aruco.cpp

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#include "precomp.hpp"
#include "opencv2/aruco.hpp"
#include <opencv2/core.hpp>
#include <opencv2/imgproc.hpp>

#include "apriltag_quad_thresh.hpp"
#include "zarray.hpp"

//#define APRIL_DEBUG
#ifdef APRIL_DEBUG
#include "opencv2/imgcodecs.hpp"
#endif

namespace cv {
namespace aruco {

using namespace std;


DetectorParameters::DetectorParameters()
    : adaptiveThreshWinSizeMin(3),
      adaptiveThreshWinSizeMax(23),
      adaptiveThreshWinSizeStep(10),
      adaptiveThreshConstant(7),
      minMarkerPerimeterRate(0.03),
      maxMarkerPerimeterRate(4.),
      polygonalApproxAccuracyRate(0.03),
      minCornerDistanceRate(0.05),
      minDistanceToBorder(3),
      minMarkerDistanceRate(0.05),
      cornerRefinementMethod(CORNER_REFINE_NONE),
      cornerRefinementWinSize(5),
      cornerRefinementMaxIterations(30),
      cornerRefinementMinAccuracy(0.1),
      markerBorderBits(1),
      perspectiveRemovePixelPerCell(4),
      perspectiveRemoveIgnoredMarginPerCell(0.13),
      maxErroneousBitsInBorderRate(0.35),
      minOtsuStdDev(5.0),
      errorCorrectionRate(0.6),
      aprilTagQuadDecimate(0.0),
      aprilTagQuadSigma(0.0),
      aprilTagMinClusterPixels(5),
      aprilTagMaxNmaxima(10),
      aprilTagCriticalRad( (float)(10* CV_PI /180) ),
      aprilTagMaxLineFitMse(10.0),
      aprilTagMinWhiteBlackDiff(5),
      aprilTagDeglitch(0),
      detectInvertedMarker(false){}


Ptr<DetectorParameters> DetectorParameters::create() {
    Ptr<DetectorParameters> params = makePtr<DetectorParameters>();
    return params;
}


static void _convertToGrey(InputArray _in, OutputArray _out) {

    CV_Assert(_in.type() == CV_8UC1 || _in.type() == CV_8UC3);

    if(_in.type() == CV_8UC3)
        cvtColor(_in, _out, COLOR_BGR2GRAY);
    else
        _in.copyTo(_out);
}


static void _threshold(InputArray _in, OutputArray _out, int winSize, double constant) {

    CV_Assert(winSize >= 3);
    if(winSize % 2 == 0) winSize++; // win size must be odd
    adaptiveThreshold(_in, _out, 255, ADAPTIVE_THRESH_MEAN_C, THRESH_BINARY_INV, winSize, constant);
}


static void _findMarkerContours(InputArray _in, vector< vector< Point2f > > &candidates,
                                vector< vector< Point > > &contoursOut, double minPerimeterRate,
                                double maxPerimeterRate, double accuracyRate,
                                double minCornerDistanceRate, int minDistanceToBorder) {

    CV_Assert(minPerimeterRate > 0 && maxPerimeterRate > 0 && accuracyRate > 0 &&
              minCornerDistanceRate >= 0 && minDistanceToBorder >= 0);

    // calculate maximum and minimum sizes in pixels
    unsigned int minPerimeterPixels =
        (unsigned int)(minPerimeterRate * max(_in.getMat().cols, _in.getMat().rows));
    unsigned int maxPerimeterPixels =
        (unsigned int)(maxPerimeterRate * max(_in.getMat().cols, _in.getMat().rows));

    Mat contoursImg;
    _in.getMat().copyTo(contoursImg);
    vector< vector< Point > > contours;
    findContours(contoursImg, contours, RETR_LIST, CHAIN_APPROX_NONE);
    // now filter list of contours
    for(unsigned int i = 0; i < contours.size(); i++) {
        // check perimeter
        if(contours[i].size() < minPerimeterPixels || contours[i].size() > maxPerimeterPixels)
            continue;

        // check is square and is convex
        vector< Point > approxCurve;
        approxPolyDP(contours[i], approxCurve, double(contours[i].size()) * accuracyRate, true);
        if(approxCurve.size() != 4 || !isContourConvex(approxCurve)) continue;

        // check min distance between corners
        double minDistSq =
            max(contoursImg.cols, contoursImg.rows) * max(contoursImg.cols, contoursImg.rows);
        for(int j = 0; j < 4; j++) {
            double d = (double)(approxCurve[j].x - approxCurve[(j + 1) % 4].x) *
                           (double)(approxCurve[j].x - approxCurve[(j + 1) % 4].x) +
                       (double)(approxCurve[j].y - approxCurve[(j + 1) % 4].y) *
                           (double)(approxCurve[j].y - approxCurve[(j + 1) % 4].y);
            minDistSq = min(minDistSq, d);
        }
        double minCornerDistancePixels = double(contours[i].size()) * minCornerDistanceRate;
        if(minDistSq < minCornerDistancePixels * minCornerDistancePixels) continue;

        // check if it is too near to the image border
        bool tooNearBorder = false;
        for(int j = 0; j < 4; j++) {
            if(approxCurve[j].x < minDistanceToBorder || approxCurve[j].y < minDistanceToBorder ||
               approxCurve[j].x > contoursImg.cols - 1 - minDistanceToBorder ||
               approxCurve[j].y > contoursImg.rows - 1 - minDistanceToBorder)
                tooNearBorder = true;
        }
        if(tooNearBorder) continue;

        // if it passes all the test, add to candidates vector
        vector< Point2f > currentCandidate;
        currentCandidate.resize(4);
        for(int j = 0; j < 4; j++) {
            currentCandidate[j] = Point2f((float)approxCurve[j].x, (float)approxCurve[j].y);
        }
        candidates.push_back(currentCandidate);
        contoursOut.push_back(contours[i]);
    }
}


static void _reorderCandidatesCorners(vector< vector< Point2f > > &candidates) {

    for(unsigned int i = 0; i < candidates.size(); i++) {
        double dx1 = candidates[i][1].x - candidates[i][0].x;
        double dy1 = candidates[i][1].y - candidates[i][0].y;
        double dx2 = candidates[i][2].x - candidates[i][0].x;
        double dy2 = candidates[i][2].y - candidates[i][0].y;
        double crossProduct = (dx1 * dy2) - (dy1 * dx2);

        if(crossProduct < 0.0) { // not clockwise direction
            swap(candidates[i][1], candidates[i][3]);
        }
    }
}


static void _filterTooCloseCandidates(const vector< vector< Point2f > > &candidatesIn,
                                      vector< vector< Point2f > > &candidatesOut,
                                      const vector< vector< Point > > &contoursIn,
                                      vector< vector< Point > > &contoursOut,
                                      double minMarkerDistanceRate) {

    CV_Assert(minMarkerDistanceRate >= 0);

    vector< pair< int, int > > nearCandidates;
    for(unsigned int i = 0; i < candidatesIn.size(); i++) {
        for(unsigned int j = i + 1; j < candidatesIn.size(); j++) {

            int minimumPerimeter = min((int)contoursIn[i].size(), (int)contoursIn[j].size() );

            // fc is the first corner considered on one of the markers, 4 combinations are possible
            for(int fc = 0; fc < 4; fc++) {
                double distSq = 0;
                for(int c = 0; c < 4; c++) {
                    // modC is the corner considering first corner is fc
                    int modC = (c + fc) % 4;
                    distSq += (candidatesIn[i][modC].x - candidatesIn[j][c].x) *
                                  (candidatesIn[i][modC].x - candidatesIn[j][c].x) +
                              (candidatesIn[i][modC].y - candidatesIn[j][c].y) *
                                  (candidatesIn[i][modC].y - candidatesIn[j][c].y);
                }
                distSq /= 4.;

