OpenCV 的 Contrast Preserving Decolorization 源码解析
【摘要】
运行效果为:
出乎我意料的是,不仅仅保留了对比度,居然还增强了图像的对比度(去雾,不过只适用于比较均匀的雾),不过运行的速度堪忧,500*500的图像都需要 1s 多!
经过 OpenMP 优化,执行时间减少了一半左右
该代码是源于 香港中文大学 计算机科学与工...
运行效果为:
出乎我意料的是,不仅仅保留了对比度,居然还增强了图像的对比度(去雾,不过只适用于比较均匀的雾),不过运行的速度堪忧,500*500的图像都需要 1s 多!
经过 OpenMP 优化,执行时间减少了一半左右
该代码是源于 香港中文大学 计算机科学与工程系 的一篇论文 Contrast Preserving Decolorization
其代码已被收录到 OpenCV 的源码中,位于(注意,3.* 以上才有)
以下是在通读了论文《IEEE International Conference on Computational Photography(ICCP), 2012》之后,对原始代码做的详细注释( OpenCV 原代码中有多处 Bug,我已 fix 掉):
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void deColor(InputArray _src, OutputArray _dst, OutputArray _color_boost)
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{
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Mat I = _src.getMat();
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_dst.create(I.size(), CV_8UC1);
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Mat dst = _dst.getMat();
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_color_boost.create(I.size(), CV_8UC3);
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Mat color_boost = _color_boost.getMat();
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CV_Assert(!I.empty() && (I.channels() == 3));
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// Parameter Setting
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const int maxIter = 15;
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const double tol = .0001;
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int iterCount = 0;
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double E = 0;
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double pre_E = std::numeric_limits<double>::infinity(); // 返回编译器允许的 double 型的正无穷大
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Mat img;
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I.convertTo(img, CV_32FC3, 1.0 / 255.0); // 8UC3 -> 32FC3,归一化
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// Initialization
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Decolor obj;
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vector <double> Cg;
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vector < vector <double> > polyGrad;
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vector <Vec3i> comb;
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vector <double> alf;
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obj.gradSystem(img, polyGrad, Cg, comb);
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obj.weakOrder(img, alf);
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// Solver
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Mat Mt = Mat(int(polyGrad.size()), int(polyGrad[0].size()), CV_32FC1);
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obj.weightUpdateMatrix(polyGrad, Cg, Mt);
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vector <double> wei;
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obj.weightInit(comb, wei);
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main loop starting
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vector <double> G_pos(alf.size());
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vector <double> G_neg(alf.size());
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vector <double> EXPsum(G_pos.size());
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vector <double> EXPterm(G_pos.size());
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vector <double> temp(polyGrad[0].size());
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vector <double> temp1(polyGrad[0].size());
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vector <double> temp2(EXPsum.size());
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vector <double> wei1(polyGrad.size());
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while (sqrt(pow(E - pre_E, 2)) > tol)
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{
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iterCount += 1;
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pre_E = E;
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// 梯度图大小
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for (size_t i = 0; i < polyGrad[0].size(); i++)
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{
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double val = 0.0;
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// 基的个数,公式(10)
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for (size_t j = 0; j < polyGrad.size(); j++)
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val = val + (polyGrad[j][i] * wei[j]);
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// 公式(4) 的绝对值内部
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temp[i] = val - Cg[i];
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temp1[i] = val + Cg[i];
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}
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// 近似公式(4)
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for (size_t i = 0; i < alf.size(); i++)
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{
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const double sqSigma = obj.sigma * obj.sigma;
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const double pos = ((1 + alf[i]) / 2) * exp(-1.0 * 0.5 * (temp[i] * temp[i]) / sqSigma);
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const double neg = ((1 - alf[i]) / 2) * exp(-1.0 * 0.5 * (temp1[i] * temp1[i]) / sqSigma);
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G_pos[i] = pos;
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G_neg[i] = neg;
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}
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// 近似公式(12)(14)
