motion_estimators.cpp

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#include "precomp.hpp"

using namespace std;
using namespace cv;
using namespace cv::detail;

namespace {

struct IncDistance
{
    IncDistance(vector<int> &dists) : dists(&dists[0]) {}
    void operator ()(const GraphEdge &edge) { dists[edge.to] = dists[edge.from] + 1; }
    int* dists;
};


struct CalcRotation
{
    CalcRotation(int num_images, const vector<MatchesInfo> &pairwise_matches, vector<CameraParams> &cameras)
        : num_images(num_images), pairwise_matches(&pairwise_matches[0]), cameras(&cameras[0]) {}

    void operator ()(const GraphEdge &edge)
    {
        int pair_idx = edge.from * num_images + edge.to;

        double f_from = cameras[edge.from].focal;
        double f_to = cameras[edge.to].focal;

        Mat K_from = Mat::eye(3, 3, CV_64F);
        K_from.at<double>(0, 0) = f_from;
        K_from.at<double>(1, 1) = f_from;

        Mat K_to = Mat::eye(3, 3, CV_64F);
        K_to.at<double>(0, 0) = f_to;
        K_to.at<double>(1, 1) = f_to;

        Mat R = K_from.inv() * pairwise_matches[pair_idx].H.inv() * K_to;
        cameras[edge.to].R = cameras[edge.from].R * R;
    }

    int num_images;
    const MatchesInfo* pairwise_matches;
    CameraParams* cameras;
};


//////////////////////////////////////////////////////////////////////////////

void calcDeriv(const Mat &err1, const Mat &err2, double h, Mat res)
{
    for (int i = 0; i < err1.rows; ++i)
        res.at<double>(i, 0) = (err2.at<double>(i, 0) - err1.at<double>(i, 0)) / h;
}

} // namespace


namespace cv {
namespace detail {

void HomographyBasedEstimator::estimate(const vector<ImageFeatures> &features, const vector<MatchesInfo> &pairwise_matches,
                                        vector<CameraParams> &cameras)
{
    LOGLN("Estimating rotations...");
    int64 t = getTickCount();

    const int num_images = static_cast<int>(features.size());

#if 0
    // Robustly estimate focal length from rotating cameras
    vector<Mat> Hs;
    for (int iter = 0; iter < 100; ++iter)
    {
        int len = 2 + rand()%(pairwise_matches.size() - 1);
        vector<int> subset;
        selectRandomSubset(len, pairwise_matches.size(), subset);
        Hs.clear();
        for (size_t i = 0; i < subset.size(); ++i)
            if (!pairwise_matches[subset[i]].H.empty())
                Hs.push_back(pairwise_matches[subset[i]].H);
        Mat_<double> K;
        if (Hs.size() >= 2)
        {
            if (calibrateRotatingCamera(Hs, K))
                cin.get();
        }
    }
#endif

    // Estimate focal length and set it for all cameras
    vector<double> focals;
    estimateFocal(features, pairwise_matches, focals);
    cameras.resize(num_images);
    for (int i = 0; i < num_images; ++i)
        cameras[i].focal = focals[i];

    // Restore global motion
    Graph span_tree;
    vector<int> span_tree_centers;
    findMaxSpanningTree(num_images, pairwise_matches, span_tree, span_tree_centers);
    span_tree.walkBreadthFirst(span_tree_centers[0], CalcRotation(num_images, pairwise_matches, cameras));

    LOGLN("Estimating rotations, time: " << ((getTickCount() - t) / getTickFrequency()) << " sec");
}


//////////////////////////////////////////////////////////////////////////////

void BundleAdjuster::estimate(const vector<ImageFeatures> &features, const vector<MatchesInfo> &pairwise_matches,
                              vector<CameraParams> &cameras)
{
    if (cost_space_ == NO)
        return;

    LOG("Bundle adjustment");
    int64 t = getTickCount();

    num_images_ = static_cast<int>(features.size());
    features_ = &features[0];
    pairwise_matches_ = &pairwise_matches[0];