                // if mean square distance is too low, remove the smaller one of the two markers
                double minMarkerDistancePixels = double(minimumPerimeter) * minMarkerDistanceRate;
                if(distSq < minMarkerDistancePixels * minMarkerDistancePixels) {
                    nearCandidates.push_back(pair< int, int >(i, j));
                    break;
                }
            }
        }
    }

    // mark smaller one in pairs to remove
    vector< bool > toRemove(candidatesIn.size(), false);
    for(unsigned int i = 0; i < nearCandidates.size(); i++) {
        // if one of the marker has been already markerd to removed, dont need to do anything
        if(toRemove[nearCandidates[i].first] || toRemove[nearCandidates[i].second]) continue;
        size_t perimeter1 = contoursIn[nearCandidates[i].first].size();
        size_t perimeter2 = contoursIn[nearCandidates[i].second].size();
        if(perimeter1 > perimeter2)
            toRemove[nearCandidates[i].second] = true;
        else
            toRemove[nearCandidates[i].first] = true;
    }

    // remove extra candidates
    candidatesOut.clear();
    unsigned long totalRemaining = 0;
    for(unsigned int i = 0; i < toRemove.size(); i++)
        if(!toRemove[i]) totalRemaining++;
    candidatesOut.resize(totalRemaining);
    contoursOut.resize(totalRemaining);
    for(unsigned int i = 0, currIdx = 0; i < candidatesIn.size(); i++) {
        if(toRemove[i]) continue;
        candidatesOut[currIdx] = candidatesIn[i];
        contoursOut[currIdx] = contoursIn[i];
        currIdx++;
    }
}


class DetectInitialCandidatesParallel : public ParallelLoopBody {
    public:
    DetectInitialCandidatesParallel(const Mat *_grey,
                                    vector< vector< vector< Point2f > > > *_candidatesArrays,
                                    vector< vector< vector< Point > > > *_contoursArrays,
                                    const Ptr<DetectorParameters> &_params)
        : grey(_grey), candidatesArrays(_candidatesArrays), contoursArrays(_contoursArrays),
          params(_params) {}

    void operator()(const Range &range) const CV_OVERRIDE {
        const int begin = range.start;
        const int end = range.end;

        for(int i = begin; i < end; i++) {
            int currScale =
                params->adaptiveThreshWinSizeMin + i * params->adaptiveThreshWinSizeStep;
            // threshold
            Mat thresh;
            _threshold(*grey, thresh, currScale, params->adaptiveThreshConstant);

            // detect rectangles
            _findMarkerContours(thresh, (*candidatesArrays)[i], (*contoursArrays)[i],
                                params->minMarkerPerimeterRate, params->maxMarkerPerimeterRate,
                                params->polygonalApproxAccuracyRate, params->minCornerDistanceRate,
                                params->minDistanceToBorder);
        }
    }

    private:
    DetectInitialCandidatesParallel &operator=(const DetectInitialCandidatesParallel &);

    const Mat *grey;
    vector< vector< vector< Point2f > > > *candidatesArrays;
    vector< vector< vector< Point > > > *contoursArrays;
    const Ptr<DetectorParameters> &params;
};


static void _detectInitialCandidates(const Mat &grey, vector< vector< Point2f > > &candidates,
                                     vector< vector< Point > > &contours,
                                     const Ptr<DetectorParameters> &params) {

    CV_Assert(params->adaptiveThreshWinSizeMin >= 3 && params->adaptiveThreshWinSizeMax >= 3);
    CV_Assert(params->adaptiveThreshWinSizeMax >= params->adaptiveThreshWinSizeMin);
    CV_Assert(params->adaptiveThreshWinSizeStep > 0);

    // number of window sizes (scales) to apply adaptive thresholding
    int nScales =  (params->adaptiveThreshWinSizeMax - params->adaptiveThreshWinSizeMin) /
                      params->adaptiveThreshWinSizeStep + 1;

    vector< vector< vector< Point2f > > > candidatesArrays((size_t) nScales);
    vector< vector< vector< Point > > > contoursArrays((size_t) nScales);

    // for(int i = 0; i < nScales; i++) {
    //    int currScale = params.adaptiveThreshWinSizeMin + i*params.adaptiveThreshWinSizeStep;
    //    // treshold
    //    Mat thresh;
    //    _threshold(grey, thresh, currScale, params.adaptiveThreshConstant);
    //    // detect rectangles
    //    _findMarkerContours(thresh, candidatesArrays[i], contoursArrays[i],
    // params.minMarkerPerimeterRate,
    //                        params.maxMarkerPerimeterRate, params.polygonalApproxAccuracyRate,
    //                        params.minCornerDistance, params.minDistanceToBorder);
    //}

    // this is the parallel call for the previous commented loop (result is equivalent)
    parallel_for_(Range(0, nScales), DetectInitialCandidatesParallel(&grey, &candidatesArrays,
                                                                     &contoursArrays, params));

    // join candidates
    for(int i = 0; i < nScales; i++) {
        for(unsigned int j = 0; j < candidatesArrays[i].size(); j++) {
            candidates.push_back(candidatesArrays[i][j]);
            contours.push_back(contoursArrays[i][j]);
        }
    }
}


static void _detectCandidates(InputArray _image, vector< vector< Point2f > >& candidatesOut,
                              vector< vector< Point > >& contoursOut, const Ptr<DetectorParameters> &_params) {

    Mat image = _image.getMat();
    CV_Assert(image.total() != 0);

    Mat grey;
    _convertToGrey(image, grey);

    vector< vector< Point2f > > candidates;
    vector< vector< Point > > contours;
    _detectInitialCandidates(grey, candidates, contours, _params);

    _reorderCandidatesCorners(candidates);

    _filterTooCloseCandidates(candidates, candidatesOut, contours, contoursOut,
                              _params->minMarkerDistanceRate);
}


static Mat _extractBits(InputArray _image, InputArray _corners, int markerSize,
                        int markerBorderBits, int cellSize, double cellMarginRate,
                        double minStdDevOtsu) {

    CV_Assert(_image.getMat().channels() == 1);
    CV_Assert(_corners.total() == 4);
    CV_Assert(markerBorderBits > 0 && cellSize > 0 && cellMarginRate >= 0 && cellMarginRate <= 1);
    CV_Assert(minStdDevOtsu >= 0);

    // number of bits in the marker
    int markerSizeWithBorders = markerSize + 2 * markerBorderBits;
    int cellMarginPixels = int(cellMarginRate * cellSize);

    Mat resultImg; // marker image after removing perspective
    int resultImgSize = markerSizeWithBorders * cellSize;
    Mat resultImgCorners(4, 1, CV_32FC2);
    resultImgCorners.ptr< Point2f >(0)[0] = Point2f(0, 0);
    resultImgCorners.ptr< Point2f >(0)[1] = Point2f((float)resultImgSize - 1, 0);
    resultImgCorners.ptr< Point2f >(0)[2] =
        Point2f((float)resultImgSize - 1, (float)resultImgSize - 1);
    resultImgCorners.ptr< Point2f >(0)[3] = Point2f(0, (float)resultImgSize - 1);

    // remove perspective
    Mat transformation = getPerspectiveTransform(_corners, resultImgCorners);
    warpPerspective(_image, resultImg, transformation, Size(resultImgSize, resultImgSize),
                    INTER_NEAREST);

    // output image containing the bits
    Mat bits(markerSizeWithBorders, markerSizeWithBorders, CV_8UC1, Scalar::all(0));