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for (size_t i = 0; i < G_pos.size(); i++)
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EXPsum[i] = G_pos[i] + G_neg[i];
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for (size_t i = 0; i < EXPsum.size(); i++)
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temp2[i] = (EXPsum[i] == 0) ? 1.0 : 0.0;
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for (size_t i = 0; i < G_pos.size(); i++)
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EXPterm[i] = (G_pos[i] - G_neg[i]) / (EXPsum[i] + temp2[i]);
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// 更新权重
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for (int i = 0; i < int(polyGrad.size()); i++)
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{
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double val1 = 0.0;
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for (int j = 0; j < int(polyGrad[0].size()); j++)
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{
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val1 = val1 + (Mt.at<float>(i, j) * EXPterm[j]);
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}
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wei1[i] = val1;
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}
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// 替换权重
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for (size_t i = 0; i < wei.size(); i++)
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wei[i] = wei1[i];
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// 公式(11)
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E = obj.energyCalcu(Cg, polyGrad, wei);
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if (iterCount > maxIter)
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break;
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}
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Mat Gray = Mat::zeros(img.size(), CV_32FC1);
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obj.grayImContruct(wei, img, Gray);
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Gray.convertTo(dst, CV_8UC1, 255);
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/// Contrast Boosting /
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Mat lab;
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cvtColor(I, lab, COLOR_BGR2Lab);
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vector <Mat> lab_channel;
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split(lab, lab_channel);
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dst.copyTo(lab_channel[0]); // 仅仅替换 L 通道
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merge(lab_channel, lab);
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cvtColor(lab, color_boost, COLOR_Lab2BGR);
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}
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double Decolor::energyCalcu(const vector <double> &Cg, const vector < vector <double> > &polyGrad, const vector <double> &wei) const
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{
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const size_t size = polyGrad[0].size();
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vector <double> energy(size);
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vector <double> temp(size);
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vector <double> temp1(size);
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// 公式(11)两个 exp {} 中的部分
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// 公式中的 l(x,y)
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for (size_t i = 0; i < polyGrad[0].size(); i++)
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{
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double val = 0.0;
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// 公式中的 i
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for (size_t j = 0; j < polyGrad.size(); j++)
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val = val + (polyGrad[j][i] * wei[j]);
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temp[i] = val - Cg[i];
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temp1[i] = val + Cg[i];
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}
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// 注意这里和公式(11)不同,左右两边的比重都为 1
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for (size_t i = 0; i < polyGrad[0].size(); i++)
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energy[i] = -1.0 * log(exp(-1.0 * pow(temp[i], 2) / sigma) + exp(-1.0 * pow(temp1[i], 2) / sigma));
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double sum = 0.0;
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// 把整幅图的能量(代价)都相加起来
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for (size_t i = 0; i < polyGrad[0].size(); i++)
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sum += energy[i];
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// 平均
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return (sum / polyGrad[0].size());
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}
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Decolor::Decolor()
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{
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kernelx = Mat(1, 2, CV_32FC1);
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kernely = Mat(2, 1, CV_32FC1);
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kernelx.at<float>(0, 0) = 1.0; // 1., -1.
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kernelx.at<float>(0, 1) = -1.0;
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kernely.at<float>(0, 0) = 1.0; // 1.; -1.