    // Prepare focals and rotations
    cameras_.create(num_images_ * 4, 1, CV_64F);
    SVD svd;
    for (int i = 0; i < num_images_; ++i)
    {
        cameras_.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);
        cameras_.at<double>(i * 4 + 1, 0) = rvec.at<float>(0, 0);
        cameras_.at<double>(i * 4 + 2, 0) = rvec.at<float>(1, 0);
        cameras_.at<double>(i * 4 + 3, 0) = rvec.at<float>(2, 0);
    }

    // Select only consistent image pairs for futher adjustment
    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));
        }
    }

    // Compute number of correspondences
    total_num_matches_ = 0;
    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_ * 4, total_num_matches_ * 3,
                     cvTermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 1000, DBL_EPSILON));

    CvMat matParams = cameras_;
    cvCopy(&matParams, solver.param);

    int count = 0;
    for(;;)
    {
        const CvMat* _param = 0;
        CvMat* _J = 0;
        CvMat* _err = 0;

        bool proceed = solver.update(_param, _J, _err);

        cvCopy( _param, &matParams );

        if( !proceed || !_err )
            break;

        if( _J )
        {
            calcJacobian();
            CvMat matJ = J_;
            cvCopy( &matJ, _J );
        }

        if (_err)
        {
            calcError(err_);
            LOG(".");
            count++;
            CvMat matErr = err_;
            cvCopy( &matErr, _err );
        }
    }
    LOGLN("");
    LOGLN("Bundle adjustment, final error: " << sqrt(err_.dot(err_)));
    LOGLN("Bundle adjustment, iterations done: " << count);

    // Obtain global motion
    for (int i = 0; i < num_images_; ++i)
    {
        cameras[i].focal = cameras_.at<double>(i * 4, 0);
        Mat rvec(3, 1, CV_64F);
        rvec.at<double>(0, 0) = cameras_.at<double>(i * 4 + 1, 0);
        rvec.at<double>(1, 0) = cameras_.at<double>(i * 4 + 2, 0);
        rvec.at<double>(2, 0) = cameras_.at<double>(i * 4 + 3, 0);
        Rodrigues(rvec, cameras[i].R);
        Mat Mf;
        cameras[i].R.convertTo(Mf, CV_32F);
        cameras[i].R = Mf;
    }

    // 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;

    LOGLN("Bundle adjustment, time: " << ((getTickCount() - t) / getTickFrequency()) << " sec");
}


void BundleAdjuster::calcError(Mat &err)
{
    err.create(total_num_matches_ * 3, 1, CV_64F);

    int match_idx = 0;
    for (size_t edge_idx = 0; edge_idx < edges_.size(); ++edge_idx)
    {
        int i = edges_[edge_idx].first;
        int j = edges_[edge_idx].second;
        double f1 = cameras_.at<double>(i * 4, 0);
        double f2 = cameras_.at<double>(j * 4, 0);
        double R1[9], R2[9];
        Mat R1_(3, 3, CV_64F, R1), R2_(3, 3, CV_64F, R2);
        Mat rvec(3, 1, CV_64F);
        rvec.at<double>(0, 0) = cameras_.at<double>(i * 4 + 1, 0);
        rvec.at<double>(1, 0) = cameras_.at<double>(i * 4 + 2, 0);
        rvec.at<double>(2, 0) = cameras_.at<double>(i * 4 + 3, 0);
        Rodrigues(rvec, R1_); CV_Assert(R1_.type() == CV_64F);
        rvec.at<double>(0, 0) = cameras_.at<double>(j * 4 + 1, 0);
        rvec.at<double>(1, 0) = cameras_.at<double>(j * 4 + 2, 0);
        rvec.at<double>(2, 0) = cameras_.at<double>(j * 4 + 3, 0);
        Rodrigues(rvec, R2_); CV_Assert(R2_.type() == CV_64F);

        const ImageFeatures& features1 = features_[i];
        const ImageFeatures& features2 = features_[j];
        const MatchesInfo& matches_info = pairwise_matches_[i * num_images_ + j];

        for (size_t k = 0; k < matches_info.matches.size(); ++k)
        {
            if (!matches_info.inliers_mask[k])
                continue;

            const DMatch& m = matches_info.matches[k];