    // check if standard deviation is enough to apply Otsu
    // if not enough, it probably means all bits are the same color (black or white)
    Mat mean, stddev;
    // Remove some border just to avoid border noise from perspective transformation
    Mat innerRegion = resultImg.colRange(cellSize / 2, resultImg.cols - cellSize / 2)
                          .rowRange(cellSize / 2, resultImg.rows - cellSize / 2);
    meanStdDev(innerRegion, mean, stddev);
    if(stddev.ptr< double >(0)[0] < minStdDevOtsu) {
        // all black or all white, depending on mean value
        if(mean.ptr< double >(0)[0] > 127)
            bits.setTo(1);
        else
            bits.setTo(0);
        return bits;
    }

    // now extract code, first threshold using Otsu
    threshold(resultImg, resultImg, 125, 255, THRESH_BINARY | THRESH_OTSU);

    // for each cell
    for(int y = 0; y < markerSizeWithBorders; y++) {
        for(int x = 0; x < markerSizeWithBorders; x++) {
            int Xstart = x * (cellSize) + cellMarginPixels;
            int Ystart = y * (cellSize) + cellMarginPixels;
            Mat square = resultImg(Rect(Xstart, Ystart, cellSize - 2 * cellMarginPixels,
                                        cellSize - 2 * cellMarginPixels));
            // count white pixels on each cell to assign its value
            size_t nZ = (size_t) countNonZero(square);
            if(nZ > square.total() / 2) bits.at< unsigned char >(y, x) = 1;
        }
    }

    return bits;
}



static int _getBorderErrors(const Mat &bits, int markerSize, int borderSize) {

    int sizeWithBorders = markerSize + 2 * borderSize;

    CV_Assert(markerSize > 0 && bits.cols == sizeWithBorders && bits.rows == sizeWithBorders);

    int totalErrors = 0;
    for(int y = 0; y < sizeWithBorders; y++) {
        for(int k = 0; k < borderSize; k++) {
            if(bits.ptr< unsigned char >(y)[k] != 0) totalErrors++;
            if(bits.ptr< unsigned char >(y)[sizeWithBorders - 1 - k] != 0) totalErrors++;
        }
    }
    for(int x = borderSize; x < sizeWithBorders - borderSize; x++) {
        for(int k = 0; k < borderSize; k++) {
            if(bits.ptr< unsigned char >(k)[x] != 0) totalErrors++;
            if(bits.ptr< unsigned char >(sizeWithBorders - 1 - k)[x] != 0) totalErrors++;
        }
    }
    return totalErrors;
}


static bool _identifyOneCandidate(const Ptr<Dictionary>& dictionary, InputArray _image,
                                  vector<Point2f>& _corners, int& idx,
                                  const Ptr<DetectorParameters>& params)
{
    CV_Assert(_corners.size() == 4);
    CV_Assert(_image.getMat().total() != 0);
    CV_Assert(params->markerBorderBits > 0);

    // get bits
    Mat candidateBits =
        _extractBits(_image, _corners, dictionary->markerSize, params->markerBorderBits,
                     params->perspectiveRemovePixelPerCell,
                     params->perspectiveRemoveIgnoredMarginPerCell, params->minOtsuStdDev);

    // analyze border bits
    int maximumErrorsInBorder =
        int(dictionary->markerSize * dictionary->markerSize * params->maxErroneousBitsInBorderRate);
    int borderErrors =
        _getBorderErrors(candidateBits, dictionary->markerSize, params->markerBorderBits);

    // check if it is a white marker
    if(params->detectInvertedMarker){
        // to get from 255 to 1
        Mat invertedImg = ~candidateBits-254;
        int invBError = _getBorderErrors(invertedImg, dictionary->markerSize, params->markerBorderBits);
        // white marker
        if(invBError<borderErrors){
            borderErrors = invBError;
            invertedImg.copyTo(candidateBits);
        }
    }
    if(borderErrors > maximumErrorsInBorder) return false;

    // take only inner bits
    Mat onlyBits =
        candidateBits.rowRange(params->markerBorderBits,
                               candidateBits.rows - params->markerBorderBits)
            .colRange(params->markerBorderBits, candidateBits.rows - params->markerBorderBits);

    // try to indentify the marker
    int rotation;
    if(!dictionary->identify(onlyBits, idx, rotation, params->errorCorrectionRate))
        return false;

    // shift corner positions to the correct rotation
    if(rotation != 0) {
        std::rotate(_corners.begin(), _corners.begin() + 4 - rotation, _corners.end());
    }
    return true;
}


class IdentifyCandidatesParallel : public ParallelLoopBody {
    public:
    IdentifyCandidatesParallel(const Mat& _grey, vector< vector< Point2f > >& _candidates,
                               const Ptr<Dictionary> &_dictionary,
                               vector< int >& _idsTmp, vector< char >& _validCandidates,
                               const Ptr<DetectorParameters> &_params)
        : grey(_grey), candidates(_candidates), dictionary(_dictionary),
          idsTmp(_idsTmp), validCandidates(_validCandidates), params(_params) {}

    void operator()(const Range &range) const CV_OVERRIDE {
        const int begin = range.start;
        const int end = range.end;

        for(int i = begin; i < end; i++) {
            int currId;
            if(_identifyOneCandidate(dictionary, grey, candidates[i], currId, params)) {
                validCandidates[i] = 1;
                idsTmp[i] = currId;
            }
        }
    }

    private:
    IdentifyCandidatesParallel &operator=(const IdentifyCandidatesParallel &); // to quiet MSVC

    const Mat &grey;
    vector< vector< Point2f > >& candidates;
    const Ptr<Dictionary> &dictionary;
    vector< int > &idsTmp;
    vector< char > &validCandidates;
    const Ptr<DetectorParameters> &params;
};



static void _copyVector2Output(vector< vector< Point2f > > &vec, OutputArrayOfArrays out) {
    out.create((int)vec.size(), 1, CV_32FC2);

    if(out.isMatVector()) {
        for (unsigned int i = 0; i < vec.size(); i++) {
            out.create(4, 1, CV_32FC2, i);
            Mat &m = out.getMatRef(i);
            Mat(Mat(vec[i]).t()).copyTo(m);
        }
    }
    else if(out.isUMatVector()) {
        for (unsigned int i = 0; i < vec.size(); i++) {
            out.create(4, 1, CV_32FC2, i);
            UMat &m = out.getUMatRef(i);
            Mat(Mat(vec[i]).t()).copyTo(m);
        }
    }
    else if(out.kind() == _OutputArray::STD_VECTOR_VECTOR){
        for (unsigned int i = 0; i < vec.size(); i++) {
            out.create(4, 1, CV_32FC2, i);
            Mat m = out.getMat(i);
            Mat(Mat(vec[i]).t()).copyTo(m);
        }
    }
    else {
        CV_Error(cv::Error::StsNotImplemented,
                 "Only Mat vector, UMat vector, and vector<vector> OutputArrays are currently supported.");
    }
}



static void _identifyCandidates(InputArray _image, vector< vector< Point2f > >& _candidates,
                                vector< vector<Point> >& _contours, const Ptr<Dictionary> &_dictionary,
                                vector< vector< Point2f > >& _accepted, vector< int >& ids,
                                const Ptr<DetectorParameters> &params,
                                OutputArrayOfArrays _rejected = noArray()) {

    int ncandidates = (int)_candidates.size();

    vector< vector< Point2f > > accepted;
    vector< vector< Point2f > > rejected;

    vector< vector< Point > > contours;

    CV_Assert(_image.getMat().total() != 0);

    Mat grey;
    _convertToGrey(_image.getMat(), grey);

    vector< int > idsTmp(ncandidates, -1);
    vector< char > validCandidates(ncandidates, 0);

    // for (int i = 0; i < ncandidates; i++) {
    //    int currId = i;
    //    Mat currentCandidate = _candidates.getMat(i);
    //    if (_identifyOneCandidate(dictionary, grey, currentCandidate, currId, params)) {
    //        validCandidates[i] = 1;
    //        idsTmp[i] = currId;
    //    }
    //}

