算法介绍¶

这是OpenCV图像处理专栏的第十一篇文章，之前介绍过两种处理白平衡的算法，分别为灰度世界算法和完美反射算法。今天来介绍另外一个自动白平衡的算法，即动态阈值法，一个看起来比较厉害的名字。论文原文链接放在附录。

算法原理¶

和灰度世界法和完美反射算法类似，动态阈值算法仍然分为两个步骤即白点检测和白点调整，具体如下：

白点检测¶

1、把尺寸为 $w\times h$ 的原图像从 $RGB$ 空间转换到 $YCrCb$ 空间。
2、把图像分成 $3\times 4$ 个块。
3、对每个块分别计算 $Cr$ ， $Cb$ 的平均值 $Mr$ ， $Mb$ 。
4、判定每个块的近白区域（near-white region）。判别准则为：
- $Cb(i, j) − (Mb + Db\times sign(Mb)) < 1.5\times Db$
- $Cr(i, j) − (1.5\times Mr + Dr \times sign(Mr )) < 1.5\times Dr$ ，其中sign为符号函数，即正数返回1，负数返回0。
5、设一个“参考白色点”的亮度矩阵 $RL$ ，大小为 $w\times h$ 。
6、若符合判别式，则作为“参考白色点”,并把该点 $（i，j）$ 的亮度（ $Y$ 分量）值赋给 $RL(i,j)$ 。若不符合，则该点的 $RL(i,j)$ 值为0。

白点调整¶

1、选取参考“参考白色点”中最大的10%的亮度（Y分量）值，并选取其中的最小值Lu_min。
2、调整RL，若RL(i,j)<Lu_min, RL(i,j)=0; 否则，RL(i,j)=1。
3、分别把R，G，B与RL相乘，得到R2，G2，B2。分别计算R2，G2，B2的平均值，Rav，Gav，Bav。
4、得到调整增益：定义Ymax=double(max(max(Y)))，则Rgain=Ymax/Rav,Ggain=Ymax/Gav, Bgain=Ymax/Bav。
5、调整原图像：Ro= R*Rgain; Go= G*Ggain; Bo= B*Bgain;

代码实现¶

块的大小取了100，没处理长或者宽不够100的结尾部分，这个可以自己添加。

const float YCbCrYRF = 0.299F;              // RGB转YCbCr的系数(浮点类型）
const float YCbCrYGF = 0.587F;
const float YCbCrYBF = 0.114F;
const float YCbCrCbRF = -0.168736F;
const float YCbCrCbGF = -0.331264F;
const float YCbCrCbBF = 0.500000F;
const float YCbCrCrRF = 0.500000F;
const float YCbCrCrGF = -0.418688F;
const float YCbCrCrBF = -0.081312F;

const float RGBRYF = 1.00000F;            // YCbCr转RGB的系数(浮点类型）
const float RGBRCbF = 0.0000F;
const float RGBRCrF = 1.40200F;
const float RGBGYF = 1.00000F;
const float RGBGCbF = -0.34414F;
const float RGBGCrF = -0.71414F;
const float RGBBYF = 1.00000F;
const float RGBBCbF = 1.77200F;
const float RGBBCrF = 0.00000F;

const int Shift = 20;
const int HalfShiftValue = 1 << (Shift - 1);

const int YCbCrYRI = (int)(YCbCrYRF * (1 << Shift) + 0.5);         // RGB转YCbCr的系数(整数类型）
const int YCbCrYGI = (int)(YCbCrYGF * (1 << Shift) + 0.5);
const int YCbCrYBI = (int)(YCbCrYBF * (1 << Shift) + 0.5);
const int YCbCrCbRI = (int)(YCbCrCbRF * (1 << Shift) + 0.5);
const int YCbCrCbGI = (int)(YCbCrCbGF * (1 << Shift) + 0.5);
const int YCbCrCbBI = (int)(YCbCrCbBF * (1 << Shift) + 0.5);
const int YCbCrCrRI = (int)(YCbCrCrRF * (1 << Shift) + 0.5);
const int YCbCrCrGI = (int)(YCbCrCrGF * (1 << Shift) + 0.5);
const int YCbCrCrBI = (int)(YCbCrCrBF * (1 << Shift) + 0.5);