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kernely.at<float>(1, 0) = -1.0;
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order = 2; // degree
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sigma = 0.02f;
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}
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vector<double> Decolor::product(const vector <Vec3i> &comb, const double initRGB[3])
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{
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vector <double> res(comb.size());
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// 从 comb 容器中,逐个取出 vec3 和 rgb 进行点乘
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for (size_t i = 0; i < comb.size(); i++)
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{
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double dp = 0.0;
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for (int j = 0; j < 3; j++)
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dp = dp + (comb[i][j] * initRGB[j]);
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res[i] = dp;
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}
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// 返回每个 vec3 点乘的结果
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return res;
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}
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// 计算横向的单通道梯度图
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void Decolor::singleChannelGradx(const Mat &img, Mat &dest) const
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{
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const int w = img.size().width;
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// kernels.cols/2-1, kernelx.rows/2-1
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// 调整卷积图像的锚点,默认是 (-1,-1)
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// Σ kernel(x',y')*src(x+x'-anchor.x, y+y'-anchor.y)
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const Point anchor(kernelx.cols - kernelx.cols / 2 - 1, kernelx.rows - kernelx.rows / 2 - 1);
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filter2D(img, dest, -1, kernelx, anchor, 0.0, BORDER_CONSTANT); // 超出边界的地方用常数填充
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dest.col(w - 1) = 0.0;// 最右侧设置为 0
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}
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// 计算纵向的单通道梯度图
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void Decolor::singleChannelGrady(const Mat &img, Mat &dest) const
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{
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const int h = img.size().height;
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const Point anchor(kernely.cols - kernely.cols / 2 - 1, kernely.rows - kernely.rows / 2 - 1);
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filter2D(img, dest, -1, kernely, anchor, 0.0, BORDER_CONSTANT);
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dest.row(h - 1) = 0.0;
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}
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// 计算横向和纵向的梯度(转置)并合并到一个容器中
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void Decolor::gradvector(const Mat &img, vector <double> &grad) const
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{
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Mat dest;
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Mat dest1;
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singleChannelGradx(img, dest);
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singleChannelGrady(img, dest1);
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// 得到转置的单通道梯度图
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Mat d_trans = dest.t();
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Mat d1_trans = dest1.t();
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const int height = d_trans.size().height;
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const int width = d_trans.size().width;
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// 把两张梯度图合并到一个容器当中(前:横向,后:纵向)
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// OpenCV 源码中此处有越界问题(难以置信)
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grad.resize(width * height * 2);
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for (int i = 0; i < height; i++)
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for (int j = 0; j < width; j++)
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grad[i * width + j] = d_trans.at<float>(i, j);
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const int offset = width * height;
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for (int i = 0; i < height; i++)
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for (int j = 0; j < width; j++)
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grad[offset + i * width + j] = d1_trans.at<float>(i, j);
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}
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// 计算 CIELab 空间的颜色对比度
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void Decolor::colorGrad(const Mat &img, vector <double> &Cg) const
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{
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Mat lab;
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// 转换到 CIELab 颜色空间
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cvtColor(img, lab, COLOR_BGR2Lab);
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vector <Mat> lab_channel;
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split(lab, lab_channel);
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vector <double> ImL;
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vector <double> Ima;
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vector <double> Imb;
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// 分别计算 Lab 三个通道的梯度图
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gradvector(lab_channel[0], ImL);
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gradvector(lab_channel[1], Ima);
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gradvector(lab_channel[2], Imb);
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Cg.resize(ImL.size());
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// 计算颜色对比度(Color Contrast)
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for (size_t i = 0; i < ImL.size(); i++)
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{
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const double res = sqrt(pow(ImL[i], 2) + pow(Ima[i], 2) + pow(Imb[i], 2)) / 100;
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Cg[i] = res;
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}
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}
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// 构造一个 vec3 张量,并添加到 comb 容器中
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void Decolor::addVector(vector <Vec3i> &comb, int &idx, int r, int g, int b)
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{
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comb.push_back(Vec3i(r, g, b));
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idx++;