    // this is the parallel call for the previous commented loop (result is equivalent)
    parallel_for_(Range(0, ncandidates),
                  IdentifyCandidatesParallel(grey, _candidates, _dictionary, idsTmp,
                                             validCandidates, params));

    for(int i = 0; i < ncandidates; i++) {
        if(validCandidates[i] == 1) {
            accepted.push_back(_candidates[i]);
            ids.push_back(idsTmp[i]);

            contours.push_back(_contours[i]);

        } else {
            rejected.push_back(_candidates[i]);
        }
    }

    // parse output
    _accepted = accepted;

    _contours= contours;

    if(_rejected.needed()) {
        _copyVector2Output(rejected, _rejected);
    }
}


static void _filterDetectedMarkers(vector< vector< Point2f > >& _corners, vector< int >& _ids, vector< vector< Point> >& _contours) {

    CV_Assert(_corners.size() == _ids.size());
    if(_corners.empty()) return;

    // mark markers that will be removed
    vector< bool > toRemove(_corners.size(), false);
    bool atLeastOneRemove = false;

    // remove repeated markers with same id, if one contains the other (doble border bug)
    for(unsigned int i = 0; i < _corners.size() - 1; i++) {
        for(unsigned int j = i + 1; j < _corners.size(); j++) {
            if(_ids[i] != _ids[j]) continue;

            // check if first marker is inside second
            bool inside = true;
            for(unsigned int p = 0; p < 4; p++) {
                Point2f point = _corners[j][p];
                if(pointPolygonTest(_corners[i], point, false) < 0) {
                    inside = false;
                    break;
                }
            }
            if(inside) {
                toRemove[j] = true;
                atLeastOneRemove = true;
                continue;
            }

            // check the second marker
            inside = true;
            for(unsigned int p = 0; p < 4; p++) {
                Point2f point = _corners[i][p];
                if(pointPolygonTest(_corners[j], point, false) < 0) {
                    inside = false;
                    break;
                }
            }
            if(inside) {
                toRemove[i] = true;
                atLeastOneRemove = true;
                continue;
            }
        }
    }

    // parse output
    if(atLeastOneRemove) {
        vector< vector< Point2f > >::iterator filteredCorners = _corners.begin();
        vector< int >::iterator filteredIds = _ids.begin();

        vector< vector< Point > >::iterator filteredContours = _contours.begin();

        for(unsigned int i = 0; i < toRemove.size(); i++) {
            if(!toRemove[i]) {
                *filteredCorners++ = _corners[i];
                *filteredIds++ = _ids[i];

                *filteredContours++ = _contours[i];
            }
        }

        _ids.erase(filteredIds, _ids.end());
        _corners.erase(filteredCorners, _corners.end());

        _contours.erase(filteredContours, _contours.end());
    }
}



static void _getSingleMarkerObjectPoints(float markerLength, OutputArray _objPoints) {

    CV_Assert(markerLength > 0);

    _objPoints.create(4, 1, CV_32FC3);
    Mat objPoints = _objPoints.getMat();
    // set coordinate system in the middle of the marker, with Z pointing out
    objPoints.ptr< Vec3f >(0)[0] = Vec3f(-markerLength / 2.f, markerLength / 2.f, 0);
    objPoints.ptr< Vec3f >(0)[1] = Vec3f(markerLength / 2.f, markerLength / 2.f, 0);
    objPoints.ptr< Vec3f >(0)[2] = Vec3f(markerLength / 2.f, -markerLength / 2.f, 0);
    objPoints.ptr< Vec3f >(0)[3] = Vec3f(-markerLength / 2.f, -markerLength / 2.f, 0);
}




class MarkerSubpixelParallel : public ParallelLoopBody {
    public:
    MarkerSubpixelParallel(const Mat *_grey, OutputArrayOfArrays _corners,
                           const Ptr<DetectorParameters> &_params)
        : grey(_grey), corners(_corners), params(_params) {}

    void operator()(const Range &range) const CV_OVERRIDE {
        const int begin = range.start;
        const int end = range.end;

        for(int i = begin; i < end; i++) {
            cornerSubPix(*grey, corners.getMat(i),
                         Size(params->cornerRefinementWinSize, params->cornerRefinementWinSize),
                         Size(-1, -1), TermCriteria(TermCriteria::MAX_ITER | TermCriteria::EPS,
                                                    params->cornerRefinementMaxIterations,
                                                    params->cornerRefinementMinAccuracy));
        }
    }

    private:
    MarkerSubpixelParallel &operator=(const MarkerSubpixelParallel &); // to quiet MSVC

    const Mat *grey;
    OutputArrayOfArrays corners;
    const Ptr<DetectorParameters> &params;
};

static Point3f _interpolate2Dline(const std::vector<cv::Point2f>& nContours){
        float minX, minY, maxX, maxY;
        minX = maxX = nContours[0].x;
        minY = maxY = nContours[0].y;

        for(unsigned int i = 0; i< nContours.size(); i++){
                minX = nContours[i].x < minX ? nContours[i].x : minX;
                minY = nContours[i].y < minY ? nContours[i].y : minY;
                maxX = nContours[i].x > maxX ? nContours[i].x : maxX;
                maxY = nContours[i].y > maxY ? nContours[i].y : maxY;
        }

        Mat A = Mat::ones((int)nContours.size(), 2, CV_32F); // Coefficient Matrix (N x 2)
        Mat B((int)nContours.size(), 1, CV_32F);                                // Variables   Matrix (N x 1)
        Mat C;                                                                                  // Constant

        if(maxX - minX > maxY - minY){
                for(unsigned int i =0; i < nContours.size(); i++){
            A.at<float>(i,0)= nContours[i].x;
            B.at<float>(i,0)= nContours[i].y;
                }

                solve(A, B, C, DECOMP_NORMAL);

                return Point3f(C.at<float>(0, 0), -1., C.at<float>(1, 0));
        }
        else{
                for(unsigned int i =0; i < nContours.size(); i++){
                        A.at<float>(i,0)= nContours[i].y;
                        B.at<float>(i,0)= nContours[i].x;
                }

                solve(A, B, C, DECOMP_NORMAL);

                return Point3f(-1., C.at<float>(0, 0), C.at<float>(1, 0));
        }

}

static Point2f _getCrossPoint(Point3f nLine1, Point3f nLine2){
        Matx22f A(nLine1.x, nLine1.y, nLine2.x, nLine2.y);
        Vec2f B(-nLine1.z, -nLine2.z);
        return Vec2f(A.solve(B).val);
}

static void _distortPoints(vector<cv::Point2f>& in, const Mat& camMatrix, const Mat& distCoeff) {
    // trivial extrinsics
    Matx31f Rvec(0,0,0);
    Matx31f Tvec(0,0,0);

    // calculate 3d points and then reproject, so opencv makes the distortion internally
    vector<cv::Point3f> cornersPoints3d;
    for (unsigned int i = 0; i < in.size(); i++){
        float x= (in[i].x - float(camMatrix.at<double>(0, 2))) / float(camMatrix.at<double>(0, 0));
        float y= (in[i].y - float(camMatrix.at<double>(1, 2))) / float(camMatrix.at<double>(1, 1));
        cornersPoints3d.push_back(Point3f(x,y,1));
    }
    cv::projectPoints(cornersPoints3d, Rvec, Tvec, camMatrix, distCoeff, in);
}

static void _refineCandidateLines(std::vector<Point>& nContours, std::vector<Point2f>& nCorners, const Mat& camMatrix, const Mat& distCoeff){
        vector<Point2f> contour2f(nContours.begin(), nContours.end());

        if(!camMatrix.empty() && !distCoeff.empty()){
                undistortPoints(contour2f, contour2f, camMatrix, distCoeff);
        }