const int RGBRYI = (int)(RGBRYF * (1 << Shift) + 0.5);              // YCbCr转RGB的系数(整数类型）
const int RGBRCbI = (int)(RGBRCbF * (1 << Shift) + 0.5);
const int RGBRCrI = (int)(RGBRCrF * (1 << Shift) + 0.5);
const int RGBGYI = (int)(RGBGYF * (1 << Shift) + 0.5);
const int RGBGCbI = (int)(RGBGCbF * (1 << Shift) + 0.5);
const int RGBGCrI = (int)(RGBGCrF * (1 << Shift) + 0.5);
const int RGBBYI = (int)(RGBBYF * (1 << Shift) + 0.5);
const int RGBBCbI = (int)(RGBBCbF * (1 << Shift) + 0.5);
const int RGBBCrI = (int)(RGBBCrF * (1 << Shift) + 0.5);

Mat RGB2YCbCr(Mat src) {
    int row = src.rows;
    int col = src.cols;
    Mat dst(row, col, CV_8UC3);
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < col; j++) {
            int Blue = src.at<Vec3b>(i, j)[0];
            int Green = src.at<Vec3b>(i, j)[1];
            int Red = src.at<Vec3b>(i, j)[2];
            dst.at<Vec3b>(i, j)[0] = (int)((YCbCrYRI * Red + YCbCrYGI * Green + YCbCrYBI * Blue + HalfShiftValue) >> Shift);
            dst.at<Vec3b>(i, j)[1] = (int)(128 + ((YCbCrCbRI * Red + YCbCrCbGI * Green + YCbCrCbBI * Blue + HalfShiftValue) >> Shift));
            dst.at<Vec3b>(i, j)[2] = (int)(128 + ((YCbCrCrRI * Red + YCbCrCrGI * Green + YCbCrCrBI * Blue + HalfShiftValue) >> Shift));
        }
    }
    return dst;
}

Mat YCbCr2RGB(Mat src) {
    int row = src.rows;
    int col = src.cols;
    Mat dst(row, col, CV_8UC3);
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < col; j++) {
            int Y = src.at<Vec3b>(i, j)[0];
            int Cb = src.at<Vec3b>(i, j)[1] - 128;
            int Cr = src.at<Vec3b>(i, j)[2] - 128;
            int Red = Y + ((RGBRCrI * Cr + HalfShiftValue) >> Shift);
            int Green = Y + ((RGBGCbI * Cb + RGBGCrI * Cr + HalfShiftValue) >> Shift);
            int Blue = Y + ((RGBBCbI * Cb + HalfShiftValue) >> Shift);
            if (Red > 255) Red = 255; else if (Red < 0) Red = 0;
            if (Green > 255) Green = 255; else if (Green < 0) Green = 0;    // 编译后应该比三目运算符的效率高
            if (Blue > 255) Blue = 255; else if (Blue < 0) Blue = 0;
            dst.at<Vec3b>(i, j)[0] = Blue;
            dst.at<Vec3b>(i, j)[1] = Green;
            dst.at<Vec3b>(i, j)[2] = Red;
        }
    }
    return dst;
}

template<typename T>
inline T sign(T const &input) {
    return input >= 0 ? 1 : -1;
}

