stitching_detail算法介绍

来源：互联网发布：plc编程器编辑：程序博客网时间：2024/05/16 12:45

原文转自：http://www.geekcome.com/content-10-8390-1.html

一、stitching_detail程序运行流程

1.命令行调用程序，输入源图像以及程序的参数

2.特征点检测，判断是使用surf还是orb，默认是surf。

3.对图像的特征点进行匹配，使用最近邻和次近邻方法，将两个最优的匹配的置信度保存下来。

4.对图像进行排序以及将置信度高的图像保存到同一个集合中，删除置信度比较低的图像间的匹配，得到能正确匹配的图像序列。这样将置信度高于门限的所有匹配合并到一个集合中。

5.对所有图像进行相机参数粗略估计，然后求出旋转矩阵

6.使用光束平均法进一步精准的估计出旋转矩阵。

7.波形校正，水平或者垂直

8.拼接

9.融合，多频段融合，光照补偿，

二、stitching_detail程序接口介绍

img1 img2 img3 输入图像

--preview 以预览模式运行程序，比正常模式要快，但输出图像分辨率低，拼接的分辨率compose_megapix 设置为0.6

--try_gpu (yes|no) 是否使用GPU(图形处理器)，默认为no

/* 运动估计参数 */

--work_megapix <--work_megapix <float>> 图像匹配的分辨率大小，图像的面积尺寸变为work_megapix*100000，默认为0.6

--features (surf|orb) 选择surf或者orb算法进行特征点计算，默认为surf

--match_conf <float> 特征点检测置信等级，最近邻匹配距离与次近邻匹配距离的比值，surf默认为0.65，orb默认为0.3

--conf_thresh <float> 两幅图来自同一全景图的置信度，默认为1.0

--ba (reproj|ray) 光束平均法的误差函数选择，默认是ray方法

--ba_refine_mask (mask) ---------------

--wave_correct (no|horiz|vert) 波形校验水平，垂直或者没有默认是horiz

--save_graph <file_name> 将匹配的图形以点的形式保存到文件中， Nm代表匹配的数量，NI代表正确匹配的数量，C表示置信度

/*图像融合参数:*/

选择融合的平面，默认是球形

--seam_megapix <float> 拼接缝像素的大小默认是0.1 ------------

--seam (no|voronoi|gc_color|gc_colorgrad) 拼接缝隙估计方法默认是gc_color

--compose_megapix <float> 拼接分辨率，默认为-1

--expos_comp (no|gain|gain_blocks) 光照补偿方法，默认是gain_blocks

--blend (no|feather|multiband) 融合方法，默认是多频段融合

--blend_strength <float> 融合强度，0-100.默认是5.

--output <result_img> 输出图像的文件名，默认是result,jpg

命令使用实例，以及程序运行时的提示：

三、程序代码分析

1.参数读入

程序参数读入分析，将程序运行是输入的参数以及需要拼接的图像读入内存，检查图像是否多于2张。

    int retval = parseCmdArgs(argc, argv);    if (retval)        return retval;    // Check if have enough images    int num_images = static_cast<int>(img_names.size());    if (num_images < 2)    {        LOGLN("Need more images");        return -1;    }

2.特征点检测

判断选择是surf还是orb特征点检测（默认是surf）以及对图像进行预处理（尺寸缩放），然后计算每幅图形的特征点，以及特征点描述子

2.1 计算work_scale，将图像resize到面积在work_megapix*10^6以下，（work_megapix 默认是0.6）

work_scale = min(1.0, sqrt(work_megapix * 1e6 / full_img.size().area()));

resize(full_img, img, Size(), work_scale, work_scale);

图像大小是740*830，面积大于6*10^5，所以计算出work_scale = 0.98,然后对图像resize。

2.2 计算seam_scale，也是根据图像的面积小于seam_megapix*10^6，（seam_megapix 默认是0.1），seam_work_aspect目前还没用到

   seam_scale = min(1.0, sqrt(seam_megapix * 1e6 / full_img.size().area()));   seam_work_aspect = seam_scale / work_scale; //seam_megapix = 0.1 seam_work_aspect = 0.69

2.3 计算图像特征点，以及计算特征点描述子，并将img_idx设置为i。

  (*finder)(img, features[i]);//matcher.cpp 348  features[i].img_idx = i;

特征点描述的结构体定义如下：

struct detail::ImageFeaturesStructure containing image keypoints and descriptors.struct CV_EXPORTS ImageFeatures{int img_idx;// Size img_size;std::vector<KeyPoint> keypoints;Mat descriptors;};

2.4 将源图像resize到seam_megapix*10^6，并存入image[]中

        resize(full_img, img, Size(), seam_scale, seam_scale);        images[i] = img.clone();

3.图像匹配

对任意两副图形进行特征点匹配，然后使用查并集法，将图片的匹配关系找出，并删除那些不属于同一全景图的图片。

3.1 使用最近邻和次近邻匹配，对任意两幅图进行特征点匹配。

    vector<MatchesInfo> pairwise_matches;//Structure containing information about matches between two images.     BestOf2NearestMatcher matcher(try_gpu, match_conf);//最近邻和次近邻法    matcher(features, pairwise_matches);//对每两个图片进行matcher，20-》400 matchers.cpp 502

介绍一下BestOf2NearestMatcher 函数：

      //Features matcher which finds two best matches for each feature and leaves the best one only if the ratio between descriptor distances is greater than the threshold match_conf.     detail::BestOf2NearestMatcher::BestOf2NearestMatcher(bool try_use_gpu=false,float match_conf=0.3f,                                                     intnum_matches_thresh1=6, int num_matches_thresh2=6)     Parameters:try_use_gpu – Should try to use GPU or notmatch_conf – Match distances ration thresholdnum_matches_thresh1 – Minimum number of matches required for the 2D projectivetransform estimation used in the inliers classification stepnum_matches_thresh2 – Minimum number of matches required for the 2D projectivetransform re-estimation on inliers