        /* 5 groups :: to group the edges
         * 4 - classified by its corner
         * extra group - (temporary) if contours do not begin with a corner
         */
        vector<Point2f> cntPts[5];
        int cornerIndex[4]={-1};
        int group=4;

        for ( unsigned int i =0; i < nContours.size(); i++ ) {
                for(unsigned int j=0; j<4; j++){
                        if ( nCorners[j] == contour2f[i] ){
                                cornerIndex[j] = i;
                                group=j;
                        }
                }
                cntPts[group].push_back(contour2f[i]);
        }

        // saves extra group into corresponding
        if( !cntPts[4].empty() ){
                for( unsigned int i=0; i < cntPts[4].size() ; i++ )
                        cntPts[group].push_back(cntPts[4].at(i));
                cntPts[4].clear();
        }

        //Evaluate contour direction :: using the position of the detected corners
        int inc=1;

        inc = ( (cornerIndex[0] > cornerIndex[1]) &&  (cornerIndex[3] > cornerIndex[0]) ) ? -1:inc;
        inc = ( (cornerIndex[2] > cornerIndex[3]) &&  (cornerIndex[1] > cornerIndex[2]) ) ? -1:inc;

        // calculate the line :: who passes through the grouped points
        Point3f lines[4];
        for(int i=0; i<4; i++){
                // Don't try to "interpolate" single points
                if (cntPts[i].size() < 2) return;
                lines[i]=_interpolate2Dline(cntPts[i]);
        }

        /*
         * calculate the corner :: where the lines crosses to each other
         * clockwise direction          no clockwise direction
         *      0                           1
         *      .---. 1                     .---. 2
         *      |   |                       |   |
         *    3 .___.                     0 .___.
         *          2                           3
         */
        for(int i=0; i < 4; i++){
                if(inc<0)
                        nCorners[i] = _getCrossPoint(lines[ i ], lines[ (i+1)%4 ]);     // 01 12 23 30
                else
                        nCorners[i] = _getCrossPoint(lines[ i ], lines[ (i+3)%4 ]);     // 30 01 12 23
        }

        if(!camMatrix.empty() && !distCoeff.empty()){
                _distortPoints(nCorners, camMatrix, distCoeff);
        }
}


class MarkerContourParallel : public ParallelLoopBody {
    public:
    MarkerContourParallel( vector< vector< Point > >& _contours, vector< vector< Point2f > >& _candidates,  const Mat& _camMatrix, const Mat& _distCoeff)
        : contours(_contours), candidates(_candidates), camMatrix(_camMatrix), distCoeff(_distCoeff){}

    void operator()(const Range &range) const CV_OVERRIDE {

        for(int i = range.start; i < range.end; i++) {
            _refineCandidateLines(contours[i], candidates[i], camMatrix, distCoeff);
        }
    }

    private:
    MarkerContourParallel &operator=(const MarkerContourParallel &){
        return *this;
    }

    vector< vector< Point > >& contours;
    vector< vector< Point2f > >& candidates;
    const Mat& camMatrix;
    const Mat& distCoeff;
};

#ifdef APRIL_DEBUG
static void _darken(const Mat &im){
    for (int y = 0; y < im.rows; y++) {
        for (int x = 0; x < im.cols; x++) {
            im.data[im.cols*y+x] /= 2;
        }
    }
}
#endif

static void _apriltag(Mat im_orig, const Ptr<DetectorParameters> & _params, std::vector< std::vector< Point2f > > &candidates,
        std::vector< std::vector< Point > > &contours){

    Mat quad_im;
    im_orig.copyTo(quad_im);

    if (_params->aprilTagQuadDecimate > 1){
        resize(im_orig, quad_im, Size(), 1/_params->aprilTagQuadDecimate, 1/_params->aprilTagQuadDecimate, INTER_AREA );
    }

    // Apply a Blur
    if (_params->aprilTagQuadSigma != 0) {
        // compute a reasonable kernel width by figuring that the
        // kernel should go out 2 std devs.
        //
        // max sigma          ksz
        // 0.499              1  (disabled)
        // 0.999              3
        // 1.499              5
        // 1.999              7

        float sigma = fabsf((float) _params->aprilTagQuadSigma);

        int ksz = cvFloor(4 * sigma); // 2 std devs in each direction
        ksz |= 1; // make odd number

        if (ksz > 1) {
            if (_params->aprilTagQuadSigma > 0)
                GaussianBlur(quad_im, quad_im, Size(ksz, ksz), sigma, sigma, BORDER_REPLICATE);
            else {
                Mat orig;
                quad_im.copyTo(orig);
                GaussianBlur(quad_im, quad_im, Size(ksz, ksz), sigma, sigma, BORDER_REPLICATE);

                // SHARPEN the image by subtracting the low frequency components.
                for (int y = 0; y < orig.rows; y++) {
                    for (int x = 0; x < orig.cols; x++) {
                        int vorig = orig.data[y*orig.step + x];
                        int vblur = quad_im.data[y*quad_im.step + x];

                        int v = 2*vorig - vblur;
                        if (v < 0)
                            v = 0;
                        if (v > 255)
                            v = 255;

                        quad_im.data[y*quad_im.step + x] = (uint8_t) v;
                    }
                }
            }
        }
    }

#ifdef APRIL_DEBUG
    imwrite("1.1 debug_preprocess.pnm", quad_im);
#endif

    zarray_t *quads = apriltag_quad_thresh(_params, quad_im, contours);

    CV_Assert(quads != NULL);

    // adjust centers of pixels so that they correspond to the
    // original full-resolution image.
    if (_params->aprilTagQuadDecimate > 1) {
        for (int i = 0; i < _zarray_size(quads); i++) {
            struct sQuad *q;
            _zarray_get_volatile(quads, i, &q);
            for (int j = 0; j < 4; j++) {
                q->p[j][0] *= _params->aprilTagQuadDecimate;
                q->p[j][1] *= _params->aprilTagQuadDecimate;
            }
        }
    }

#ifdef APRIL_DEBUG
    Mat im_quads = im_orig.clone();
    im_quads = im_quads*0.5;
    srandom(0);

    for (int i = 0; i < _zarray_size(quads); i++) {
        struct sQuad *quad;
        _zarray_get_volatile(quads, i, &quad);

        const int bias = 100;
        int color = bias + (random() % (255-bias));

        line(im_quads, Point(quad->p[0][0], quad->p[0][1]), Point(quad->p[1][0], quad->p[1][1]), color, 1);
        line(im_quads, Point(quad->p[1][0], quad->p[1][1]), Point(quad->p[2][0], quad->p[2][1]), color, 1);
        line(im_quads, Point(quad->p[2][0], quad->p[2][1]), Point(quad->p[3][0], quad->p[3][1]), color, 1);
        line(im_quads, Point(quad->p[3][0], quad->p[3][1]), Point(quad->p[0][0], quad->p[0][1]), color, 1);
    }
    imwrite("1.2 debug_quads_raw.pnm", im_quads);
#endif

    for (int i = 0; i < _zarray_size(quads); i++) {
        struct sQuad *quad;
        _zarray_get_volatile(quads, i, &quad);

        std::vector< Point2f > corners;
        corners.push_back(Point2f(quad->p[3][0], quad->p[3][1]));   //pA
        corners.push_back(Point2f(quad->p[0][0], quad->p[0][1]));   //pB
        corners.push_back(Point2f(quad->p[1][0], quad->p[1][1]));   //pC
        corners.push_back(Point2f(quad->p[2][0], quad->p[2][1]));   //pD

        candidates.push_back(corners);
    }

    _zarray_destroy(quads);
}


void detectMarkers(InputArray _image, const Ptr<Dictionary> &_dictionary, OutputArrayOfArrays _corners,
                   OutputArray _ids, const Ptr<DetectorParameters> &_params,
                   OutputArrayOfArrays _rejectedImgPoints, InputArrayOfArrays camMatrix, InputArrayOfArrays distCoeff) {

