G G

• Parametric global color-to-grayscale mapping

grayscale value (color vector, )f

Small Scale


31 21 2 3span{ : =0, 1, 2, ... n}dd d

n ir g b d d d d

• Parametric color-to-grayscale( , ) i i

i

f c m n

When n = 2, a grayscale is a linear combination of elements

imthiis the monomial basis of , .

2 2 2{ , , , , , , , , }r g b rg gb rb r g b

{ , , }c r g b



i

f c m



i

f c m

2b2g2r

gbrbrg

bgr



i

f c m

2b2g2r

gbrbrg

bg



i

f c m

2b2g2r

gbrbrg

b



i

f c m

2b2g2r

gbrbrg



i

f c m

2b2g2r

gbrb



i

f c m

2b2g2r

gb



i

f c m

2b2g2r



i

f c m

2b2g



i

f c m

2b



i

f c m



i

f c m

0.1550 0.8835 0.3693

0.1817 0.4977 -1.7275

-0.4479 0.6417 0.6234

Our Model

, ,xy x y x y i ix iyi

g g g f c f c m m

• Objective function:

2 2, ,

( , )

max , 1 ,x y xy x y xyx y N

G G

Numerical Solution

2 2, ,

( , )

max , 1 ,x y xy x y xyx y N

G G

2 2, ,

( , )

min In , 1 ,x y xy x y xyx y N

G G

2 2, ,

( , )

In , 1 ,x y xy x y xyx y N

E G G

Define:

Numerical Solution

0

E

2, ,

, 2 2, , , ,

,

, 1 ,

x y x y

x y

x y x y x y x y

G

G G

min E

, ,( , )

1 2 0i xi yi xj yj x y xj yj x yx y N ij

Em m m m m m

Numerical Solution

, ,( , )

2 1i xi yi xj yj x y xj yj x yx y N i

m m m m m m

Initialize :

Numerical Solution

2, ,

, 2 2, , , ,

,

, 1 ,

x y x y

x y

x y x y x y x y

G

G G

, ,( , )


m m m m m m

obtain

Numerical Solution

2, ,

, 2 2, , , ,

,

, 1 ,

x y x y

x y

x y x y x y x y

G

G G

, ,( , )


m m m m m m

obtainobtain ,x y

Numerical Solution (Example)

2 2 2 r g b rg rb gb r g bIter 1

0.33 0.33 0.33 0.00 0.00 0.00 0.00 0.00 0.00



0.97 0.91 0.38 -3.71 2.46 -4.01 -4.02 4.00 0.79



1.14 -0.25 1.22 -1.55 -1.53 -3.51 -1.18 3.32 0.69



1.33 -1.61 2.10 1.35 -0.36 -1.61 -1.69 1.70 0.29



1.52 -2.25 2.46 2.69 -1.38 -0.30 -1.95 0.79 -0.02



1.98 -3.29 3.02 5.94 -3.38 2.81 -2.91 -1.56 -0.96



1.99 -3.31 3.03 6.03 -3.42 2.89 -2.95 -1.62 -0.98



2.00 -3.32 3.04 6.10 -3.45 2.94 -2.98 -1.67 -1.00

Results

Input

Ours [Rasche et al. 2005] [Kim et al. 2009]

Results (Quantitative Evaluation)

• color contrast preserving ratio (CCPR)

# ( , ) | ( , ) ,| |CCPR=

| |x yx y x y g g

the set containing all neighboring pixel pairs with the original color difference .

,x y


10

Our Results (Quantitative Evaluation)

10

,x y


10

,x y , ,&x y x yg


10

,x y , ,&x y x yg

Number: 38740 Number: 24853


Number: 38740 Number: 24853

24853CCPR= 64.2%

38740

Results (contrast boosting)

substituting our grayscale image for the L channel in the Lab space

Conclusion

• A new color-to-grayscale method that can well maintain the color contrast.

• Weak color constraint.

• Polynomial Mapping Function for global mapping.

The End

Limitations

• Color2gray is very subjective visual experience. Contrast enhancement may not be acceptable for everyone.

• Compared to the naive color2grayscale mapping, our method is less efficient due to the extra operations.

An arguable result

Running Time

• For a 600 × 600 color input, our Matlab implementation takes 0.8s

• A C-language implementation can be 10 times faster at least.

Contrast Preserving Decolorization Cewu Lu, Li Xu, Jiaya Jia, The Chinese University of Hong Kong.

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