Detailed Description

Introduction

The purpose of color correction is to adjust the color response of input and output devices to a known state. The device being calibrated is sometimes called the calibration source; the color space used as the standard is sometimes called the calibration target. Color calibration has been used in many industries, such as television production, games, photography, engineering, chemistry, medicine, etc. Due to the manufacturing process of the input and output equipment, the channel response has nonlinear distortion. In order to correct the picture output of the equipment, it is nessary to calibrate the captured color and the actual color.

Classes
class	cv::ccm::ColorCorrectionModel
	Core class of ccm model. More...

Enumerations
enum	cv::ccm::CCM_TYPE { cv::ccm::CCM_3x3 , cv::ccm::CCM_4x3 }
	Enum of the possible types of ccm. More...

enum	cv::ccm::COLOR_SPACE { cv::ccm::COLOR_SPACE_sRGB , cv::ccm::COLOR_SPACE_sRGBL , cv::ccm::COLOR_SPACE_AdobeRGB , cv::ccm::COLOR_SPACE_AdobeRGBL , cv::ccm::COLOR_SPACE_WideGamutRGB , cv::ccm::COLOR_SPACE_WideGamutRGBL , cv::ccm::COLOR_SPACE_ProPhotoRGB , cv::ccm::COLOR_SPACE_ProPhotoRGBL , cv::ccm::COLOR_SPACE_DCI_P3_RGB , cv::ccm::COLOR_SPACE_DCI_P3_RGBL , cv::ccm::COLOR_SPACE_AppleRGB , cv::ccm::COLOR_SPACE_AppleRGBL , cv::ccm::COLOR_SPACE_REC_709_RGB , cv::ccm::COLOR_SPACE_REC_709_RGBL , cv::ccm::COLOR_SPACE_REC_2020_RGB , cv::ccm::COLOR_SPACE_REC_2020_RGBL , cv::ccm::COLOR_SPACE_XYZ_D65_2 , cv::ccm::COLOR_SPACE_XYZ_D65_10 , cv::ccm::COLOR_SPACE_XYZ_D50_2 , cv::ccm::COLOR_SPACE_XYZ_D50_10 , cv::ccm::COLOR_SPACE_XYZ_A_2 , cv::ccm::COLOR_SPACE_XYZ_A_10 , cv::ccm::COLOR_SPACE_XYZ_D55_2 , cv::ccm::COLOR_SPACE_XYZ_D55_10 , cv::ccm::COLOR_SPACE_XYZ_D75_2 , cv::ccm::COLOR_SPACE_XYZ_D75_10 , cv::ccm::COLOR_SPACE_XYZ_E_2 , cv::ccm::COLOR_SPACE_XYZ_E_10 , cv::ccm::COLOR_SPACE_Lab_D65_2 , cv::ccm::COLOR_SPACE_Lab_D65_10 , cv::ccm::COLOR_SPACE_Lab_D50_2 , cv::ccm::COLOR_SPACE_Lab_D50_10 , cv::ccm::COLOR_SPACE_Lab_A_2 , cv::ccm::COLOR_SPACE_Lab_A_10 , cv::ccm::COLOR_SPACE_Lab_D55_2 , cv::ccm::COLOR_SPACE_Lab_D55_10 , cv::ccm::COLOR_SPACE_Lab_D75_2 , cv::ccm::COLOR_SPACE_Lab_D75_10 , cv::ccm::COLOR_SPACE_Lab_E_2 , cv::ccm::COLOR_SPACE_Lab_E_10 }

enum	cv::ccm::CONST_COLOR { cv::ccm::COLORCHECKER_Macbeth , cv::ccm::COLORCHECKER_Vinyl , cv::ccm::COLORCHECKER_DigitalSG }
	Macbeth and Vinyl ColorChecker with 2deg D50. More...