            Point2d kp1 = features1.keypoints[m.queryIdx].pt;
            kp1.x -= 0.5 * features1.img_size.width;
            kp1.y -= 0.5 * features1.img_size.height;
            Point2d kp2 = features2.keypoints[m.trainIdx].pt;
            kp2.x -= 0.5 * features2.img_size.width;
            kp2.y -= 0.5 * features2.img_size.height;
            double len1 = sqrt(kp1.x * kp1.x + kp1.y * kp1.y + f1 * f1);
            double len2 = sqrt(kp2.x * kp2.x + kp2.y * kp2.y + f2 * f2);
            Point3d p1(kp1.x / len1, kp1.y / len1, f1 / len1);
            Point3d p2(kp2.x / len2, kp2.y / len2, f2 / len2);

            Point3d d1(p1.x * R1[0] + p1.y * R1[1] + p1.z * R1[2],
                       p1.x * R1[3] + p1.y * R1[4] + p1.z * R1[5],
                       p1.x * R1[6] + p1.y * R1[7] + p1.z * R1[8]);
            Point3d d2(p2.x * R2[0] + p2.y * R2[1] + p2.z * R2[2],
                       p2.x * R2[3] + p2.y * R2[4] + p2.z * R2[5],
                       p2.x * R2[6] + p2.y * R2[7] + p2.z * R2[8]);

            double mult = 1; // For cost_space_ == RAY_SPACE
            if (cost_space_ == FOCAL_RAY_SPACE)
                mult = sqrt(f1 * f2);
            err.at<double>(3 * match_idx, 0) = mult * (d1.x - d2.x);
            err.at<double>(3 * match_idx + 1, 0) = mult * (d1.y - d2.y);
            err.at<double>(3 * match_idx + 2, 0) = mult * (d1.z - d2.z);
            match_idx++;
        }
    }
}


void BundleAdjuster::calcJacobian()
{
    J_.create(total_num_matches_ * 3, num_images_ * 4, CV_64F);

    double f, r;
    const double df = 0.001; // Focal length step
    const double dr = 0.001; // Angle step

    for (int i = 0; i < num_images_; ++i)
    {
        f = cameras_.at<double>(i * 4, 0);
        cameras_.at<double>(i * 4, 0) = f - df;
        calcError(err1_);
        cameras_.at<double>(i * 4, 0) = f + df;
        calcError(err2_);
        calcDeriv(err1_, err2_, 2 * df, J_.col(i * 4));
        cameras_.at<double>(i * 4, 0) = f;

        r = cameras_.at<double>(i * 4 + 1, 0);
        cameras_.at<double>(i * 4 + 1, 0) = r - dr;
        calcError(err1_);
        cameras_.at<double>(i * 4 + 1, 0) = r + dr;
        calcError(err2_);
        calcDeriv(err1_, err2_, 2 * dr, J_.col(i * 4 + 1));
        cameras_.at<double>(i * 4 + 1, 0) = r;

        r = cameras_.at<double>(i * 4 + 2, 0);
        cameras_.at<double>(i * 4 + 2, 0) = r - dr;
        calcError(err1_);
        cameras_.at<double>(i * 4 + 2, 0) = r + dr;
        calcError(err2_);
        calcDeriv(err1_, err2_, 2 * dr, J_.col(i * 4 + 2));
        cameras_.at<double>(i * 4 + 2, 0) = r;

        r = cameras_.at<double>(i * 4 + 3, 0);
        cameras_.at<double>(i * 4 + 3, 0) = r - dr;
        calcError(err1_);
        cameras_.at<double>(i * 4 + 3, 0) = r + dr;
        calcError(err2_);
        calcDeriv(err1_, err2_, 2 * dr, J_.col(i * 4 + 3));
        cameras_.at<double>(i * 4 + 3, 0) = r;
    }
}


//////////////////////////////////////////////////////////////////////////////

// TODO replace SVD with eigen
void waveCorrect(vector<Mat> &rmats)
{
    LOGLN("Wave correcting...");
    int64 t = getTickCount();

    float data[9];
    Mat r0(1, 3, CV_32F, data);
    Mat r1(1, 3, CV_32F, data + 3);
    Mat r2(1, 3, CV_32F, data + 6);
    Mat R(3, 3, CV_32F, data);