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}
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// 保存梯度容器到一个容器的容器
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void Decolor::addToVectorPoly(vector < vector <double> > &polyGrad, const vector <double> &curGrad, int &idx1)
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{
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polyGrad.push_back(curGrad);
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idx1++;
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}
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// 和论文上公式不同
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void Decolor::weakOrder(const Mat &src, vector <double> &alf) const
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{
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const int h = src.size().height;
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const int w = src.size().width;
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cv::Mat img;
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if ((h + w) > 800)
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{
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const double sizefactor = double(800) / (h + w);
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resize(src, img, Size(cvRound(w * sizefactor), cvRound(h * sizefactor)));
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}
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else
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img = src;
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Mat curIm = Mat(img.size(), CV_32FC1);
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vector <Mat> rgb_channel;
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split(img, rgb_channel);// 又对图像进行了分裂
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vector <double> Rg, Gg, Bg;
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gradvector(rgb_channel[2], Rg); // 计算 RGB 三个通道的梯度图
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gradvector(rgb_channel[1], Gg);
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gradvector(rgb_channel[0], Bg);
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vector <double> t1(Rg.size()), t2(Rg.size()), t3(Rg.size());
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vector <double> tmp1(Rg.size()), tmp2(Rg.size()), tmp3(Rg.size());
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const double level = .05;
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// 和 level 、-level 进行比较
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for (size_t i = 0; i < Rg.size(); i++)
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{
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t1[i] = (Rg[i] > level) ? 1.0 : 0.0;
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t2[i] = (Gg[i] > level) ? 1.0 : 0.0;
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t3[i] = (Bg[i] > level) ? 1.0 : 0.0;
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tmp1[i] = (Rg[i] < -1.0 * level) ? 1.0 : 0.0;
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tmp2[i] = (Gg[i] < -1.0 * level) ? 1.0 : 0.0;
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tmp3[i] = (Bg[i] < -1.0 * level) ? 1.0 : 0.0;
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}
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alf.resize(Rg.size());
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for (size_t i = 0; i < Rg.size(); i++)
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alf[i] = (t1[i] * t2[i] * t3[i]);
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for (size_t i = 0; i < Rg.size(); i++)
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alf[i] -= tmp1[i] * tmp2[i] * tmp3[i];
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}
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// 构造 polynomial space 每个基的梯度图,还有得到 CIELab 颜色空间的对比度,以及 polynomial space 的基
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void Decolor::gradSystem(const Mat &src, vector < vector < double > > &polyGrad,
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vector < double > &Cg, vector <Vec3i> &comb) const
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{
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int h = src.size().height;
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int w = src.size().width;
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cv::Mat img;
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// 如果宽高和超过一定大小则进行缩放
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if ((h + w) > 800)
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{
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const double sizefactor = double(800) / (h + w);
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resize(src, img, Size(cvRound(w * sizefactor), cvRound(h * sizefactor)));
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}
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else
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img = src;
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h = img.size().height;
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w = img.size().width;
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colorGrad(img, Cg);
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// 将一副图像映射到 polynomial space
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Mat curIm = Mat(img.size(), CV_32FC1);
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vector <Mat> rgb_channel;
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split(img, rgb_channel); // 得到 BGR 三个通道
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int idx = 0, idx1 = 0;
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for (int r = 0; r <= order; r++)
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for (int g = 0; g <= order; g++)
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for (int b = 0; b <= order; b++)
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{
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if ((r + g + b) <= order && (r + g + b) > 0)
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{
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// 保存 polynomial space 的基
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addVector(comb, idx, r, g, b);
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// 每个 polynomial space 的基(r, g, b) 都要对整张图像进行计算(w*h 大小)
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for (int i = 0; i < h; i++)
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for (int j = 0; j < w; j++)
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// 映射每一个 rgb 像素
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curIm.at<float>(i, j) =
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pow(rgb_channel[2].at<float>(i, j), r) *
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pow(rgb_channel[1].at<float>(i, j), g) *
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pow(rgb_channel[0].at<float>(i, j), b);
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vector <double> curGrad;
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gradvector(curIm, curGrad);