函数的定义（只是设置一下参数，属于构造函数）：

BestOf2NearestMatcher::BestOf2NearestMatcher(bool try_use_gpu, float match_conf, int num_matches_thresh1, int num_matches_thresh2){#ifdef HAVE_OPENCV_GPU    if (try_use_gpu && getCudaEnabledDeviceCount() > 0)        impl_ = new GpuMatcher(match_conf);    else#else    (void)try_use_gpu;#endif        impl_ = new CpuMatcher(match_conf);    is_thread_safe_ = impl_->isThreadSafe();    num_matches_thresh1_ = num_matches_thresh1;    num_matches_thresh2_ = num_matches_thresh2;}

以及MatchesInfo的结构体定义：

Structure containing information about matches between two images. It’s assumed that there is a homography between those images.struct CV_EXPORTS MatchesInfo{MatchesInfo();MatchesInfo(const MatchesInfo &other);const MatchesInfo& operator =(const MatchesInfo &other);int src_img_idx, dst_img_idx; // Images indices (optional)std::vector<DMatch> matches;std::vector<uchar> inliers_mask; // Geometrically consistent matches maskint num_inliers; // Number of geometrically consistent matchesMat H; // Estimated homographydouble confidence; // Confidence two images are from the same panorama};

求出图像匹配的结果如下（具体匹配参见sift特征点匹配），任意两幅图都进行匹配（3*3=9），其中1-》2和2-》1只计算了一次，以1-》2为准，：

3.2 根据任意两幅图匹配的置信度，将所有置信度高于conf_thresh（默认是1.0）的图像合并到一个全集中。

我们通过函数的参数 save_graph打印匹配结果如下（我稍微修改了一下输出）：

"outimage101.jpg" -- "outimage102.jpg"[label="Nm=866, Ni=637, C=2.37864"];"outimage101.jpg" -- "outimage103.jpg"[label="Nm=165, Ni=59, C=1.02609"];"outimage102.jpg" -- "outimage103.jpg"[label="Nm=460, Ni=260, C=1.78082"];

Nm代表匹配的数量，NI代表正确匹配的数量，C表示置信度

通过查并集方法，查并集介绍请参见博文：

http://blog.csdn.net/skeeee/article/details/20471949

    vector<int> indices = leaveBiggestComponent(features, pairwise_matches, conf_thresh);//将置信度高于门限的所有匹配合并到一个集合中    vector<Mat> img_subset;    vector<string> img_names_subset;    vector<Size> full_img_sizes_subset;    for (size_t i = 0; i < indices.size(); ++i)    {        img_names_subset.push_back(img_names[indices[i]]);        img_subset.push_back(images[indices[i]]);        full_img_sizes_subset.push_back(full_img_sizes[indices[i]]);    }    images = img_subset;    img_names = img_names_subset;    full_img_sizes = full_img_sizes_subset;

4.根据单应性矩阵粗略估计出相机参数（焦距）

4.1 焦距参数的估计

根据前面求出的任意两幅图的匹配，我们根据两幅图的单应性矩阵H，求出符合条件的f，（4副图，16个匹配，求出8个符合条件的f），然后求出f的均值或者中值当成所有图形的粗略估计的f。

estimateFocal(features, pairwise_matches, focals);

函数的主要源码如下：

    for (int i = 0; i < num_images; ++i)    {        for (int j = 0; j < num_images; ++j)        {            const MatchesInfo &m = pairwise_matches[i*num_images + j];            if (m.H.empty())                continue;            double f0, f1;            bool f0ok, f1ok;focalsFromHomography(m.H, f0, f1, f0ok, f1ok);//Tries to estimate focal lengths from the given homography  79//under the assumption that the camera undergoes rotations around its centre only.            if (f0ok && f1ok)                all_focals.push_back(sqrt(f0 * f1));        }    }

其中函数focalsFromHomography的定义如下：

Tries to estimate focal lengths from the given homographyunder the assumption that the camera undergoes rotations around its centre only.  ParametersH – Homography.f0 – Estimated focal length along X axis.f1 – Estimated focal length along Y axis.f0_ok – True, if f0 was estimated successfully, false otherwise.f1_ok – True, if f1 was estimated successfully, false otherwise.

函数的源码：

void focalsFromHomography(const Mat& H, double &f0, double &f1, bool &f0_ok, bool &f1_ok){    CV_Assert(H.type() == CV_64F && H.size() == Size(3, 3));//Checks a condition at runtime and throws exception if it fails    const double* h = reinterpret_cast<const double*>(H.data);//强制类型转换    double d1, d2; // Denominators    double v1, v2; // Focal squares value candidates//具体的计算过程有点看不懂啊    f1_ok = true;    d1 = h[6] * h[7];    d2 = (h[7] - h[6]) * (h[7] + h[6]);    v1 = -(h[0] * h[1] + h[3] * h[4]) / d1;    v2 = (h[0] * h[0] + h[3] * h[3] - h[1] * h[1] - h[4] * h[4]) / d2;    if (v1 < v2) std::swap(v1, v2);    if (v1 > 0 && v2 > 0) f1 = sqrt(std::abs(d1) > std::abs(d2) ? v1 : v2);    else if (v1 > 0) f1 = sqrt(v1);    else f1_ok = false;    f0_ok = true;    d1 = h[0] * h[3] + h[1] * h[4];    d2 = h[0] * h[0] + h[1] * h[1] - h[3] * h[3] - h[4] * h[4];    v1 = -h[2] * h[5] / d1;    v2 = (h[5] * h[5] - h[2] * h[2]) / d2;    if (v1 < v2) std::swap(v1, v2);    if (v1 > 0 && v2 > 0) f0 = sqrt(std::abs(d1) > std::abs(d2) ? v1 : v2);    else if (v1 > 0) f0 = sqrt(v1);    else f0_ok = false;}

求出的焦距有8个

求出的焦距取中值或者平均值，然后就是所有图片的焦距。

并构建camera参数，将矩阵写入camera：

        cameras.assign(num_images, CameraParams());        for (int i = 0; i < num_images; ++i)            cameras[i].focal = focals[i];

4.2 根据匹配的内点构建最大生成树，然后广度优先搜索求出根节点，并求出camera的R矩阵，K矩阵以及光轴中心

camera其他参数：

aspect = 1.0，ppx，ppy目前等于0，最后会赋值成图像中心点的。

K矩阵的值：

Mat CameraParams::K() const{    Mat_<double> k = Mat::eye(3, 3, CV_64F);    k(0,0) = focal; k(0,2) = ppx;    k(1,1) = focal * aspect; k(1,2) = ppy;    return k;}