enum	cv::ccm::DISTANCE_TYPE { cv::ccm::DISTANCE_CIE76 , cv::ccm::DISTANCE_CIE94_GRAPHIC_ARTS , cv::ccm::DISTANCE_CIE94_TEXTILES , cv::ccm::DISTANCE_CIE2000 , cv::ccm::DISTANCE_CMC_1TO1 , cv::ccm::DISTANCE_CMC_2TO1 , cv::ccm::DISTANCE_RGB , cv::ccm::DISTANCE_RGBL }
	Enum of possible functions to calculate the distance between colors. More...

enum	cv::ccm::INITIAL_METHOD_TYPE { cv::ccm::INITIAL_METHOD_WHITE_BALANCE , cv::ccm::INITIAL_METHOD_LEAST_SQUARE }
	Enum of the possible types of initial method. More...

enum	cv::ccm::LINEAR_TYPE { cv::ccm::LINEARIZATION_IDENTITY , cv::ccm::LINEARIZATION_GAMMA , cv::ccm::LINEARIZATION_COLORPOLYFIT , cv::ccm::LINEARIZATION_COLORLOGPOLYFIT , cv::ccm::LINEARIZATION_GRAYPOLYFIT , cv::ccm::LINEARIZATION_GRAYLOGPOLYFIT }
	Linearization transformation type. More...

Enumeration Type Documentation

◆ CCM_TYPE

enum cv::ccm::CCM_TYPE

#include <opencv2/mcc/ccm.hpp>

Enum of the possible types of ccm.

Enumerator
CCM_3x3 Python: cv.ccm.CCM_3x3	The CCM with the shape \(3\times3\) performs linear transformation on color values.
CCM_4x3 Python: cv.ccm.CCM_4x3	The CCM with the shape \(4\times3\) performs affine transformation.