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// 保存每个基计算的梯度图
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addToVectorPoly(polyGrad, curGrad, idx1);
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}
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}
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}
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void Decolor::weightUpdateMatrix(const vector < vector <double> > &poly, const vector <double> &Cg, Mat &X)
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{
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// 容器转为矩阵
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const int size = static_cast<int>(poly.size());
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const int size0 = static_cast<int>(poly[0].size());
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Mat P = Mat(size, size0, CV_32FC1);
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for (int i = 0; i < size; i++)
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for (int j = 0; j < size0; j++)
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P.at<float>(i, j) = static_cast<float>(poly[i][j]);
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// 转置
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const Mat P_trans = P.t();
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Mat B = Mat(size, size0, CV_32FC1);
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for (int i = 0; i < size; i++)
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{
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for (int j = 0, end = int(Cg.size()); j < end; j++)
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B.at<float>(i, j) = static_cast<float>(poly[i][j] * Cg[j]);
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}
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// 得到一个方阵,大小为 size*size
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Mat A = P * P_trans;
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// 求解线性方程组,这里的 X 应该是论文公式(14)的部分
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// cv::solve -- https://docs.opencv.org/3.1.0/d2/de8/group__core__array.html#ga12b43690dbd31fed96f213eefead2373
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// DECOMP_NORMAL -- https://docs.opencv.org/3.1.0/d2/de8/group__core__array.html#gaaf9ea5dcc392d5ae04eacb9920b9674c
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// 这意味着求解的方程是 src1 T⋅src1⋅dst = src1 T src2,而不是原始方程 src1⋅dst = src2
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solve(A, B, X, DECOMP_NORMAL);
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//---------------------
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// DECOMP_LU(LU分解)
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// http://blog.csdn.net/myhaspl/article/details/49450743
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// DECOMP_CHOLESKY(CHOLESKY分解)
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// http://blog.csdn.net/acdreamers/article/details/44656847
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// DECOMP_EIG(EIG分解)
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// DECOMP_SVD(SVD分解)
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// http://www.cnblogs.com/LeftNotEasy/archive/2011/01/19/svd-and-applications.html
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// DECOMP_QR(QR分解)
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// http://blog.sina.com.cn/s/blog_3f41287a0101ke2s.html
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//---------------------
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}
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void Decolor::weightInit(const vector <Vec3i> &comb, vector <double> &wei)
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{
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double initRGB[3] = { .33, .33, .33 };
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// 通过 polynomial space 的基和 rgb 系数进行点乘,对 weight 进行初始化
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wei = product(comb, initRGB);
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vector <int> sum(comb.size());
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for (size_t i = 0; i < comb.size(); i++)
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sum[i] = (comb[i][0] + comb[i][1] + comb[i][2]);
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// 除了 r,g,b 这三种基,其他基的权重初始化为 0
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for (size_t i = 0; i < sum.size(); i++)
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{
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if (sum[i] == 1)
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wei[i] = wei[i] * double(1);
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else
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wei[i] = wei[i] * double(0);
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}
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sum.clear();
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}
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// 将迭代出各个基的权重和各个基相乘,并把结果累加到原灰度上
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void Decolor::grayImContruct(vector <double> &wei, const Mat &img, Mat &Gray) const
-
{
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const int h = img.size().height;
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const int w = img.size().width;
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-
vector <Mat> rgb_channel;
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split(img, rgb_channel);
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-
int kk = 0;
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for (int r = 0; r <= order; r++)
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for (int g = 0; g <= order; g++)
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for (int b = 0; b <= order; b++)
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if ((r + g + b) <= order && (r + g + b) > 0)
-
{
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for (int i = 0; i < h; i++)
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for (int j = 0; j < w; j++)
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Gray.at<float>(i, j) = Gray.at<float>(i, j) +
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static_cast<float>(wei[kk]) * pow(rgb_channel[2].at<float>(i, j), r) * pow(rgb_channel[1].at<float>(i, j), g) *
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pow(rgb_channel[0].at<float>(i, j), b);
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-
kk = kk + 1; // 遍历各个基
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}
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// 找出最值,并调整归一化便于显示
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double minval, maxval;
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minMaxLoc(Gray, &minval, &maxval);
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Gray -= minval;
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Gray /= maxval - minval;
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}
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