R矩阵的值：

    void operator ()(const GraphEdge &edge)    {        int pair_idx = edge.from * num_images + edge.to;        Mat_<double> K_from = Mat::eye(3, 3, CV_64F);        K_from(0,0) = cameras[edge.from].focal;        K_from(1,1) = cameras[edge.from].focal * cameras[edge.from].aspect;        K_from(0,2) = cameras[edge.from].ppx;        K_from(0,2) = cameras[edge.from].ppy;        Mat_<double> K_to = Mat::eye(3, 3, CV_64F);        K_to(0,0) = cameras[edge.to].focal;        K_to(1,1) = cameras[edge.to].focal * cameras[edge.to].aspect;        K_to(0,2) = cameras[edge.to].ppx;        K_to(0,2) = cameras[edge.to].ppy;        Mat R = K_from.inv() * pairwise_matches[pair_idx].H.inv() * K_to;        cameras[edge.to].R = cameras[edge.from].R * R;    }

光轴中心的值

    for (int i = 0; i < num_images; ++i)    {        cameras[i].ppx += 0.5 * features[i].img_size.width;        cameras[i].ppy += 0.5 * features[i].img_size.height;    }

5.使用Bundle Adjustment方法对所有图片进行相机参数校正

Bundle Adjustment（光束法平差）算法主要是解决所有相机参数的联合。这是全景拼接必须的一步，因为多个成对的单应性矩阵合成全景图时，会忽略全局的限制，造成累积误差。因此每一个图像都要加上光束法平差值，使图像被初始化成相同的旋转和焦距长度。

光束法平差的目标函数是一个具有鲁棒性的映射误差的平方和函数。即每一个特征点都要映射到其他的图像中，计算出使误差的平方和最小的相机参数。具体的推导过程可以参见Automatic Panoramic Image Stitching using Invariant Features.pdf的第五章，本文只介绍一下opencv实现的过程（完整的理论和公式暂时还没看懂，希望有人能一起交流）

opencv中误差描述函数有两种如下：（opencv默认是BundleAdjusterRay ）：

BundleAdjusterReproj // BundleAdjusterBase(7, 2)//最小投影误差平方和Implementation of the camera parameters refinement algorithm which minimizes sum of the reprojection error squaresBundleAdjusterRay //  BundleAdjusterBase(4, 3)//最小特征点与相机中心点的距离和Implementation of the camera parameters refinement algorithm which minimizes sum of the distances between therays passing through the camera center and a feature.

5.1 首先计算cam_params_的值：

    setUpInitialCameraParams(cameras);

函数主要源码：

    cam_params_.create(num_images_ * 4, 1, CV_64F);    SVD svd;//奇异值分解    for (int i = 0; i < num_images_; ++i)    {        cam_params_.at<double>(i * 4, 0) = cameras[i].focal;        svd(cameras[i].R, SVD::FULL_UV);        Mat R = svd.u * svd.vt;        if (determinant(R) < 0)            R *= -1;        Mat rvec;        Rodrigues(R, rvec);        CV_Assert(rvec.type() == CV_32F);        cam_params_.at<double>(i * 4 + 1, 0) = rvec.at<float>(0, 0);        cam_params_.at<double>(i * 4 + 2, 0) = rvec.at<float>(1, 0);        cam_params_.at<double>(i * 4 + 3, 0) = rvec.at<float>(2, 0);    }

计算cam_params_的值，先初始化cam_params(num_images_*4,1,CV_64F);

cam_params_[i*4+0] = cameras[i].focal;

cam_params_后面3个值，是cameras[i].R先经过奇异值分解，然后对u*vt进行Rodrigues运算，得到的rvec第一行3个值赋给cam_params_。

奇异值分解的定义：

在矩阵M的奇异值分解中 M = UΣV*

·U的列(columns)组成一套对M的正交"输入"或"分析"的基向量。这些向量是MM*的特征向量。

·V的列(columns)组成一套对M的正交"输出"的基向量。这些向量是M*M的特征向量。

·Σ对角线上的元素是奇异值，可视为是在输入与输出间进行的标量的"膨胀控制"。这些是M*M及MM*的奇异值，并与U和V的行向量相对应。

5.2 删除置信度小于门限的匹配对

    // Leave only consistent image pairs    edges_.clear();    for (int i = 0; i < num_images_ - 1; ++i)    {        for (int j = i + 1; j < num_images_; ++j)        {            const MatchesInfo& matches_info = pairwise_matches_[i * num_images_ + j];            if (matches_info.confidence > conf_thresh_)                edges_.push_back(make_pair(i, j));        }    }

5.3 使用LM算法计算camera参数。

首先初始化LM的参数（具体理论还没有看懂）

//计算所有内点之和    for (size_t i = 0; i < edges_.size(); ++i)        total_num_matches_ += static_cast<int>(pairwise_matches[edges_[i].first * num_images_ +                                                                edges_[i].second].num_inliers);    CvLevMarq solver(num_images_ * num_params_per_cam_,                     total_num_matches_ * num_errs_per_measurement_,                     term_criteria_);    Mat err, jac;    CvMat matParams = cam_params_;    cvCopy(&matParams, solver.param);    int iter = 0;    for(;;)//类似于while（1）,但是比while（1）效率高    {        const CvMat* _param = 0;        CvMat* _jac = 0;        CvMat* _err = 0;        bool proceed = solver.update(_param, _jac, _err);        cvCopy(_param, &matParams);        if (!proceed || !_err)            break;        if (_jac)        {            calcJacobian(jac); //构造雅阁比行列式            CvMat tmp = jac;            cvCopy(&tmp, _jac);        }        if (_err)        {            calcError(err);//计算err            LOG_CHAT(".");            iter++;            CvMat tmp = err;            cvCopy(&tmp, _err);        }    }

计算camera

 obtainRefinedCameraParams(cameras);//Gets the refined camera parameters.