    CV_Assert(!_image.empty());

    Mat grey;
    _convertToGrey(_image.getMat(), grey);

    vector< vector< Point2f > > candidates;
    vector< vector< Point > > contours;
    vector< int > ids;

    if(_params->cornerRefinementMethod == CORNER_REFINE_APRILTAG)
        _apriltag(grey, _params, candidates, contours);

    else
        _detectCandidates(grey, candidates, contours, _params);

    _identifyCandidates(grey, candidates, contours, _dictionary, candidates, ids, _params,
                        _rejectedImgPoints);

    _filterDetectedMarkers(candidates, ids, contours);

    // copy to output arrays
    _copyVector2Output(candidates, _corners);
    Mat(ids).copyTo(_ids);

    if( _params->cornerRefinementMethod == CORNER_REFINE_SUBPIX ) {
        CV_Assert(_params->cornerRefinementWinSize > 0 && _params->cornerRefinementMaxIterations > 0 &&
                  _params->cornerRefinementMinAccuracy > 0);

        // for (unsigned int i = 0; i < _corners.cols(); i++) {
        //    cornerSubPix(grey, _corners.getMat(i),
        //                 Size(params.cornerRefinementWinSize, params.cornerRefinementWinSize),
        //                 Size(-1, -1), TermCriteria(TermCriteria::MAX_ITER | TermCriteria::EPS,
        //                                            params.cornerRefinementMaxIterations,
        //                                            params.cornerRefinementMinAccuracy));
        //}

        // this is the parallel call for the previous commented loop (result is equivalent)
        parallel_for_(Range(0, _corners.cols()),
                      MarkerSubpixelParallel(&grey, _corners, _params));
    }

    if( _params->cornerRefinementMethod == CORNER_REFINE_CONTOUR){

        if(! _ids.empty()){

            // do corner refinement using the contours for each detected markers
            parallel_for_(Range(0, _corners.cols()), MarkerContourParallel(contours, candidates, camMatrix.getMat(), distCoeff.getMat()));

            // copy the corners to the output array
            _copyVector2Output(candidates, _corners);
        }
    }
}



class SinglePoseEstimationParallel : public ParallelLoopBody {
    public:
    SinglePoseEstimationParallel(Mat& _markerObjPoints, InputArrayOfArrays _corners,
                                 InputArray _cameraMatrix, InputArray _distCoeffs,
                                 Mat& _rvecs, Mat& _tvecs)
        : markerObjPoints(_markerObjPoints), corners(_corners), cameraMatrix(_cameraMatrix),
          distCoeffs(_distCoeffs), rvecs(_rvecs), tvecs(_tvecs) {}

    void operator()(const Range &range) const CV_OVERRIDE {
        const int begin = range.start;
        const int end = range.end;

        for(int i = begin; i < end; i++) {
            solvePnP(markerObjPoints, corners.getMat(i), cameraMatrix, distCoeffs,
                    rvecs.at<Vec3d>(i), tvecs.at<Vec3d>(i));
        }
    }

    private:
    SinglePoseEstimationParallel &operator=(const SinglePoseEstimationParallel &); // to quiet MSVC

    Mat& markerObjPoints;
    InputArrayOfArrays corners;
    InputArray cameraMatrix, distCoeffs;
    Mat& rvecs, tvecs;
};




void estimatePoseSingleMarkers(InputArrayOfArrays _corners, float markerLength,
                               InputArray _cameraMatrix, InputArray _distCoeffs,
                               OutputArray _rvecs, OutputArray _tvecs, OutputArray _objPoints) {

    CV_Assert(markerLength > 0);

    Mat markerObjPoints;
    _getSingleMarkerObjectPoints(markerLength, markerObjPoints);
    int nMarkers = (int)_corners.total();
    _rvecs.create(nMarkers, 1, CV_64FC3);
    _tvecs.create(nMarkers, 1, CV_64FC3);

    Mat rvecs = _rvecs.getMat(), tvecs = _tvecs.getMat();

    // for (int i = 0; i < nMarkers; i++) {
    //    solvePnP(markerObjPoints, _corners.getMat(i), _cameraMatrix, _distCoeffs,
    //             _rvecs.getMat(i), _tvecs.getMat(i));
    //}

    // this is the parallel call for the previous commented loop (result is equivalent)
    parallel_for_(Range(0, nMarkers),
                  SinglePoseEstimationParallel(markerObjPoints, _corners, _cameraMatrix,
                                               _distCoeffs, rvecs, tvecs));
    if(_objPoints.needed()){
        markerObjPoints.convertTo(_objPoints, -1);
    }
}



void getBoardObjectAndImagePoints(const Ptr<Board> &board, InputArrayOfArrays detectedCorners,
    InputArray detectedIds, OutputArray objPoints, OutputArray imgPoints) {

    CV_Assert(board->ids.size() == board->objPoints.size());
    CV_Assert(detectedIds.total() == detectedCorners.total());

    size_t nDetectedMarkers = detectedIds.total();

    vector< Point3f > objPnts;
    objPnts.reserve(nDetectedMarkers);

    vector< Point2f > imgPnts;
    imgPnts.reserve(nDetectedMarkers);

    // look for detected markers that belong to the board and get their information
    for(unsigned int i = 0; i < nDetectedMarkers; i++) {
        int currentId = detectedIds.getMat().ptr< int >(0)[i];
        for(unsigned int j = 0; j < board->ids.size(); j++) {
            if(currentId == board->ids[j]) {
                for(int p = 0; p < 4; p++) {
                    objPnts.push_back(board->objPoints[j][p]);
                    imgPnts.push_back(detectedCorners.getMat(i).ptr< Point2f >(0)[p]);
                }
            }
        }
    }

    // create output
    Mat(objPnts).copyTo(objPoints);
    Mat(imgPnts).copyTo(imgPoints);
}



static void _projectUndetectedMarkers(const Ptr<Board> &_board, InputOutputArrayOfArrays _detectedCorners,
                                      InputOutputArray _detectedIds, InputArray _cameraMatrix,
                                      InputArray _distCoeffs,
                                      vector< vector< Point2f > >& _undetectedMarkersProjectedCorners,
                                      OutputArray _undetectedMarkersIds) {

    // first estimate board pose with the current avaible markers
    Mat rvec, tvec;
    int boardDetectedMarkers;
    boardDetectedMarkers = aruco::estimatePoseBoard(_detectedCorners, _detectedIds, _board,
                                                    _cameraMatrix, _distCoeffs, rvec, tvec);

    // at least one marker from board so rvec and tvec are valid
    if(boardDetectedMarkers == 0) return;

    // search undetected markers and project them using the previous pose
    vector< vector< Point2f > > undetectedCorners;
    vector< int > undetectedIds;
    for(unsigned int i = 0; i < _board->ids.size(); i++) {
        int foundIdx = -1;
        for(unsigned int j = 0; j < _detectedIds.total(); j++) {
            if(_board->ids[i] == _detectedIds.getMat().ptr< int >()[j]) {
                foundIdx = j;
                break;
            }
        }

        // not detected
        if(foundIdx == -1) {
            undetectedCorners.push_back(vector< Point2f >());
            undetectedIds.push_back(_board->ids[i]);
            projectPoints(_board->objPoints[i], rvec, tvec, _cameraMatrix, _distCoeffs,
                          undetectedCorners.back());
        }
    }


    // parse output
    Mat(undetectedIds).copyTo(_undetectedMarkersIds);
    _undetectedMarkersProjectedCorners = undetectedCorners;
}



static void _projectUndetectedMarkers(const Ptr<Board> &_board, InputOutputArrayOfArrays _detectedCorners,
                                      InputOutputArray _detectedIds,
                                      vector< vector< Point2f > >& _undetectedMarkersProjectedCorners,
                                      OutputArray _undetectedMarkersIds) {