Mat AutomaticWhiteBalanceMethod(Mat src) {
    int row = src.rows;
    int col = src.cols;
    if (src.channels() == 4) {
        cvtColor(src, src, CV_BGRA2BGR);
    }
    Mat input = RGB2YCbCr(src);
    Mat mark(row, col, CV_8UC1);
    int sum = 0;
    for (int i = 0; i < row; i += 100) {
        for (int j = 0; j < col; j += 100) {
            if (i + 100 < row && j + 100 < col) {
                Rect rect(j, i, 100, 100);
                Mat temp = input(rect);
                Scalar global_mean = mean(temp);
                double dr = 0, db = 0;
                for (int x = 0; x < 100; x++) {
                    uchar *ptr = temp.ptr<uchar>(x) + 1;
                    for (int y = 0; y < 100; y++) {
                        dr += pow(abs(*ptr - global_mean[1]), 2);
                        ptr++;
                        db += pow(abs(*ptr - global_mean[2]), 2);
                        ptr++;
                        ptr++;
                    }
                }
                dr /= 10000;
                db /= 10000;
                double cr_left_criteria = 1.5 * global_mean[1] + dr * sign(global_mean[1]);
                double cr_right_criteria = 1.5 * dr;
                double cb_left_criteria = global_mean[2] + db * sign(global_mean[2]);
                double cb_right_criteria = 1.5 * db;
                for (int x = 0; x < 100; x++) {
                    uchar *ptr = temp.ptr<uchar>(x) + 1;
                    for (int y = 0; y < 100; y++) {
                        uchar cr = *ptr;
                        ptr++;
                        uchar cb = *ptr;
                        ptr++;
                        ptr++;
                        if ((cr - cb_left_criteria) < cb_right_criteria && (cb - cr_left_criteria) < cr_right_criteria) {
                            sum++;
                            mark.at<uchar>(i + x, j + y) = 1;
                        }
                        else {
                            mark.at<uchar>(i + x, j + y) = 0;
                        }
                    }
                }
            }
        }
    }

    int Threshold = 0;
    int Ymax = 0;
    int Light[256] = { 0 };
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < col; j++) {
            if (mark.at<uchar>(i, j) == 1) {
                Light[(int)(input.at<Vec3b>(i, j)[0])]++;
            }
            Ymax = max(Ymax, (int)(input.at<Vec3b>(i, j)[0]));
        }
    }
    printf("maxY: %d\n", Ymax);
    int sum2 = 0;
    for (int i = 255; i >= 0; i--) {
        sum2 += Light[i];
        if (sum2 >= sum * 0.1) {
            Threshold = i;
            break;
        }
    }
    printf("Threshold: %d\n", Threshold);
    printf("Sum: %d Sum2: %d\n", sum, sum2);
    double Blue = 0;
    double Green = 0;
    double Red = 0;
    int cnt2 = 0;
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < col; j++) {
            if (mark.at<uchar>(i, j) == 1 && (int)(input.at<Vec3b>(i, j)[0]) >= Threshold) {
                Blue += 1.0 * src.at<Vec3b>(i, j)[0];
                Green += 1.0 * src.at<Vec3b>(i, j)[1];
                Red += 1.0 * src.at<Vec3b>(i, j)[2];
                cnt2++;
            }
        }
    }
    Blue /= cnt2;
    Green /= cnt2;
    Red /= cnt2;
    printf("%.5f %.5f %.5f\n", Blue, Green, Red);
    Mat dst(row, col, CV_8UC3);
    double maxY = Ymax;
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < col; j++) {
            int B = (int)(maxY * src.at<Vec3b>(i, j)[0] / Blue);
            int G = (int)(maxY * src.at<Vec3b>(i, j)[1] / Green);
            int R = (int)(maxY * src.at<Vec3b>(i, j)[2] / Red);
            if (B > 255) B = 255; else if (B < 0) B = 0;
            if (G > 255) G = 255; else if (G < 0) G = 0;
            if (R > 255) R = 255; else if (R < 0) R = 0;
            dst.at<Vec3b>(i, j)[0] = B;
            dst.at<Vec3b>(i, j)[1] = G;
            dst.at<Vec3b>(i, j)[2] = R;
        }
    }
    return dst;
}