函数源代码：

void BundleAdjusterRay::obtainRefinedCameraParams(vector<CameraParams> &cameras) const{    for (int i = 0; i < num_images_; ++i)    {        cameras[i].focal = cam_params_.at<double>(i * 4, 0);        Mat rvec(3, 1, CV_64F);        rvec.at<double>(0, 0) = cam_params_.at<double>(i * 4 + 1, 0);        rvec.at<double>(1, 0) = cam_params_.at<double>(i * 4 + 2, 0);        rvec.at<double>(2, 0) = cam_params_.at<double>(i * 4 + 3, 0);        Rodrigues(rvec, cameras[i].R);        Mat tmp;        cameras[i].R.convertTo(tmp, CV_32F);        cameras[i].R = tmp;    }}

求出根节点，然后归一化旋转矩阵R

    // Normalize motion to center image    Graph span_tree;    vector<int> span_tree_centers;    findMaxSpanningTree(num_images_, pairwise_matches, span_tree, span_tree_centers);    Mat R_inv = cameras[span_tree_centers[0]].R.inv();    for (int i = 0; i < num_images_; ++i)        cameras[i].R = R_inv * cameras[i].R;

6 波形校正

前面几节把相机旋转矩阵计算出来，但是还有一个因素需要考虑，就是由于拍摄者拍摄图片的时候不一定是水平的，轻微的倾斜会导致全景图像出现飞机曲线，因此我们要对图像进行波形校正，主要是寻找每幅图形的“上升向量”（up_vector），使他校正成。

波形校正的效果图

opencv实现的源码如下（也是暂时没看懂，囧）

 <span style="white-space:pre"></span>vector<Mat> rmats;        for (size_t i = 0; i < cameras.size(); ++i)            rmats.push_back(cameras[i].R);        waveCorrect(rmats, wave_correct);//Tries to make panorama more horizontal (or vertical).        for (size_t i = 0; i < cameras.size(); ++i)            cameras[i].R = rmats[i];

其中waveCorrect(rmats, wave_correct)源码如下：

void waveCorrect(vector<Mat> &rmats, WaveCorrectKind kind){    LOGLN("Wave correcting...");#if ENABLE_LOG    int64 t = getTickCount();#endif    Mat moment = Mat::zeros(3, 3, CV_32F);    for (size_t i = 0; i < rmats.size(); ++i)    {        Mat col = rmats[i].col(0);        moment += col * col.t();//相机R矩阵第一列转置相乘然后相加    }    Mat eigen_vals, eigen_vecs;    eigen(moment, eigen_vals, eigen_vecs);//Calculates eigenvalues and eigenvectors of a symmetric matrix.    Mat rg1;    if (kind == WAVE_CORRECT_HORIZ)        rg1 = eigen_vecs.row(2).t();//如果是水平校正，去特征向量的第三行    else if (kind == WAVE_CORRECT_VERT)        rg1 = eigen_vecs.row(0).t();//如果是垂直校正，特征向量第一行    else        CV_Error(CV_StsBadArg, "unsupported kind of wave correction");    Mat img_k = Mat::zeros(3, 1, CV_32F);    for (size_t i = 0; i < rmats.size(); ++i)        img_k += rmats[i].col(2);//R函数第3列相加    Mat rg0 = rg1.cross(img_k);//rg1与img_k向量积    rg0 /= norm(rg0);//归一化？    Mat rg2 = rg0.cross(rg1);    double conf = 0;    if (kind == WAVE_CORRECT_HORIZ)    {        for (size_t i = 0; i < rmats.size(); ++i)            conf += rg0.dot(rmats[i].col(0));//Computes a dot-product of two vectors.数量积        if (conf < 0)        {            rg0 *= -1;            rg1 *= -1;        }    }    else if (kind == WAVE_CORRECT_VERT)    {        for (size_t i = 0; i < rmats.size(); ++i)            conf -= rg1.dot(rmats[i].col(0));        if (conf < 0)        {            rg0 *= -1;            rg1 *= -1;        }    }    Mat R = Mat::zeros(3, 3, CV_32F);    Mat tmp = R.row(0);    Mat(rg0.t()).copyTo(tmp);    tmp = R.row(1);    Mat(rg1.t()).copyTo(tmp);    tmp = R.row(2);    Mat(rg2.t()).copyTo(tmp);    for (size_t i = 0; i < rmats.size(); ++i)        rmats[i] = R * rmats[i];    LOGLN("Wave correcting, time: " << ((getTickCount() - t) / getTickFrequency()) << " sec");}

7.单应性矩阵变换

由图像匹配，Bundle Adjustment算法以及波形校验，求出了图像的相机参数以及旋转矩阵，接下来就对图形进行单应性矩阵变换，亮度的增量补偿以及多波段融合（图像金字塔）。首先介绍的就是单应性矩阵变换：

源图像的点（x，y，z=1），图像的旋转矩阵R，图像的相机参数矩阵K，经过变换后的同一坐标（x_,y_,z_），然后映射到球形坐标（u，v，w），他们之间的关系如下：

void SphericalProjector::mapForward(float x, float y, float &u, float &v){    float x_ = r_kinv[0] * x + r_kinv[1] * y + r_kinv[2];    float y_ = r_kinv[3] * x + r_kinv[4] * y + r_kinv[5];    float z_ = r_kinv[6] * x + r_kinv[7] * y + r_kinv[8];    u = scale * atan2f(x_, z_);    float w = y_ / sqrtf(x_ * x_ + y_ * y_ + z_ * z_);    v = scale * (static_cast<float>(CV_PI) - acosf(w == w ? w : 0));}