    // check board points are in the same plane, if not, global homography cannot be applied
    CV_Assert(_board->objPoints.size() > 0);
    CV_Assert(_board->objPoints[0].size() > 0);
    float boardZ = _board->objPoints[0][0].z;
    for(unsigned int i = 0; i < _board->objPoints.size(); i++) {
        for(unsigned int j = 0; j < _board->objPoints[i].size(); j++) {
            CV_Assert(boardZ == _board->objPoints[i][j].z);
        }
    }

    vector< Point2f > detectedMarkersObj2DAll; // Object coordinates (without Z) of all the detected
                                               // marker corners in a single vector
    vector< Point2f > imageCornersAll; // Image corners of all detected markers in a single vector
    vector< vector< Point2f > > undetectedMarkersObj2D; // Object coordinates (without Z) of all
                                                        // missing markers in different vectors
    vector< int > undetectedMarkersIds; // ids of missing markers
    // find markers included in board, and missing markers from board. Fill the previous vectors
    for(unsigned int j = 0; j < _board->ids.size(); j++) {
        bool found = false;
        for(unsigned int i = 0; i < _detectedIds.total(); i++) {
            if(_detectedIds.getMat().ptr< int >()[i] == _board->ids[j]) {
                for(int c = 0; c < 4; c++) {
                    imageCornersAll.push_back(_detectedCorners.getMat(i).ptr< Point2f >()[c]);
                    detectedMarkersObj2DAll.push_back(
                        Point2f(_board->objPoints[j][c].x, _board->objPoints[j][c].y));
                }
                found = true;
                break;
            }
        }
        if(!found) {
            undetectedMarkersObj2D.push_back(vector< Point2f >());
            for(int c = 0; c < 4; c++) {
                undetectedMarkersObj2D.back().push_back(
                    Point2f(_board->objPoints[j][c].x, _board->objPoints[j][c].y));
            }
            undetectedMarkersIds.push_back(_board->ids[j]);
        }
    }
    if(imageCornersAll.size() == 0) return;

    // get homography from detected markers
    Mat transformation = findHomography(detectedMarkersObj2DAll, imageCornersAll);

    _undetectedMarkersProjectedCorners.resize(undetectedMarkersIds.size());

    // for each undetected marker, apply transformation
    for(unsigned int i = 0; i < undetectedMarkersObj2D.size(); i++) {
        perspectiveTransform(undetectedMarkersObj2D[i], _undetectedMarkersProjectedCorners[i], transformation);
    }

    Mat(undetectedMarkersIds).copyTo(_undetectedMarkersIds);
}



void refineDetectedMarkers(InputArray _image, const Ptr<Board> &_board,
                           InputOutputArrayOfArrays _detectedCorners, InputOutputArray _detectedIds,
                           InputOutputArrayOfArrays _rejectedCorners, InputArray _cameraMatrix,
                           InputArray _distCoeffs, float minRepDistance, float errorCorrectionRate,
                           bool checkAllOrders, OutputArray _recoveredIdxs,
                           const Ptr<DetectorParameters> &_params) {

    CV_Assert(minRepDistance > 0);

    if(_detectedIds.total() == 0 || _rejectedCorners.total() == 0) return;

    DetectorParameters &params = *_params;

    // get projections of missing markers in the board
    vector< vector< Point2f > > undetectedMarkersCorners;
    vector< int > undetectedMarkersIds;
    if(_cameraMatrix.total() != 0) {
        // reproject based on camera projection model
        _projectUndetectedMarkers(_board, _detectedCorners, _detectedIds, _cameraMatrix, _distCoeffs,
                                  undetectedMarkersCorners, undetectedMarkersIds);

    } else {
        // reproject based on global homography
        _projectUndetectedMarkers(_board, _detectedCorners, _detectedIds, undetectedMarkersCorners,
                                  undetectedMarkersIds);
    }

    // list of missing markers indicating if they have been assigned to a candidate
    vector< bool > alreadyIdentified(_rejectedCorners.total(), false);

    // maximum bits that can be corrected
    Dictionary &dictionary = *(_board->dictionary);
    int maxCorrectionRecalculated =
        int(double(dictionary.maxCorrectionBits) * errorCorrectionRate);

    Mat grey;
    _convertToGrey(_image, grey);

    // vector of final detected marker corners and ids
    vector< Mat > finalAcceptedCorners;
    vector< int > finalAcceptedIds;
    // fill with the current markers
    finalAcceptedCorners.resize(_detectedCorners.total());
    finalAcceptedIds.resize(_detectedIds.total());
    for(unsigned int i = 0; i < _detectedIds.total(); i++) {
        finalAcceptedCorners[i] = _detectedCorners.getMat(i).clone();
        finalAcceptedIds[i] = _detectedIds.getMat().ptr< int >()[i];
    }
    vector< int > recoveredIdxs; // original indexes of accepted markers in _rejectedCorners

    // for each missing marker, try to find a correspondence
    for(unsigned int i = 0; i < undetectedMarkersIds.size(); i++) {

        // best match at the moment
        int closestCandidateIdx = -1;
        double closestCandidateDistance = minRepDistance * minRepDistance + 1;
        Mat closestRotatedMarker;

        for(unsigned int j = 0; j < _rejectedCorners.total(); j++) {
            if(alreadyIdentified[j]) continue;

            // check distance
            double minDistance = closestCandidateDistance + 1;
            bool valid = false;
            int validRot = 0;
            for(int c = 0; c < 4; c++) { // first corner in rejected candidate
                double currentMaxDistance = 0;
                for(int k = 0; k < 4; k++) {
                    Point2f rejCorner = _rejectedCorners.getMat(j).ptr< Point2f >()[(c + k) % 4];
                    Point2f distVector = undetectedMarkersCorners[i][k] - rejCorner;
                    double cornerDist = distVector.x * distVector.x + distVector.y * distVector.y;
                    currentMaxDistance = max(currentMaxDistance, cornerDist);
                }
                // if distance is better than current best distance
                if(currentMaxDistance < closestCandidateDistance) {
                    valid = true;
                    validRot = c;
                    minDistance = currentMaxDistance;
                }
                if(!checkAllOrders) break;
            }

            if(!valid) continue;

            // apply rotation
            Mat rotatedMarker;
            if(checkAllOrders) {
                rotatedMarker = Mat(4, 1, CV_32FC2);
                for(int c = 0; c < 4; c++)
                    rotatedMarker.ptr< Point2f >()[c] =
                        _rejectedCorners.getMat(j).ptr< Point2f >()[(c + 4 + validRot) % 4];
            }
            else rotatedMarker = _rejectedCorners.getMat(j);

            // last filter, check if inner code is close enough to the assigned marker code
            int codeDistance = 0;
            // if errorCorrectionRate, dont check code
            if(errorCorrectionRate >= 0) {

                // extract bits
                Mat bits = _extractBits(
                    grey, rotatedMarker, dictionary.markerSize, params.markerBorderBits,
                    params.perspectiveRemovePixelPerCell,
                    params.perspectiveRemoveIgnoredMarginPerCell, params.minOtsuStdDev);

                Mat onlyBits =
                    bits.rowRange(params.markerBorderBits, bits.rows - params.markerBorderBits)
                        .colRange(params.markerBorderBits, bits.rows - params.markerBorderBits);

                codeDistance =
                    dictionary.getDistanceToId(onlyBits, undetectedMarkersIds[i], false);
            }

            // if everythin is ok, assign values to current best match
            if(errorCorrectionRate < 0 || codeDistance < maxCorrectionRecalculated) {
                closestCandidateIdx = j;
                closestCandidateDistance = minDistance;
                closestRotatedMarker = rotatedMarker;
            }
        }

