A detailed descriptions and results for different color constancy algorithms

Color ConstancyAlgorithms

Pi19404

December 30, 2012

❈♦♥t❡♥ts

❈♦♥t❡♥ts

❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡ ✸

0.1 Color Constancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

0.2 Gray world assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

0.3 normalized minkowski p-norm . . . . . . . . . . . . . . . . . . . . . . . . 10

0.4 Max-RGB Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

0.5 Gray-Edge Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

0.6 Max-Edge Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

0.7 Gray World Algorithm and Shades of Gray in Lab Color Space . . . . . . 19

0.8 A Simple White Balance Algorithm . . . . . . . . . . . . . . . . . . . . . . 26

0.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

0.10 Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

✵✳✶ ❈♦❧♦r ❈♦♥st❛♥❝②

Color constancy is a mechanism of detection of color independent of light source. The

light source many introduce color casts in captured digital images To solve the color

constancy problem a standard method is to estimate the color of the prevailing light

and then, at the second stage, remove it. Once the color of light in individual channels

is obtained the each color pixel is normalized by a scaling factor .

Two of the most commonly used simple techniques for estimating the color of the light

are the Grey-World and Max-RGB algorithms. These two methods will work well in

practice if the average scene color is gray or the maximum is white

✵✳✷ ●r❛② ✇♦r❧❞ ❛ss✉♠♣t✐♦♥

The Gray World Assumption is a white balance method that assumes that your scene, on

average, is a neutral gray. Gray-world assumption hold if we have a good distribution of

colors in the scene. Assuming that we have a good distribution of colors in our scene,the

average reflected color is assumed to be the color of the light. Therefore, we can esti-

mate the illumination color cast by looking at the average color and comparing it to gray.

Gray world algorithm produces an estimate of illumination by computing the mean

of each channel of the image.

One of the methods of normalization is that the mean of the three components is used

as illumination estimate of the image. To normalize the image of channel i ,the pixel

value is scaled by s1 = avgavgi

where avgi is the channel mean and avg is the illumination

estimate .

Another method of normalization is normalizing to the maximum channel by scaling

by si

ri =max(avgR, avgG, avgB)

avgi

Another method of normalization is normalizing to the maximum channel by scaling

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

by norm mi

mi =√

(avgr ∗ avgr + avgg ∗ avgg + avgb ∗ avgb)

ri =max(mR, mG, mB)

mi

Attached are output of standard contrast stretching and present algorithm

(a) original (b) ld normalization method 1 (c) normalization method 2

(d) normalization method 3

Figure 1: Example 1.1:gray world




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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡







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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡







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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡







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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡




(a) original (b) normalization method 1 (c) normalization method 2



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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

✵✳✸ ♥♦r♠❛❧✐③❡❞ ♠✐♥❦♦✇s❦✐ ♣✲♥♦r♠

Another variant to estimate illumination vector is to calculate the normalized minkowski

p-norm for each color channel color constancy algorithm which is based on Minkowski

norm - for each color channel, the Minkowski p-norm is calculated and the normalized

result forms the estimated illumination vector.

ei =

(

1

N ∑i

pi

)1/p

where summation if over all the pixels.

Gray world algorithm is obtained by setting p=1 The shades of gray, is given by Fin-

layson and Trezzi concluded that using Minkowski norm with p = 6 gave the best

estimation results on their data set.



Figure 13: Example 2.a1:minkowski norm 6

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Figure 14: Example 2.a2:minkowski norm 6



Figure 15: Example 2.4:shades of gray

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡







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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡







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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡







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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

✵✳✹ ▼❛①✲❘●❇ ❆❧❣♦r✐t❤♠

This method is based on the assumption that human visual system achieves color con-

stancy by detecting the area of highest reflectance in the field of view and normalizes

the response according to these maximal values. The algorithm calculate the maximum

value in R,G,B channels and normalizes the pixels according to the maximum value.