◆ COLOR_SPACE

enum cv::ccm::COLOR_SPACE

#include <opencv2/mcc/ccm.hpp>

Enumerator
COLOR_SPACE_sRGB Python: cv.ccm.COLOR_SPACE_sRGB	https://en.wikipedia.org/wiki/SRGB , RGB color space
COLOR_SPACE_sRGBL Python: cv.ccm.COLOR_SPACE_sRGBL	https://en.wikipedia.org/wiki/SRGB , linear RGB color space
COLOR_SPACE_AdobeRGB Python: cv.ccm.COLOR_SPACE_AdobeRGB	https://en.wikipedia.org/wiki/Adobe_RGB_color_space , RGB color space
COLOR_SPACE_AdobeRGBL Python: cv.ccm.COLOR_SPACE_AdobeRGBL	https://en.wikipedia.org/wiki/Adobe_RGB_color_space , linear RGB color space
COLOR_SPACE_WideGamutRGB Python: cv.ccm.COLOR_SPACE_WideGamutRGB	https://en.wikipedia.org/wiki/Wide-gamut_RGB_color_space , RGB color space
COLOR_SPACE_WideGamutRGBL Python: cv.ccm.COLOR_SPACE_WideGamutRGBL	https://en.wikipedia.org/wiki/Wide-gamut_RGB_color_space , linear RGB color space
COLOR_SPACE_ProPhotoRGB Python: cv.ccm.COLOR_SPACE_ProPhotoRGB	https://en.wikipedia.org/wiki/ProPhoto_RGB_color_space , RGB color space
COLOR_SPACE_ProPhotoRGBL Python: cv.ccm.COLOR_SPACE_ProPhotoRGBL	https://en.wikipedia.org/wiki/ProPhoto_RGB_color_space , linear RGB color space
COLOR_SPACE_DCI_P3_RGB Python: cv.ccm.COLOR_SPACE_DCI_P3_RGB	https://en.wikipedia.org/wiki/DCI-P3 , RGB color space
COLOR_SPACE_DCI_P3_RGBL Python: cv.ccm.COLOR_SPACE_DCI_P3_RGBL	https://en.wikipedia.org/wiki/DCI-P3 , linear RGB color space
COLOR_SPACE_AppleRGB Python: cv.ccm.COLOR_SPACE_AppleRGB	https://en.wikipedia.org/wiki/RGB_color_space , RGB color space
COLOR_SPACE_AppleRGBL Python: cv.ccm.COLOR_SPACE_AppleRGBL	https://en.wikipedia.org/wiki/RGB_color_space , linear RGB color space
COLOR_SPACE_REC_709_RGB Python: cv.ccm.COLOR_SPACE_REC_709_RGB	https://en.wikipedia.org/wiki/Rec._709 , RGB color space
COLOR_SPACE_REC_709_RGBL Python: cv.ccm.COLOR_SPACE_REC_709_RGBL	https://en.wikipedia.org/wiki/Rec._709 , linear RGB color space
COLOR_SPACE_REC_2020_RGB Python: cv.ccm.COLOR_SPACE_REC_2020_RGB	https://en.wikipedia.org/wiki/Rec._2020 , RGB color space
COLOR_SPACE_REC_2020_RGBL Python: cv.ccm.COLOR_SPACE_REC_2020_RGBL	https://en.wikipedia.org/wiki/Rec._2020 , linear RGB color space
COLOR_SPACE_XYZ_D65_2 Python: cv.ccm.COLOR_SPACE_XYZ_D65_2	https://en.wikipedia.org/wiki/CIE_1931_color_space , non-RGB color space
COLOR_SPACE_XYZ_D65_10 Python: cv.ccm.COLOR_SPACE_XYZ_D65_10	non-RGB color space
COLOR_SPACE_XYZ_D50_2 Python: cv.ccm.COLOR_SPACE_XYZ_D50_2	non-RGB color space
COLOR_SPACE_XYZ_D50_10 Python: cv.ccm.COLOR_SPACE_XYZ_D50_10	non-RGB color space
COLOR_SPACE_XYZ_A_2 Python: cv.ccm.COLOR_SPACE_XYZ_A_2	non-RGB color space
COLOR_SPACE_XYZ_A_10 Python: cv.ccm.COLOR_SPACE_XYZ_A_10	non-RGB color space
COLOR_SPACE_XYZ_D55_2 Python: cv.ccm.COLOR_SPACE_XYZ_D55_2	non-RGB color space
COLOR_SPACE_XYZ_D55_10 Python: cv.ccm.COLOR_SPACE_XYZ_D55_10	non-RGB color space
COLOR_SPACE_XYZ_D75_2 Python: cv.ccm.COLOR_SPACE_XYZ_D75_2	non-RGB color space
COLOR_SPACE_XYZ_D75_10 Python: cv.ccm.COLOR_SPACE_XYZ_D75_10	non-RGB color space
COLOR_SPACE_XYZ_E_2 Python: cv.ccm.COLOR_SPACE_XYZ_E_2	non-RGB color space
COLOR_SPACE_XYZ_E_10 Python: cv.ccm.COLOR_SPACE_XYZ_E_10	non-RGB color space
COLOR_SPACE_Lab_D65_2 Python: cv.ccm.COLOR_SPACE_Lab_D65_2	https://en.wikipedia.org/wiki/CIELAB_color_space , non-RGB color space
COLOR_SPACE_Lab_D65_10 Python: cv.ccm.COLOR_SPACE_Lab_D65_10	non-RGB color space
COLOR_SPACE_Lab_D50_2 Python: cv.ccm.COLOR_SPACE_Lab_D50_2	non-RGB color space
COLOR_SPACE_Lab_D50_10 Python: cv.ccm.COLOR_SPACE_Lab_D50_10	non-RGB color space
COLOR_SPACE_Lab_A_2 Python: cv.ccm.COLOR_SPACE_Lab_A_2	non-RGB color space
COLOR_SPACE_Lab_A_10 Python: cv.ccm.COLOR_SPACE_Lab_A_10	non-RGB color space
COLOR_SPACE_Lab_D55_2 Python: cv.ccm.COLOR_SPACE_Lab_D55_2	non-RGB color space
COLOR_SPACE_Lab_D55_10 Python: cv.ccm.COLOR_SPACE_Lab_D55_10	non-RGB color space
COLOR_SPACE_Lab_D75_2 Python: cv.ccm.COLOR_SPACE_Lab_D75_2	non-RGB color space
COLOR_SPACE_Lab_D75_10 Python: cv.ccm.COLOR_SPACE_Lab_D75_10	non-RGB color space
COLOR_SPACE_Lab_E_2 Python: cv.ccm.COLOR_SPACE_Lab_E_2	non-RGB color space
COLOR_SPACE_Lab_E_10 Python: cv.ccm.COLOR_SPACE_Lab_E_10	non-RGB color space