    Mat cov = Mat::zeros(3, 3, CV_32F);
    for (size_t i = 0; i < rmats.size(); ++i)
    {   
        Mat r0 = rmats[i].col(0);
        cov += r0 * r0.t();
    }

    SVD svd;
    svd(cov, SVD::FULL_UV);
    svd.vt.row(2).copyTo(r1);
    if (determinant(svd.vt) < 0) r1 *= -1;

    Mat avgz = Mat::zeros(3, 1, CV_32F);
    for (size_t i = 0; i < rmats.size(); ++i)
        avgz += rmats[i].col(2);
    r1.cross(avgz.t()).copyTo(r0);
    normalize(r0, r0);

    r1.cross(r0).copyTo(r2);
    if (determinant(R) < 0) R *= -1;

    for (size_t i = 0; i < rmats.size(); ++i)
        rmats[i] = R * rmats[i];

    LOGLN("Wave correcting, time: " << ((getTickCount() - t) / getTickFrequency()) << " sec");
}


//////////////////////////////////////////////////////////////////////////////

string matchesGraphAsString(vector<string> &pathes, vector<MatchesInfo> &pairwise_matches,
                                float conf_threshold)
{
    stringstream str;
    str << "graph matches_graph{\n";

    const int num_images = static_cast<int>(pathes.size());
    set<pair<int,int> > span_tree_edges;
    DisjointSets comps(num_images);

    for (int i = 0; i < num_images; ++i)
    {
        for (int j = 0; j < num_images; ++j)
        {
            if (pairwise_matches[i*num_images + j].confidence < conf_threshold)
                continue;
            int comp1 = comps.findSetByElem(i);
            int comp2 = comps.findSetByElem(j);
            if (comp1 != comp2)
            {
                comps.mergeSets(comp1, comp2);
                span_tree_edges.insert(make_pair(i, j));
            }
        }
    }

    for (set<pair<int,int> >::const_iterator itr = span_tree_edges.begin();
         itr != span_tree_edges.end(); ++itr)
    {
        pair<int,int> edge = *itr;
        if (span_tree_edges.find(edge) != span_tree_edges.end())
        {
            string name_src = pathes[edge.first];
            size_t prefix_len = name_src.find_last_of("/\\");
            if (prefix_len != string::npos) prefix_len++; else prefix_len = 0;
            name_src = name_src.substr(prefix_len, name_src.size() - prefix_len);

            string name_dst = pathes[edge.second];
            prefix_len = name_dst.find_last_of("/\\");
            if (prefix_len != string::npos) prefix_len++; else prefix_len = 0;
            name_dst = name_dst.substr(prefix_len, name_dst.size() - prefix_len);

            int pos = edge.first*num_images + edge.second;
            str << "\"" << name_src << "\" -- \"" << name_dst << "\""
                << "[label=\"Nm=" << pairwise_matches[pos].matches.size()
                << ", Ni=" << pairwise_matches[pos].num_inliers
                << ", C=" << pairwise_matches[pos].confidence << "\"];\n";
        }
    }

    for (size_t i = 0; i < comps.size.size(); ++i)
    {
        if (comps.size[comps.findSetByElem(i)] == 1)
        {
            string name = pathes[i];
            size_t prefix_len = name.find_last_of("/\\");
            if (prefix_len != string::npos) prefix_len++; else prefix_len = 0;
            name = name.substr(prefix_len, name.size() - prefix_len);
            str << "\"" << name << "\";\n";
        }
    }

    str << "}";
    return str.str();
}

vector<int> leaveBiggestComponent(vector<ImageFeatures> &features,  vector<MatchesInfo> &pairwise_matches,
                                      float conf_threshold)
{
    const int num_images = static_cast<int>(features.size());