根据映射公式，对图像的上下左右四个边界求映射后的坐标，然后确定变换后图像的左上角和右上角的坐标，

如果是球形拼接，则需要再加上判断（暂时还没研究透）：

    float tl_uf = static_cast<float>(dst_tl.x);    float tl_vf = static_cast<float>(dst_tl.y);    float br_uf = static_cast<float>(dst_br.x);    float br_vf = static_cast<float>(dst_br.y);    float x = projector_.rinv[1];    float y = projector_.rinv[4];    float z = projector_.rinv[7];    if (y > 0.f)    {        float x_ = (projector_.k[0] * x + projector_.k[1] * y) / z + projector_.k[2];        float y_ = projector_.k[4] * y / z + projector_.k[5];        if (x_ > 0.f && x_ < src_size.width && y_ > 0.f && y_ < src_size.height)        {            tl_uf = min(tl_uf, 0.f); tl_vf = min(tl_vf, static_cast<float>(CV_PI * projector_.scale));            br_uf = max(br_uf, 0.f); br_vf = max(br_vf, static_cast<float>(CV_PI * projector_.scale));        }    }    x = projector_.rinv[1];    y = -projector_.rinv[4];    z = projector_.rinv[7];    if (y > 0.f)    {        float x_ = (projector_.k[0] * x + projector_.k[1] * y) / z + projector_.k[2];        float y_ = projector_.k[4] * y / z + projector_.k[5];        if (x_ > 0.f && x_ < src_size.width && y_ > 0.f && y_ < src_size.height)        {            tl_uf = min(tl_uf, 0.f); tl_vf = min(tl_vf, static_cast<float>(0));            br_uf = max(br_uf, 0.f); br_vf = max(br_vf, static_cast<float>(0));        }    }

然后利用反投影将图形反投影到变换的图像上，像素计算默认是二维线性插值。

反投影的公式：

void SphericalProjector::mapBackward(float u, float v, float &x, float &y){    u /= scale;    v /= scale;    float sinv = sinf(static_cast<float>(CV_PI) - v);    float x_ = sinv * sinf(u);    float y_ = cosf(static_cast<float>(CV_PI) - v);    float z_ = sinv * cosf(u);    float z;    x = k_rinv[0] * x_ + k_rinv[1] * y_ + k_rinv[2] * z_;    y = k_rinv[3] * x_ + k_rinv[4] * y_ + k_rinv[5] * z_;    z = k_rinv[6] * x_ + k_rinv[7] * y_ + k_rinv[8] * z_;    if (z > 0) { x /= z; y /= z; }    else x = y = -1;}

然后将反投影求出的x，y值写入Mat矩阵xmap和ymap中

 xmap.create(dst_br.y - dst_tl.y + 1, dst_br.x - dst_tl.x + 1, CV_32F);    ymap.create(dst_br.y - dst_tl.y + 1, dst_br.x - dst_tl.x + 1, CV_32F);    float x, y;    for (int v = dst_tl.y; v <= dst_br.y; ++v)    {        for (int u = dst_tl.x; u <= dst_br.x; ++u)        {            projector_.mapBackward(static_cast<float>(u), static_cast<float>(v), x, y);            xmap.at<float>(v - dst_tl.y, u - dst_tl.x) = x;            ymap.at<float>(v - dst_tl.y, u - dst_tl.x) = y;        }    }

最后使用opencv自带的remap函数将图像重新绘制:

remap(src, dst, xmap, ymap, interp_mode, border_mode);//重映射，xmap，yamp分别是u，v反投影对应的x，y值，默认是双线性插值

8.光照补偿

图像拼接中，由于拍摄的图片有可能因为光圈或者光线的问题，导致相邻图片重叠区域出现亮度差，所以在拼接时就需要对图像进行亮度补偿，（opencv只对重叠区域进行了亮度补偿，这样会导致图像融合处虽然光照渐变，但是图像整体的光强没有柔和的过渡）。

首先，将所有图像，mask矩阵进行分块（大小在32*32附近）。

  for (int img_idx = 0; img_idx < num_images; ++img_idx)    {        Size bl_per_img((images[img_idx].cols + bl_width_ - 1) / bl_width_,                        (images[img_idx].rows + bl_height_ - 1) / bl_height_);        int bl_width = (images[img_idx].cols + bl_per_img.width - 1) / bl_per_img.width;        int bl_height = (images[img_idx].rows + bl_per_img.height - 1) / bl_per_img.height;        bl_per_imgs[img_idx] = bl_per_img;        for (int by = 0; by < bl_per_img.height; ++by)        {            for (int bx = 0; bx < bl_per_img.width; ++bx)            {                Point bl_tl(bx * bl_width, by * bl_height);                Point bl_br(min(bl_tl.x + bl_width, images[img_idx].cols),                            min(bl_tl.y + bl_height, images[img_idx].rows));                block_corners.push_back(corners[img_idx] + bl_tl);                block_images.push_back(images[img_idx](Rect(bl_tl, bl_br)));                block_masks.push_back(make_pair(masks[img_idx].first(Rect(bl_tl, bl_br)),                                                masks[img_idx].second));            }        }    }

然后，求出任意两块图像的重叠区域的平均光强，

//计算每一块区域的光照均值sqrt(sqrt（R）+sqrt(G)+sqrt(B))//光照均值是对称矩阵，所以一次循环计算两个光照值，（i，j），与（j，i）    for (int i = 0; i < num_images; ++i)    {        for (int j = i; j < num_images; ++j)        {            Rect roi;//判断image[i]与image[j]是否有重叠部分            if (overlapRoi(corners[i], corners[j], images[i].size(), images[j].size(), roi))            {                subimg1 = images[i](Rect(roi.tl() - corners[i], roi.br() - corners[i]));                subimg2 = images[j](Rect(roi.tl() - corners[j], roi.br() - corners[j]));                submask1 = masks[i].first(Rect(roi.tl() - corners[i], roi.br() - corners[i]));                submask2 = masks[j].first(Rect(roi.tl() - corners[j], roi.br() - corners[j]));                intersect = (submask1 == masks[i].second) & (submask2 == masks[j].second);                N(i, j) = N(j, i) = max(1, countNonZero(intersect));                double Isum1 = 0, Isum2 = 0;                for (int y = 0; y < roi.height; ++y)                {                    const Point3_<uchar>* r1 = subimg1.ptr<Point3_<uchar> >(y);                    const Point3_<uchar>* r2 = subimg2.ptr<Point3_<uchar> >(y);                    for (int x = 0; x < roi.width; ++x)                    {                        if (intersect(y, x))                        {                            Isum1 += sqrt(static_cast<double>(sqr(r1[x].x) + sqr(r1[x].y) + sqr(r1[x].z)));                            Isum2 += sqrt(static_cast<double>(sqr(r2[x].x) + sqr(r2[x].y) + sqr(r2[x].z)));                        }                    }                }                I(i, j) = Isum1 / N(i, j);                I(j, i) = Isum2 / N(i, j);            }        }    }