◆ CONST_COLOR

enum cv::ccm::CONST_COLOR

#include <opencv2/mcc/ccm.hpp>

Macbeth and Vinyl ColorChecker with 2deg D50.

Enumerator
COLORCHECKER_Macbeth Python: cv.ccm.COLORCHECKER_Macbeth	Macbeth ColorChecker.
COLORCHECKER_Vinyl Python: cv.ccm.COLORCHECKER_Vinyl	DKK ColorChecker.
COLORCHECKER_DigitalSG Python: cv.ccm.COLORCHECKER_DigitalSG	DigitalSG ColorChecker with 140 squares.

◆ DISTANCE_TYPE

enum cv::ccm::DISTANCE_TYPE

#include <opencv2/mcc/ccm.hpp>

Enum of possible functions to calculate the distance between colors.

See https://en.wikipedia.org/wiki/Color_difference for details

Enumerator
DISTANCE_CIE76 Python: cv.ccm.DISTANCE_CIE76	The 1976 formula is the first formula that related a measured color difference to a known set of CIELAB coordinates.
DISTANCE_CIE94_GRAPHIC_ARTS Python: cv.ccm.DISTANCE_CIE94_GRAPHIC_ARTS	The 1976 definition was extended to address perceptual non-uniformities.
DISTANCE_CIE94_TEXTILES Python: cv.ccm.DISTANCE_CIE94_TEXTILES
DISTANCE_CIE2000 Python: cv.ccm.DISTANCE_CIE2000
DISTANCE_CMC_1TO1 Python: cv.ccm.DISTANCE_CMC_1TO1	In 1984, the Colour Measurement Committee of the Society of Dyers and Colourists defined a difference measure, also based on the LCh color model.
DISTANCE_CMC_2TO1 Python: cv.ccm.DISTANCE_CMC_2TO1
DISTANCE_RGB Python: cv.ccm.DISTANCE_RGB	Euclidean distance of rgb color space.
DISTANCE_RGBL Python: cv.ccm.DISTANCE_RGBL	Euclidean distance of rgbl color space.

◆ INITIAL_METHOD_TYPE

enum cv::ccm::INITIAL_METHOD_TYPE

#include <opencv2/mcc/ccm.hpp>

Enum of the possible types of initial method.

Enumerator

INITIAL_METHOD_WHITE_BALANCE

Python: cv.ccm.INITIAL_METHOD_WHITE_BALANCE

The white balance method. The initial value is:

INITIAL_METHOD_LEAST_SQUARE

Python: cv.ccm.INITIAL_METHOD_LEAST_SQUARE

the least square method is an optimal solution under the linear RGB distance function

\( M_{CCM}= \begin{bmatrix} k_R & 0 & 0\\ 0 & k_G & 0\\ 0 & 0 & k_B\\ \end{bmatrix} \)
where
\( k_R=mean(R_{li}')/mean(R_{li})\\ k_R=mean(G_{li}')/mean(G_{li})\\ k_R=mean(B_{li}')/mean(B_{li}) \)

◆ LINEAR_TYPE

enum cv::ccm::LINEAR_TYPE

#include <opencv2/mcc/ccm.hpp>

Linearization transformation type.

The first step in color correction is to linearize the detected colors. Because the input color space has not been calibrated, we usually use some empirical methods to linearize. There are several common linearization methods. The first is identical transformation, the second is gamma correction, and the third is polynomial fitting.