    DisjointSets comps(num_images);
    for (int i = 0; i < num_images; ++i)
    {
        for (int j = 0; j < num_images; ++j)
        {
            if (pairwise_matches[i*num_images + j].confidence < conf_threshold)
                continue;
            int comp1 = comps.findSetByElem(i);
            int comp2 = comps.findSetByElem(j);
            if (comp1 != comp2) 
                comps.mergeSets(comp1, comp2);
        }
    }

    int max_comp = static_cast<int>(max_element(comps.size.begin(), comps.size.end()) - comps.size.begin());

    vector<int> indices;
    vector<int> indices_removed;
    for (int i = 0; i < num_images; ++i)
        if (comps.findSetByElem(i) == max_comp)
            indices.push_back(i);    
        else
            indices_removed.push_back(i);

    vector<ImageFeatures> features_subset;
    vector<MatchesInfo> pairwise_matches_subset;
    for (size_t i = 0; i < indices.size(); ++i)
    {
        features_subset.push_back(features[indices[i]]);
        for (size_t j = 0; j < indices.size(); ++j)
        {
            pairwise_matches_subset.push_back(pairwise_matches[indices[i]*num_images + indices[j]]);
            pairwise_matches_subset.back().src_img_idx = static_cast<int>(i);
            pairwise_matches_subset.back().dst_img_idx = static_cast<int>(j);
        }
    }

    if (static_cast<int>(features_subset.size()) == num_images)
        return indices;

    LOG("Removed some images, because can't match them: (");
    LOG(indices_removed[0]+1);
    for (size_t i = 1; i < indices_removed.size(); ++i) 
        LOG(", " << indices_removed[i]+1);
    LOGLN("). Try to decrease --match_conf value.");

    features = features_subset;
    pairwise_matches = pairwise_matches_subset;

    return indices;
}


void findMaxSpanningTree(int num_images, const vector<MatchesInfo> &pairwise_matches,
                             Graph &span_tree, vector<int> &centers)
{
    Graph graph(num_images);
    vector<GraphEdge> edges;

    // Construct images graph and remember its edges
    for (int i = 0; i < num_images; ++i)
    {
        for (int j = 0; j < num_images; ++j)
        {
            if (pairwise_matches[i * num_images + j].H.empty())
                continue;
            float conf = static_cast<float>(pairwise_matches[i * num_images + j].num_inliers);
            graph.addEdge(i, j, conf);
            edges.push_back(GraphEdge(i, j, conf));
        }
    }

    DisjointSets comps(num_images);
    span_tree.create(num_images);
    vector<int> span_tree_powers(num_images, 0);

    // Find maximum spanning tree
    sort(edges.begin(), edges.end(), greater<GraphEdge>());
    for (size_t i = 0; i < edges.size(); ++i)
    {
        int comp1 = comps.findSetByElem(edges[i].from);
        int comp2 = comps.findSetByElem(edges[i].to);
        if (comp1 != comp2)
        {
            comps.mergeSets(comp1, comp2);
            span_tree.addEdge(edges[i].from, edges[i].to, edges[i].weight);
            span_tree.addEdge(edges[i].to, edges[i].from, edges[i].weight);
            span_tree_powers[edges[i].from]++;
            span_tree_powers[edges[i].to]++;
        }
    }

    // Find spanning tree leafs
    vector<int> span_tree_leafs;
    for (int i = 0; i < num_images; ++i)
        if (span_tree_powers[i] == 1)
            span_tree_leafs.push_back(i);

    // Find maximum distance from each spanning tree vertex
    vector<int> max_dists(num_images, 0);
    vector<int> cur_dists;
    for (size_t i = 0; i < span_tree_leafs.size(); ++i)
    {
        cur_dists.assign(num_images, 0);
        span_tree.walkBreadthFirst(span_tree_leafs[i], IncDistance(cur_dists));
        for (int j = 0; j < num_images; ++j)
            max_dists[j] = max(max_dists[j], cur_dists[j]);
    }

    // Find min-max distance
    int min_max_dist = max_dists[0];
    for (int i = 1; i < num_images; ++i)
        if (min_max_dist > max_dists[i])
            min_max_dist = max_dists[i];

    // Find spanning tree centers
    centers.clear();
    for (int i = 0; i < num_images; ++i)
        if (max_dists[i] == min_max_dist)
            centers.push_back(i);
    CV_Assert(centers.size() > 0 && centers.size() <= 2);
}

} // namespace detail
} // namespace cv