建立方程，求出每个光强的调整系数

    Mat_<double> A(num_images, num_images); A.setTo(0);    Mat_<double> b(num_images, 1); b.setTo(0);//beta*N(i,j)    for (int i = 0; i < num_images; ++i)    {        for (int j = 0; j < num_images; ++j)        {            b(i, 0) += beta * N(i, j);            A(i, i) += beta * N(i, j);            if (j == i) continue;            A(i, i) += 2 * alpha * I(i, j) * I(i, j) * N(i, j);            A(i, j) -= 2 * alpha * I(i, j) * I(j, i) * N(i, j);        }    }    solve(A, b, gains_);//求方程的解A*gains = B

gains_原理分析:

num_images ：表示图像分块的个数，零num_images = n

N矩阵，大小n*n，N(i,j)表示第i幅图像与第j幅图像重合的像素点数，N(i,j)=N(j,i)

I矩阵，大小n*n，I(i,j)与I(j,i)表示第i，j块区域重合部分的像素平均值，I(i，j)是重合区域中i快的平均亮度值，

参数alpha和beta，默认值是alpha=0.01，beta=100.

A矩阵，大小n*n，公式图片不全

b矩阵，大小n*1，

然后根据求解矩阵

gains_矩阵，大小1*n，A*gains = B

然后将gains_进行线性滤波

    Mat_<float> ker(1, 3);    ker(0,0) = 0.25; ker(0,1) = 0.5; ker(0,2) = 0.25;    int bl_idx = 0;    for (int img_idx = 0; img_idx < num_images; ++img_idx)    {Size bl_per_img = bl_per_imgs[img_idx];gain_maps_[img_idx].create(bl_per_img);        for (int by = 0; by < bl_per_img.height; ++by)            for (int bx = 0; bx < bl_per_img.width; ++bx, ++bl_idx)                gain_maps_[img_idx](by, bx) = static_cast<float>(gains[bl_idx]);//用分解的核函数对图像做卷积。首先，图像的每一行与一维的核kernelX做卷积；然后，运算结果的每一列与一维的核kernelY做卷积        sepFilter2D(gain_maps_[img_idx], gain_maps_[img_idx], CV_32F, ker, ker);        sepFilter2D(gain_maps_[img_idx], gain_maps_[img_idx], CV_32F, ker, ker);    }

然后构建一个gain_maps的三维矩阵，gain_main[图像的个数][图像分块的行数][图像分块的列数]，然后对没一副图像的gain进行滤波。

9.Seam Estimation

缝隙估计有6种方法，默认就是第三种方法，seam_find_type == "gc_color"，该方法是利用最大流方法检测。

 if (seam_find_type == "no")        seam_finder = new detail::NoSeamFinder();//Stub seam estimator which does nothing.    else if (seam_find_type == "voronoi")        seam_finder = new detail::VoronoiSeamFinder();//Voronoi diagram-based seam estimator. 泰森多边形缝隙估计    else if (seam_find_type == "gc_color")    {#ifdef HAVE_OPENCV_GPU        if (try_gpu && gpu::getCudaEnabledDeviceCount() > 0)            seam_finder = new detail::GraphCutSeamFinderGpu(GraphCutSeamFinderBase::COST_COLOR);        else#endif            seam_finder = new detail::GraphCutSeamFinder(GraphCutSeamFinderBase::COST_COLOR);//Minimum graph cut-based seam estimator    }    else if (seam_find_type == "gc_colorgrad")    {#ifdef HAVE_OPENCV_GPU        if (try_gpu && gpu::getCudaEnabledDeviceCount() > 0)            seam_finder = new detail::GraphCutSeamFinderGpu(GraphCutSeamFinderBase::COST_COLOR_GRAD);        else#endif            seam_finder = new detail::GraphCutSeamFinder(GraphCutSeamFinderBase::COST_COLOR_GRAD);    }    else if (seam_find_type == "dp_color")        seam_finder = new detail::DpSeamFinder(DpSeamFinder::COLOR);    else if (seam_find_type == "dp_colorgrad")        seam_finder = new detail::DpSeamFinder(DpSeamFinder::COLOR_GRAD);    if (seam_finder.empty())    {        cout << "Can't create the following seam finder '" << seam_find_type << "'\n";        return 1;    }

程序解读可参见：

http://blog.csdn.net/chlele0105/article/details/12624541

http://blog.csdn.net/zouxy09/article/details/8534954

http://blog.csdn.net/yangtrees/article/details/7930640

10.多波段融合

由于以前进行处理的图片都是以work_scale（3.1节有介绍）进行缩放的，所以图像的内参，corner（同一坐标后的顶点），mask（融合的掩码）都需要重新计算。以及将之前计算的光照增强的gain也要计算进去。

  // Read image and resize it if necessary        full_img = imread(img_names[img_idx]);        if (!is_compose_scale_set)        {            if (compose_megapix > 0)                compose_scale = min(1.0, sqrt(compose_megapix * 1e6 / full_img.size().area()));            is_compose_scale_set = true;            // Compute relative scales            //compose_seam_aspect = compose_scale / seam_scale;            compose_work_aspect = compose_scale / work_scale;            // Update warped image scale            warped_image_scale *= static_cast<float>(compose_work_aspect);            warper = warper_creator->create(warped_image_scale);            // Update corners and sizes            for (int i = 0; i < num_images; ++i)            {                // Update intrinsics                cameras[i].focal *= compose_work_aspect;                cameras[i].ppx *= compose_work_aspect;                cameras[i].ppy *= compose_work_aspect;                // Update corner and size                Size sz = full_img_sizes[i];                if (std::abs(compose_scale - 1) > 1e-1)                {                    sz.width = cvRound(full_img_sizes[i].width * compose_scale);//取整                    sz.height = cvRound(full_img_sizes[i].height * compose_scale);                }                Mat K;                cameras[i].K().convertTo(K, CV_32F);                Rect roi = warper->warpRoi(sz, K, cameras[i].R);//Returns Projected image minimum bounding box                corners[i] = roi.tl();//! the top-left corner                sizes[i] = roi.size();//! size of the real buffer            }        }        if (abs(compose_scale - 1) > 1e-1)            resize(full_img, img, Size(), compose_scale, compose_scale);        else            img = full_img;        full_img.release();        Size img_size = img.size();        Mat K;        cameras[img_idx].K().convertTo(K, CV_32F);        // Warp the current image        warper->warp(img, K, cameras[img_idx].R, INTER_LINEAR, BORDER_REFLECT, img_warped);        // Warp the current image mask        mask.create(img_size, CV_8U);        mask.setTo(Scalar::all(255));        warper->warp(mask, K, cameras[img_idx].R, INTER_NEAREST, BORDER_CONSTANT, mask_warped);        // Compensate exposure        compensator->apply(img_idx, corners[img_idx], img_warped, mask_warped);//光照补偿        img_warped.convertTo(img_warped_s, CV_16S);        img_warped.release();        img.release();        mask.release();        dilate(masks_warped[img_idx], dilated_mask, Mat());        resize(dilated_mask, seam_mask, mask_warped.size());        mask_warped = seam_mask & mask_warped;