Linearization is generally an elementwise function. The mathematical symbols are as follows:

\(C\): any channel of a color, could be \(R, G\) or \(B\).

\(R, G, B\): \(R, G, B\) channels respectively.

\(G\): grayscale;

\(s,sl\): subscript, which represents the detected data and its linearized value, the former is the input and the latter is the output;

\(d,dl\): subscript, which represents the reference data and its linearized value

Identical Transformation

No change is made during the Identical transformation linearization, usually because the tristimulus values of the input RGB image is already proportional to the luminance. For example, if the input measurement data is in RAW format, the measurement data is already linear, so no linearization is required.

The identity transformation formula is as follows:

\[ C_{sl}=C_s \]

Gamma Correction

Gamma correction is a means of performing nonlinearity in RGB space, see the Color Space documentation for details. In the linearization part, the value of \(\gamma\) is usually set to 2.2. You can also customize the value.

The formula for gamma correction linearization is as follows:

\[ C_{sl}=C_s^{\gamma},\qquad C_s\ge0\\ C_{sl}=-(-C_s)^{\gamma},\qquad C_s<0\\\\ \]

Polynomial Fitting

Polynomial fitting uses polynomials to linearize. Provided the polynomial is:

\[ f(x)=a_nx^n+a_{n-1}x^{n-1}+... +a_0 \]

Then:

\[ C_{sl}=f(C_s) \]

In practice, \(n\le3\) is used to prevent overfitting.

There are many variants of polynomial fitting, the difference lies in the way of generating \(f(x)\). It is usually necessary to use linearized reference colors and corresponding detected colors to calculate the polynomial parameters. However, not all colors can participate in the calculation. The saturation detected colors needs to be removed. See the algorithm introduction document for details.

Fitting Channels Respectively

Use three polynomials, \(r(x), g(x), b(x)\), to linearize each channel of the RGB color space[1-3]:

\[ R_{sl}=r(R_s)\\ G_{sl}=g(G_s)\\ B_{sl}=b(B_s)\\ \]

The polynomial is generated by minimizing the residual sum of squares between the detected data and the linearized reference data. Take the R-channel as an example:

\[ R=\arg min_{f}(\Sigma(R_{dl}-f(R_S)^2) \]

It's equivalent to finding the least square regression for below equations:

\[ f(R_{s1})=R_{dl1}\\ f(R_{s2})=R_{dl2}\\ ... \]

With a polynomial, the above equations becomes:

\[ \begin{bmatrix} R_{s1}^{n} & R_{s1}^{n-1} & ... & 1\\ R_{s2}^{n} & R_{s2}^{n-1} & ... & 1\\ ... & ... & ... & ... \end{bmatrix} \begin{bmatrix} a_{n}\\ a_{n-1}\\ ... \\ a_0 \end{bmatrix} = \begin{bmatrix} R_{dl1}\\ R_{dl2}\\ ... \end{bmatrix} \]

It can be expressed as a system of linear equations:

\[ AX=B \]

When the number of reference colors is not less than the degree of the polynomial, the linear system has a least-squares solution:

\[ X=(A^TA)^{-1}A^TB \]

Once we get the polynomial coefficients, we can get the polynomial r.

This method of finding polynomial coefficients can be implemented by numpy.polyfit in numpy, expressed here as:

\[ R=polyfit(R_S, R_{dl}) \]

Note that, in general, the polynomial that we want to obtain is guaranteed to monotonically increase in the interval [0,1] , but this means that nonlinear method is needed to generate the polynomials(see [4] for detail). This would greatly increases the complexity of the program. Considering that the monotonicity does not affect the correct operation of the color correction program, polyfit is still used to implement the program.

Parameters for other channels can also be derived in a similar way.

Grayscale Polynomial Fitting

In this method[2], single polynomial is used for all channels. The polynomial is still a polyfit result from the detected colors to the linear reference colors. However, only the gray of the reference colors can participate in the calculation.

