Opencv L*a*b* to RGB conversion produces grayscale output

Question

I've been assigned to change a picture from the Lab* color space to RGB using OpenCV. In order to do that I used the information presented here and here.

EDIT: Was assigned to do it without the cvtColor function that comes with OpenCV.

Also tried to implement the formulas directly from here. I'm still a newbie in image processing and don't know if my result is functional. I can see each of the channels and the parameters for the RGB image are between 0 and 255 but when merging the channels I obtain a grayscale image. I expected that after converting from Lab* to RGB I would get the original color image. Is that normal?

    Mat image = imread(argv[1], CV_LOAD_IMAGE_UNCHANGED);    
    Mat labimage = Mat::zeros(image.size(), image.type());  //Matriz para almacenar imagen LAB.
        cvtColor(image, labimage, CV_BGR2Lab);  //Conversion automatica RGB to lab.

        Mat lchannel = Mat::zeros(image.size(), labimage.type());   //Matriz para almacenar canal b.
        Mat achannel = Mat::zeros(image.size(), labimage.type());   //Matriz para almacenar canal g.
        Mat bchannel = Mat::zeros(image.size(), labimage.type());   //Matriz para almacenar canal r.
        Mat bwchannel = Mat::zeros(image.size(), labimage.type());  //Matriz para almacenar canal r.

for(int x = 0;x < cols;x++){
            for(int y = 0;y < rows;y++){
                lchannel.at<Vec3b>(y,x)[0] = labimage.at<Vec3b>(y,x)[0];
                achannel.at<Vec3b>(y,x)[1] = labimage.at<Vec3b>(y,x)[1];
                bchannel.at<Vec3b>(y,x)[2] = labimage.at<Vec3b>(y,x)[2];
            }
        }

Mat color = Mat::zeros(image.size(), labimage.type());
    double X, Y, Z, dX, dY, dZ;
    double R, G, B;
    double L, a, b;
    X = Y = Z = dX = dY = dZ = R = G = B = L = a = b = 0;

    for(int x = 0;x < cols;x++){
                for(int y = 0;y < rows;y++){
                    L = (double)(lchannel.at<Vec3b>(y,x)[0] / 255.0) * 100.0;       //Rango 0 a 100.
                    a = (double)(achannel.at<Vec3b>(y,x)[1] / 255) * 128;   //Rango -128 a 128.
                    b = (double)(bchannel.at<Vec3b>(y,x)[2] / 255) * 128;   //Rango -128 a 128.

                // Lab -> normalized XYZ (X,Y,Z are all in 0...1)
                Y = L * (1.0/116.0) + 16.0/116.0;
                X = a * (1.0/500.0) + Y;
                Z = b * (-1.0/200.0) + Y;

                X = X > 6.0/29.0 ? X * X * X : X * (108.0/841.0) - 432.0/24389.0;
                Y = L > 8.0 ? Y * Y * Y : L * (27.0/24389.0);
                Z = Z > 6.0/29.0 ? Z * Z * Z : Z * (108.0/841.0) - 432.0/24389.0;

                // normalized XYZ -> linear sRGB (in 0...1)

                R = X * (1219569.0/395920.0)     + Y * (-608687.0/395920.0)    + Z * (-107481.0/197960.0);
                G = X * (-80960619.0/87888100.0) + Y * (82435961.0/43944050.0) + Z * (3976797.0/87888100.0);
                B = X * (93813.0/1774030.0)      + Y * (-180961.0/887015.0)    + Z * (107481.0/93370.0);

                // linear sRGB -> gamma-compressed sRGB (in 0...1)

                R = R > 0.0031308 ? pow(R, 1.0 / 2.4) * 1.055 - 0.055 : R * 12.92;
                G = G > 0.0031308 ? pow(G, 1.0 / 2.4) * 1.055 - 0.055 : G * 12.92;
                B = B > 0.0031308 ? pow(B, 1.0 / 2.4) * 1.055 - 0.055 : B * 12.92;

                //printf("a0: %d\t L0: %d\t b0: %d\n", achannel.at<Vec3b>(y,x)[1], lchannel.at<Vec3b>(y,x)[0], bchannel.at<Vec3b>(y,x)[2]);
                //printf("a: %f\t L: %f\t b: %f\n", a, L, b);
                //printf("X: %f\t Y: %f\t Z: %f\n", X, Y, Z);
                //printf("R: %f\t G: %f\t B: %f\n", R, G, B);
                //cout<<"R: "<<R<<" G: "<<G<<" B: "<<B<<endl;
                //string str = type2str(color.type());
                //cout<<"Matrix type: "<<str<<endl;

                color.at<Vec3b>(y,x)[0] = R*255;
                color.at<Vec3b>(y,x)[1] = G*255;
                color.at<Vec3b>(y,x)[2] = B*255;
            }
        }

Is what I'm doing right or I'm misinterpreting the information?

Answer 1

do not roll your own per-pixel loops, that's horribly ineffective.

instead use cvtColor(src,dst,COLOR_Lab2BGR)

(also, if i may say that, prefer the docs to SO answers..)