对图像进行光照补偿，就是将对应区域乘以gain：

//块光照补偿void BlocksGainCompensator::apply(int index, Point /*corner*/, Mat &image, const Mat &/*mask*/){    CV_Assert(image.type() == CV_8UC3);    Mat_<float> gain_map;    if (gain_maps_[index].size() == image.size())        gain_map = gain_maps_[index];    else        resize(gain_maps_[index], gain_map, image.size(), 0, 0, INTER_LINEAR);    for (int y = 0; y < image.rows; ++y)    {        const float* gain_row = gain_map.ptr<float>(y);        Point3_<uchar>* row = image.ptr<Point3_<uchar> >(y);        for (int x = 0; x < image.cols; ++x)        {            row[x].x = saturate_cast<uchar>(row[x].x * gain_row[x]);            row[x].y = saturate_cast<uchar>(row[x].y * gain_row[x]);            row[x].z = saturate_cast<uchar>(row[x].z * gain_row[x]);        }    }}

进行多波段融合，首先初始化blend，确定blender的融合的方式，默认是多波段融合MULTI_BAND，以及根据corners顶点和图像的大小确定最终全景图的尺寸。

<span></span>//初始化blender        if (blender.empty())        {            blender = Blender::createDefault(blend_type, try_gpu);            Size dst_sz = resultRoi(corners, sizes).size();//计算最后图像的大小            float blend_width = sqrt(static_cast<float>(dst_sz.area())) * blend_strength / 100.f;            if (blend_width < 1.f)                blender = Blender::createDefault(Blender::NO, try_gpu);            else if (blend_type == Blender::MULTI_BAND)            {                MultiBandBlender* mb = dynamic_cast<MultiBandBlender*>(static_cast<Blender*>(blender));                mb->setNumBands(static_cast<int>(ceil(log(blend_width)/log(2.)) - 1.));                LOGLN("Multi-band blender, number of bands: " << mb->numBands());            }            else if (blend_type == Blender::FEATHER)            {                FeatherBlender* fb = dynamic_cast<FeatherBlender*>(static_cast<Blender*>(blender));                fb->setSharpness(1.f/blend_width);                LOGLN("Feather blender, sharpness: " << fb->sharpness());            }            blender->prepare(corners, sizes);//根据corners顶点和图像的大小确定最终全景图的尺寸        }

然后对每幅图图形构建金字塔，层数可以由输入的系数确定，默认是5层。

先对顶点以及图像的宽和高做处理，使其能被2^num_bands除尽，这样才能将进行向下采样num_bands次，首先从源图像pyrDown向下采样，在由最底部的图像pyrUp向上采样，把对应层得上采样和下采样的相减，就得到了图像的高频分量，存储到每一个金字塔中。然后根据mask，将每幅图像的各层金字塔分别写入最终的金字塔层src_pyr_laplace中。