Since the detected colors corresponding to the gray of reference colors is not necessarily gray, it needs to be grayed. Grayscale refers to the Y channel of the XYZ color space. The color space of the detected data is not determined and cannot be converted into the XYZ space. Therefore, the sRGB formula is used to approximate[5].

\[ G_{s}=0.2126R_{s}+0.7152G_{s}+0.0722B_{s} \]

Then the polynomial parameters can be obtained by using the polyfit.

\[ f=polyfit(G_{s}, G_{dl}) \]

After \(f\) is obtained, linearization can be performed.

Logarithmic Polynomial Fitting

For gamma correction formula, we take the logarithm:

\[ ln(C_{sl})={\gamma}ln(C_s),\qquad C_s\ge0\ \]

It can be seen that there is a linear relationship between \(ln(C_s)\) and \(ln(C_{sl})\). It can be considered that the formula is an approximation of a polynomial relationship, that is, there exists a polynomial \(f\), which makes[2]:

\[ ln(C_{sl})=f(ln(C_s)), \qquad C_s>0\\ C_{sl}=0, \qquad C_s=0 \]

Because \(exp(ln(0))\to\infty \), the channel whose component is 0 is directly mapped to 0 in the formula above.

For fitting channels respectively, we have:

\[ r=polyfit(ln(R_s),ln(R_{dl}))\\ g=polyfit(ln(G_s),ln(G_{dl}))\\ b=polyfit(ln(B_s),ln(B_{dl}))\\ \]

Note that the parameter of \(ln(*) \) cannot be 0. Therefore, we need to delete the channels whose values are 0 from \(R_s \) and \(R_{dl} \), \(G_s\) and \(G_{dl}\), \(B_s\) and \(B_{dl}\).

Therefore:

\[ ln(R_{sl})=r(ln(R_s)), \qquad R_s>0\\ R_{sl}=0, \qquad R_s=0\\ ln(G_{sl})=g(ln(G_s)),\qquad G_s>0\\ G_{sl}=0, \qquad G_s=0\\ ln(B_{sl})=b(ln(B_s)),\qquad B_s>0\\ B_{sl}=0, \qquad B_s=0\\ \]

For grayscale polynomials, there are also:

\[ f=polyfit(ln(G_{sl}),ln(G_{dl})) \]

and:

\[ ln(C_{sl})=f(ln(C_s)), \qquad C_s>0\\ C_sl=0, \qquad C_s=0 \]

Enumerator
LINEARIZATION_IDENTITY Python: cv.ccm.LINEARIZATION_IDENTITY	no change is made
LINEARIZATION_GAMMA Python: cv.ccm.LINEARIZATION_GAMMA	gamma correction; Need assign a value to gamma simultaneously
LINEARIZATION_COLORPOLYFIT Python: cv.ccm.LINEARIZATION_COLORPOLYFIT	polynomial fitting channels respectively; Need assign a value to deg simultaneously
LINEARIZATION_COLORLOGPOLYFIT Python: cv.ccm.LINEARIZATION_COLORLOGPOLYFIT	logarithmic polynomial fitting channels respectively; Need assign a value to deg simultaneously
LINEARIZATION_GRAYPOLYFIT Python: cv.ccm.LINEARIZATION_GRAYPOLYFIT	grayscale polynomial fitting; Need assign a value to deg and dst_whites simultaneously
LINEARIZATION_GRAYLOGPOLYFIT Python: cv.ccm.LINEARIZATION_GRAYLOGPOLYFIT	grayscale Logarithmic polynomial fitting; Need assign a value to deg and dst_whites simultaneously

Detailed Description

Introduction

Classes

Enumerations

Enumeration Type Documentation

◆ CCM_TYPE

◆ COLOR_SPACE

◆ CONST_COLOR

◆ DISTANCE_TYPE

◆ INITIAL_METHOD_TYPE

◆ LINEAR_TYPE

Identical Transformation

Gamma Correction

Polynomial Fitting

Fitting Channels Respectively

Grayscale Polynomial Fitting

Logarithmic Polynomial Fitting