Answer 2

Never mind. I managed to solve it myself and it was very enjoyable. For anyone that's interested and having the same troubles as I once had, here's the algorithm and some code:

1. Convert CIE-Lab* to XYZ. This is necessary because CIE-Lab* is not a linear color space so there's no known direct conversion to RGB.

   void CIElabtoXYZ(cv::Mat& image, cv::Mat& output){
        float WhitePoint[3] = {0.950456, 1, 1.088754};
        Mat fX = Mat::zeros(image.size(), CV_32FC1);
        Mat fY = Mat::zeros(image.size(), CV_32FC1);
        Mat fZ = Mat::zeros(image.size(), CV_32FC1);
        Mat invfX = Mat::zeros(image.size(), CV_32FC1);
        Mat invfY = Mat::zeros(image.size(), CV_32FC1);
        Mat invfZ = Mat::zeros(image.size(), CV_32FC1);
   
        for(int x = 0;x < image.rows;x++){
            for(int y = 0;y < image.cols;y++){
                fY.at<float>(x,y) = (image.at<Vec3f>(x,y)[0] + 16.0) / 116.0;
                fX.at<float>(x,y) = fY.at<float>(x,y) + image.at<Vec3f>(x,y)[1] / 500.0;
                fZ.at<float>(x,y) = fY.at<float>(x,y) - image.at<Vec3f>(x,y)[2] / 200.0;
            }
        }
        invf(fX, invfX);
        invf(fY, invfY);
        invf(fZ, invfZ);
        for(int x = 0;x < image.rows;x++){
            for(int y = 0;y < image.cols;y++){
                output.at<Vec3f>(x,y)[0] = WhitePoint[0] * invfX.at<float>(x,y);
                output.at<Vec3f>(x,y)[1] = WhitePoint[1] * invfY.at<float>(x,y);
                output.at<Vec3f>(x,y)[2] = WhitePoint[2] * invfZ.at<float>(x,y);
            }
        }
    }
   
    void invf(cv::Mat& input, cv::Mat& output){
        for(int x = 0;x < input.rows;x++){
            for(int y = 0;y < input.cols;y++){
                output.at<float>(x,y) = pow(input.at<float>(x,y), 3);
                if(output.at<float>(x,y) < 0.008856){
                    output.at<float>(x,y) = (input.at<float>(x,y) - 4.0/29.0)*(108.0/841.0);
                }
            }
        }
    }
   

2. Convert XYZ to RGB

   void XYZtoRGB(cv::Mat& input, cv::Mat& output){
       float data[3][3] = {{3.240479, -1.53715, -0.498535}, {-0.969256, 1.875992, 0.041556}, {0.055648, -0.204043, 1.057311}};
       Mat T = Mat(3, 3, CV_32FC1, &data);
       Mat R = Mat::zeros(input.size(), CV_32FC1);
       Mat G = Mat::zeros(input.size(), CV_32FC1);
       Mat B = Mat::zeros(input.size(), CV_32FC1);
   
       for(int x = 0;x < input.rows;x++){
           for(int y = 0;y < input.cols;y++){
               R.at<float>(x,y) = T.at<float>(0,0)*input.at<Vec3f>(x,y)[0] + T.at<float>(1,0)*input.at<Vec3f>(x,y)[1] + T.at<float>(2,0)*input.at<Vec3f>(x,y)[2];
               G.at<float>(x,y) = T.at<float>(0,1)*input.at<Vec3f>(x,y)[0] + T.at<float>(1,1)*input.at<Vec3f>(x,y)[1] + T.at<float>(2,1)*input.at<Vec3f>(x,y)[2];
               B.at<float>(x,y) = T.at<float>(0,2)*input.at<Vec3f>(x,y)[0] + T.at<float>(1,2)*input.at<Vec3f>(x,y)[1] + T.at<float>(2,2)*input.at<Vec3f>(x,y)[2];
           }
       }
   
       //Desaturate and rescale to constrain resulting RGB values to [0,1]
       double RminVal, GminVal, BminVal;
       double RmaxVal, GmaxVal, BmaxVal;
       Point minLoc;
       Point maxLoc;
   
       minMaxLoc( R, &RminVal, &RmaxVal, &minLoc, &maxLoc );
       minMaxLoc( G, &GminVal, &GmaxVal, &minLoc, &maxLoc );
       minMaxLoc( B, &BminVal, &BmaxVal, &minLoc, &maxLoc );
   
       Mat matMin = Mat::zeros(1, 4, CV_32FC1), matMax = Mat::zeros(1, 4, CV_32FC1);
       matMin.at<float>(0,0) = RminVal; matMin.at<float>(0,1) = GminVal; matMin.at<float>(0,2) = BminVal; matMin.at<float>(0,3) = 0;
       double min, max;
       minMaxLoc( matMin, &min, &max, &minLoc, &maxLoc );
       float addWhite = -min;
       matMax.at<float>(0,0) = RmaxVal + addWhite; matMax.at<float>(0,1) = GmaxVal + addWhite; matMax.at<float>(0,2) = BmaxVal + addWhite; matMax.at<float>(0,3) = 1;
       minMaxLoc( matMax, &min, &max, &minLoc, &maxLoc );
       float Scale = max;
   
       for(int x = 0;x < input.rows;x++){
           for(int y = 0;y < input.cols;y++){
               output.at<Vec3f>(x,y)[2] = (R.at<float>(x,y) + addWhite) / Scale;
               output.at<Vec3f>(x,y)[1] = (G.at<float>(x,y) + addWhite) / Scale;
               output.at<Vec3f>(x,y)[0] = (B.at<float>(x,y) + addWhite) / Scale;
           }
       }
       imshow("Unscaled RGB", output);
   }