最后将各层的金字塔叠加，就得到了最终完整的全景图。

 blender->feed(img_warped_s, mask_warped, corners[img_idx]);//将图像写入金字塔中

源码：

void MultiBandBlender::feed(const Mat &img, const Mat &mask, Point tl){    CV_Assert(img.type() == CV_16SC3 || img.type() == CV_8UC3);    CV_Assert(mask.type() == CV_8U);    // Keep source image in memory with small border    int gap = 3 * (1 << num_bands_);    Point tl_new(max(dst_roi_.x, tl.x - gap),                 max(dst_roi_.y, tl.y - gap));    Point br_new(min(dst_roi_.br().x, tl.x + img.cols + gap),                 min(dst_roi_.br().y, tl.y + img.rows + gap));    // Ensure coordinates of top-left, bottom-right corners are divided by (1 << num_bands_).    // After that scale between layers is exactly 2.    //    // We do it to avoid interpolation problems when keeping sub-images only. There is no such problem when    // image is bordered to have size equal to the final image size, but this is too memory hungry approach.//将顶点调整成能被2^num_bank次方除尽的值    tl_new.x = dst_roi_.x + (((tl_new.x - dst_roi_.x) >> num_bands_) << num_bands_);    tl_new.y = dst_roi_.y + (((tl_new.y - dst_roi_.y) >> num_bands_) << num_bands_);    int width = br_new.x - tl_new.x;    int height = br_new.y - tl_new.y;    width += ((1 << num_bands_) - width % (1 << num_bands_)) % (1 << num_bands_);    height += ((1 << num_bands_) - height % (1 << num_bands_)) % (1 << num_bands_);    br_new.x = tl_new.x + width;    br_new.y = tl_new.y + height;    int dy = max(br_new.y - dst_roi_.br().y, 0);    int dx = max(br_new.x - dst_roi_.br().x, 0);    tl_new.x -= dx; br_new.x -= dx;    tl_new.y -= dy; br_new.y -= dy;    int top = tl.y - tl_new.y;    int left = tl.x - tl_new.x;    int bottom = br_new.y - tl.y - img.rows;    int right = br_new.x - tl.x - img.cols;    // Create the source image Laplacian pyramid    Mat img_with_border;    copyMakeBorder(img, img_with_border, top, bottom, left, right,                   BORDER_REFLECT);//给图像设置一个边界，BORDER_REFLECT边界颜色任意    vector<Mat> src_pyr_laplace;    if (can_use_gpu_ && img_with_border.depth() == CV_16S)        createLaplacePyrGpu(img_with_border, num_bands_, src_pyr_laplace);    else        createLaplacePyr(img_with_border, num_bands_, src_pyr_laplace);//创建高斯金字塔，每一层保存的全是高频信息    // Create the weight map Gaussian pyramid    Mat weight_map;    vector<Mat> weight_pyr_gauss(num_bands_ + 1);    if(weight_type_ == CV_32F)    {        mask.convertTo(weight_map, CV_32F, 1./255.);//将mask的0，255归一化成0,1    }    else// weight_type_ == CV_16S    {        mask.convertTo(weight_map, CV_16S);        add(weight_map, 1, weight_map, mask != 0);    }    copyMakeBorder(weight_map, weight_pyr_gauss[0], top, bottom, left, right, BORDER_CONSTANT);    for (int i = 0; i < num_bands_; ++i)        pyrDown(weight_pyr_gauss[i], weight_pyr_gauss[i + 1]);    int y_tl = tl_new.y - dst_roi_.y;    int y_br = br_new.y - dst_roi_.y;    int x_tl = tl_new.x - dst_roi_.x;    int x_br = br_new.x - dst_roi_.x;    // Add weighted layer of the source image to the final Laplacian pyramid layer    if(weight_type_ == CV_32F)    {        for (int i = 0; i <= num_bands_; ++i)        {            for (int y = y_tl; y < y_br; ++y)            {                int y_ = y - y_tl;                const Point3_<short>* src_row = src_pyr_laplace[i].ptr<Point3_<short> >(y_);                Point3_<short>* dst_row = dst_pyr_laplace_[i].ptr<Point3_<short> >(y);                const float* weight_row = weight_pyr_gauss[i].ptr<float>(y_);                float* dst_weight_row = dst_band_weights_[i].ptr<float>(y);                for (int x = x_tl; x < x_br; ++x)                {                    int x_ = x - x_tl;                    dst_row[x].x += static_cast<short>(src_row[x_].x * weight_row[x_]);                    dst_row[x].y += static_cast<short>(src_row[x_].y * weight_row[x_]);                    dst_row[x].z += static_cast<short>(src_row[x_].z * weight_row[x_]);                    dst_weight_row[x] += weight_row[x_];                }            }            x_tl /= 2; y_tl /= 2;            x_br /= 2; y_br /= 2;        }    }    else// weight_type_ == CV_16S    {        for (int i = 0; i <= num_bands_; ++i)        {            for (int y = y_tl; y < y_br; ++y)            {                int y_ = y - y_tl;                const Point3_<short>* src_row = src_pyr_laplace[i].ptr<Point3_<short> >(y_);                Point3_<short>* dst_row = dst_pyr_laplace_[i].ptr<Point3_<short> >(y);                const short* weight_row = weight_pyr_gauss[i].ptr<short>(y_);                short* dst_weight_row = dst_band_weights_[i].ptr<short>(y);                for (int x = x_tl; x < x_br; ++x)                {                    int x_ = x - x_tl;                    dst_row[x].x += short((src_row[x_].x * weight_row[x_]) >> 8);                    dst_row[x].y += short((src_row[x_].y * weight_row[x_]) >> 8);                    dst_row[x].z += short((src_row[x_].z * weight_row[x_]) >> 8);                    dst_weight_row[x] += weight_row[x_];                }            }            x_tl /= 2; y_tl /= 2;            x_br /= 2; y_br /= 2;        }    }}

其中，金字塔构建的源码：

void createLaplacePyr(const Mat &img, int num_levels, vector<Mat> &pyr){#ifdef HAVE_TEGRA_OPTIMIZATION    if(tegra::createLaplacePyr(img, num_levels, pyr))        return;#endif    pyr.resize(num_levels + 1);    if(img.depth() == CV_8U)    {        if(num_levels == 0)        {            img.convertTo(pyr[0], CV_16S);            return;        }        Mat downNext;        Mat current = img;        pyrDown(img, downNext);        for(int i = 1; i < num_levels; ++i)        {            Mat lvl_up;            Mat lvl_down;            pyrDown(downNext, lvl_down);            pyrUp(downNext, lvl_up, current.size());            subtract(current, lvl_up, pyr[i-1], noArray(), CV_16S);            current = downNext;            downNext = lvl_down;        }        {            Mat lvl_up;            pyrUp(downNext, lvl_up, current.size());            subtract(current, lvl_up, pyr[num_levels-1], noArray(), CV_16S);            downNext.convertTo(pyr[num_levels], CV_16S);        }    }    else    {        pyr[0] = img;//构建高斯金字塔        for (int i = 0; i < num_levels; ++i)            pyrDown(pyr[i], pyr[i + 1]);//先高斯滤波，在亚采样，得到比pyr【i】缩小一半的图像        Mat tmp;        for (int i = 0; i < num_levels; ++i)        {            pyrUp(pyr[i + 1], tmp, pyr[i].size());//插值（偶数行，偶数列赋值为0），然后高斯滤波，核是5*5。            subtract(pyr[i], tmp, pyr[i]);//pyr[i] = pyr[i]-tmp，得到的全是高频信息        }    }}

最终把所有层得金字塔叠加的程序：

    Mat result, result_mask;    blender->blend(result, result_mask);//将多层金字塔图形叠加

源码：

void MultiBandBlender::blend(Mat &dst, Mat &dst_mask){    for (int i = 0; i <= num_bands_; ++i)        normalizeUsingWeightMap(dst_band_weights_[i], dst_pyr_laplace_[i]);    if (can_use_gpu_)        restoreImageFromLaplacePyrGpu(dst_pyr_laplace_);    else        restoreImageFromLaplacePyr(dst_pyr_laplace_);    dst_ = dst_pyr_laplace_[0];    dst_ = dst_(Range(0, dst_roi_final_.height), Range(0, dst_roi_final_.width));    dst_mask_ = dst_band_weights_[0] > WEIGHT_EPS;    dst_mask_ = dst_mask_(Range(0, dst_roi_final_.height), Range(0, dst_roi_final_.width));    dst_pyr_laplace_.clear();    dst_band_weights_.clear();    Blender::blend(dst, dst_mask);}

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