This algorithm would produce correct results if the scene contains a white patch which

reflects all light equally such that maximum of R,G,B would be found on the white

patch. It would be good to ignore the pixels above 95% of the dynamic range so that

pixel values are not clipped or saturated. The shades of gray algorithm is a combination

of gray world and max-RGB algorithm. However this method may not work in all

cases.Below are examples for the same The enhancement is also very subtle in both the

cases.The changes are visible once program is run of images of actual size and difference

and be clearly observed


Figure 24: Example 3:max-RGB algorithm

(a) original (b) original (c) normalization method 2


Figure 25: Example 4 : max-RGB Algorithm

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

✵✳✺ ●r❛②✲❊❞❣❡ ❆❧❣♦r✐t❤♠

This method is similar to shades of gray algorithm but considers the image derivatives

instead of image itself.This assumption is based on the observation that the distribu-

tion of derivatives of images forms an ellipsoid in R, G, B space, of which the long

axis coincides with the illumination vector. The first step of algorithm is to apply a

Gaussian filter on each color channel separately. This is done to remove the noise since

the noise could be amplified by the derivative The minkowski norm of the derivative

of each of channel is computed. The vector components are normalized to obtain es-

timate of illumination vector and the normalization can be performed on any of the

above mentioned techniques Like the max-RGB it shows very little improvement for

the underwater image.



Figure 26: Example 4.1 :Gray-Edge

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

(a) original (b) normalization method 1 (c) 6 normalization method 2





Figure 28: Example 4.3 :Gray-Edge minkowski norm 6

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Figure 29: Example 4.4 :Gray-Edge minkowski norm 6

✵✳✻ ▼❛①✲❊❞❣❡ ❆❧❣♦r✐t❤♠

This method is similar to max-RGB algorithm but considers the image derivatives in-

stead of image itself.This assumption is based on the observation that the distribution

of derivatives of images forms an ellipsoid in R, G, B space, of which the long axis

coincides with the illumination vector. The first step of algorithm is to apply a Gaussian

filter on each color channel separately. This is done to remove the noise since the noise

could be amplified by the derivative the maximum value in each channel is computed

and vector is used to estimate illumination vector. The vector components are normal-

ized to obtain estimate of illumination vector and the normalization can be performed

on any of the above mentioned techniques Like the max-RGB it shows very little subtel

changes for the underwater image.

✵✳✼ ●r❛② ❲♦r❧❞ ❆❧❣♦r✐t❤♠ ❛♥❞ ❙❤❛❞❡s ♦❢ ●r❛② ✐♥ ▲❛❜ ❈♦❧♦r

❙♣❛❝❡

This is the same gray world algorithm implemented in Lab Color space. The mean

value of chromatic components are computed in a,b spaces. The a,b value of each pixel

in the image are added/subtracted based on a by value proportional to mean a,b values

computed.The constant of proportionality is normalized luminosity component llmax .

OpenCV uses 0-255 range for all the components .Thus we convert values so that l takes

values in range 0-100 , and a and b take values in the range -128 to +128.

The shades of gray algorithm can also be modified using the same approach. However

no appreciable difference is observed.

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Figure 30: Example 5.1 :Max-Edge

(a) original (b) normalization method 1 (c) 6 normalization method 2



(a) original (b) normalization method 1

Figure 32: Example 6.1 :Gray-World in Lab Color Space

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡


Figure 33: Example 6.2 :Gray-World in Lab Color space

(a) original (b) ld normalization method 1

Figure 34: Example 6.1:gray world in Lab color space




Figure 36: Example 6.3:shades of graygray world in Lab color space

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡






Figure 43: Example 7.a :shades of gray in Lab Color Space


Figure 44: Example 7b :Shades of gray in Lab Color space

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡


Figure 45: Example 7.1:shades of gray in Lab Color Space






Figure 48: Example 7.4:sshades of gray in Lab Color Space

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡



✵✳✽ ❆ ❙✐♠♣❧❡ ❲❤✐t❡ ❇❛❧❛♥❝❡ ❆❧❣♦r✐t❤♠

This a variant of contrast stretching algorithm.A contrast stretching is a method to im-

prove the contrast of the image so that values of channel occupy the maximal range of

[0,255] for 8 Bit image.This can be performed by applying a affine transformation ax+b

to each channel,we need to chose a,b such that maximal value becomes 255 and minimal

value 0.

But this method has the drawback that it may introduce artifacts in some cases . consider

the situation that Red channel occupies values in the range 0-10 . Contrast stretching

stretches the range to take values in the range 0-255 ,initially pixels near zero values will

begin to take large values.

The same is the case if bright pixels dominate the channel,it will lead to some of values

becoming dark after stretching ,this would not provide a visually appealing output.

To avoid the above cases ,the contrast stretching is performed for only on a subset

of range occupied by the channel.The present algorithm based on the predefined crite-

ria determine the range [vmin, vmax].The values below vmin are saturated to take value 0

,value above vmax are saturated to take value 255 and contrast stretching is performed

for the pixels in the range [vmin, vmax]

The input to algorithm is the % of pixels to saturate above and below. Let parameters

be s1% and s2% for higher and lower saturation thresholds. Let N be the total number

of pixels in the image.s1 ∗ N% of pixels in lower range and s2 ∗ N% of pixels in higher

range are pixels to be saturated.

The algorithm can be implemented as follows :

1. Compute Histogram of image

2. Compute the Cumulative distribution function of image

3. Find pixel index i1 and i2 such that CDF = s1 ∗ N%,and pixel index such that

CDF = (1 − s2) ∗ N%

4. Set all pixels less than i1 to 0 and all pixel greater than i2 to 255.

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡

5. For all pixels in the range [i1, i2] apply affine transformation to perform contrast

stretching.

pi =(pi − i1) ∗ 255

(i2 − i1)

For color images the above algorithm is applied on each of channels of the image.

(a) contrast stretching (b) present algorithm

Figure 54: Example 1


Figure 55: Example 7.a :shades of gray in Lab Color Space


Figure 56: Example 7b :Shades of gray in Lab Color space

All the images are taken from http : //research.edm.uhasselt.be/ oancuti/UnderwaterCVPR2012/imagese

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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡


Figure 57: Example 8.1:color contrast







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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡









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❆✉t♦♠❛t✐❝ ❲❤✐t❡ ❇❛❧❛♥❝❡



✵✳✾ ❘❡❢❡r❡♥❝❡s

1. A New Color Balancing Method ❤tt♣✿✴✴✇✇✇✳st❛♥❢♦r❞✳❡❞✉✴❝❧❛ss✴❡❡✸✻✽✴Pr♦❥❡❝t❴

✶✶✴❘❡♣♦rts✴❈♦❤❡♥❴❆❴◆❡✇❴❈♦❧♦r❴❇❛❧❛♥❝✐♥❣❴▼❡t❤♦❞✳♣❞❢❛✉t❤♦r

2. ❤tt♣✿✴✴r❡s❡❛r❝❤✳❡❞♠✳✉❤❛ss❡❧t✳❜❡✴⑦♦❛♥❝✉t✐✴❯♥❞❡r✇❛t❡r❴❈❱P❘❴✷✵✶✷✴❈❱P❘❴✉♥❞❡r✇❛t❡r❴

❢✐♥❛❧✳♣❞❢

3. ❤tt♣✿✴✴✇✇✇✳✐♠❛❣✐♥❣✳♦r❣✴■❙❚✴st♦r❡✴❡♣✉❜✳❝❢♠❄❛❜str✐❞❂✸✷✶✶✼

4. ❤tt♣s✿✴✴✉❡❛❡♣r✐♥ts✳✉❡❛✳❛❝✳✉❦✴✷✸✻✽✷✴

5. http://www.ipol.im/pub/art/2011/llmps-scb/

6. Limare, Nicolas, Jose-Luis Lisani, Jean-Michel Morel, Ana Belén Petro, and Catalina

Sbert. “Simplest Color Balance.” Image Processing On Line 2011 (2011).

7. Wikipedia contributors, "Color balance", Wikipedia, The Free Encyclopedia

8. ❤tt♣✿✴✴r❡s❡❛r❝❤✳❡❞♠✳✉❤❛ss❡❧t✳❜❡✴⑦♦❛♥❝✉t✐✴❯♥❞❡r✇❛t❡r❴❈❱P❘❴✷✵✶✷

✵✳✶✵ ❈♦❞❡

For code refer to site ❤tt♣✿✴✴❝♦❞❡✳❣♦♦❣❧❡✳❝♦♠✴♣✴♠✶✾✹✵✹✴s♦✉r❝❡✴❜r♦✇s❡✴❈♦❧♦r❈♦♥st❛♥❝②✴

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http://www.stanford.edu/class/ee368/Project_11/Reports/Cohen_A_New_Color_Balancing_Method.pdfauthor

http://www.stanford.edu/class/ee368/Project_11/Reports/Cohen_A_New_Color_Balancing_Method.pdfauthor

http://research.edm.uhasselt.be/~oancuti/Underwater_CVPR_2012/CVPR_underwater_final.pdf

http://research.edm.uhasselt.be/~oancuti/Underwater_CVPR_2012/CVPR_underwater_final.pdf

http://www.imaging.org/IST/store/epub.cfm?abstrid=32117

https://ueaeprints.uea.ac.uk/23682/

http://research.edm.uhasselt.be/~oancuti/Underwater_CVPR_2012

http://code.google.com/p/m19404/source/browse/ColorConstancy/

A detailed descriptions and results for different color constancy algorithms

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