        // if at least one good match, we have rescue the missing marker
        if(closestCandidateIdx >= 0) {

            // subpixel refinement
            if(_params->cornerRefinementMethod == CORNER_REFINE_SUBPIX) {
                CV_Assert(params.cornerRefinementWinSize > 0 &&
                          params.cornerRefinementMaxIterations > 0 &&
                          params.cornerRefinementMinAccuracy > 0);
                cornerSubPix(grey, closestRotatedMarker,
                             Size(params.cornerRefinementWinSize, params.cornerRefinementWinSize),
                             Size(-1, -1), TermCriteria(TermCriteria::MAX_ITER | TermCriteria::EPS,
                                                        params.cornerRefinementMaxIterations,
                                                        params.cornerRefinementMinAccuracy));
            }

            // remove from rejected
            alreadyIdentified[closestCandidateIdx] = true;

            // add to detected
            finalAcceptedCorners.push_back(closestRotatedMarker);
            finalAcceptedIds.push_back(undetectedMarkersIds[i]);

            // add the original index of the candidate
            recoveredIdxs.push_back(closestCandidateIdx);
        }
    }

    // parse output
    if(finalAcceptedIds.size() != _detectedIds.total()) {
        _detectedCorners.clear();
        _detectedIds.clear();

        // parse output
        Mat(finalAcceptedIds).copyTo(_detectedIds);

        _detectedCorners.create((int)finalAcceptedCorners.size(), 1, CV_32FC2);
        for(unsigned int i = 0; i < finalAcceptedCorners.size(); i++) {
            _detectedCorners.create(4, 1, CV_32FC2, i, true);
            for(int j = 0; j < 4; j++) {
                _detectedCorners.getMat(i).ptr< Point2f >()[j] =
                    finalAcceptedCorners[i].ptr< Point2f >()[j];
            }
        }

        // recalculate _rejectedCorners based on alreadyIdentified
        vector< Mat > finalRejected;
        for(unsigned int i = 0; i < alreadyIdentified.size(); i++) {
            if(!alreadyIdentified[i]) {
                finalRejected.push_back(_rejectedCorners.getMat(i).clone());
            }
        }

        _rejectedCorners.clear();
        _rejectedCorners.create((int)finalRejected.size(), 1, CV_32FC2);
        for(unsigned int i = 0; i < finalRejected.size(); i++) {
            _rejectedCorners.create(4, 1, CV_32FC2, i, true);
            for(int j = 0; j < 4; j++) {
                _rejectedCorners.getMat(i).ptr< Point2f >()[j] =
                    finalRejected[i].ptr< Point2f >()[j];
            }
        }

        if(_recoveredIdxs.needed()) {
            Mat(recoveredIdxs).copyTo(_recoveredIdxs);
        }
    }
}




int estimatePoseBoard(InputArrayOfArrays _corners, InputArray _ids, const Ptr<Board> &board,
                      InputArray _cameraMatrix, InputArray _distCoeffs, OutputArray _rvec,
                      OutputArray _tvec, bool useExtrinsicGuess) {

    CV_Assert(_corners.total() == _ids.total());

    // get object and image points for the solvePnP function
    Mat objPoints, imgPoints;
    getBoardObjectAndImagePoints(board, _corners, _ids, objPoints, imgPoints);

    CV_Assert(imgPoints.total() == objPoints.total());

    if(objPoints.total() == 0) // 0 of the detected markers in board
        return 0;

    solvePnP(objPoints, imgPoints, _cameraMatrix, _distCoeffs, _rvec, _tvec, useExtrinsicGuess);

    // divide by four since all the four corners are concatenated in the array for each marker
    return (int)objPoints.total() / 4;
}




void GridBoard::draw(Size outSize, OutputArray _img, int marginSize, int borderBits) {
    _drawPlanarBoardImpl(this, outSize, _img, marginSize, borderBits);
}


Ptr<Board> Board::create(InputArrayOfArrays objPoints, const Ptr<Dictionary> &dictionary, InputArray ids) {

    CV_Assert(objPoints.total() == ids.total());
    CV_Assert(objPoints.type() == CV_32FC3 || objPoints.type() == CV_32FC1);

    std::vector< std::vector< Point3f > > obj_points_vector;
    for (unsigned int i = 0; i < objPoints.total(); i++) {
        std::vector<Point3f> corners;
        Mat corners_mat = objPoints.getMat(i);

        if(corners_mat.type() == CV_32FC1)
            corners_mat = corners_mat.reshape(3);
        CV_Assert(corners_mat.total() == 4);

        for (int j = 0; j < 4; j++) {
            corners.push_back(corners_mat.at<Point3f>(j));
        }
        obj_points_vector.push_back(corners);
    }

    Ptr<Board> res = makePtr<Board>();
    ids.copyTo(res->ids);
    res->objPoints = obj_points_vector;
    res->dictionary = cv::makePtr<Dictionary>(dictionary);
    return res;
}

Ptr<GridBoard> GridBoard::create(int markersX, int markersY, float markerLength, float markerSeparation,
                            const Ptr<Dictionary> &dictionary, int firstMarker) {

    CV_Assert(markersX > 0 && markersY > 0 && markerLength > 0 && markerSeparation > 0);

    Ptr<GridBoard> res = makePtr<GridBoard>();

    res->_markersX = markersX;
    res->_markersY = markersY;
    res->_markerLength = markerLength;
    res->_markerSeparation = markerSeparation;
    res->dictionary = dictionary;

    size_t totalMarkers = (size_t) markersX * markersY;
    res->ids.resize(totalMarkers);
    res->objPoints.reserve(totalMarkers);

    // fill ids with first identifiers
    for(unsigned int i = 0; i < totalMarkers; i++) {
        res->ids[i] = i + firstMarker;
    }

    // calculate Board objPoints
    float maxY = (float)markersY * markerLength + (markersY - 1) * markerSeparation;
    for(int y = 0; y < markersY; y++) {
        for(int x = 0; x < markersX; x++) {
            vector< Point3f > corners;
            corners.resize(4);
            corners[0] = Point3f(x * (markerLength + markerSeparation),
                                 maxY - y * (markerLength + markerSeparation), 0);
            corners[1] = corners[0] + Point3f(markerLength, 0, 0);
            corners[2] = corners[0] + Point3f(markerLength, -markerLength, 0);
            corners[3] = corners[0] + Point3f(0, -markerLength, 0);
            res->objPoints.push_back(corners);
        }
    }

    return res;
}



void drawDetectedMarkers(InputOutputArray _image, InputArrayOfArrays _corners,
                         InputArray _ids, Scalar borderColor) {


    CV_Assert(_image.getMat().total() != 0 &&
              (_image.getMat().channels() == 1 || _image.getMat().channels() == 3));
    CV_Assert((_corners.total() == _ids.total()) || _ids.total() == 0);

    // calculate colors
    Scalar textColor, cornerColor;
    textColor = cornerColor = borderColor;
    swap(textColor.val[0], textColor.val[1]);     // text color just sawp G and R
    swap(cornerColor.val[1], cornerColor.val[2]); // corner color just sawp G and B

    int nMarkers = (int)_corners.total();
    for(int i = 0; i < nMarkers; i++) {
        Mat currentMarker = _corners.getMat(i);
        CV_Assert(currentMarker.total() == 4 && currentMarker.type() == CV_32FC2);

        // draw marker sides
        for(int j = 0; j < 4; j++) {
            Point2f p0, p1;
            p0 = currentMarker.ptr< Point2f >(0)[j];
            p1 = currentMarker.ptr< Point2f >(0)[(j + 1) % 4];
            line(_image, p0, p1, borderColor, 1);
        }
        // draw first corner mark
        rectangle(_image, currentMarker.ptr< Point2f >(0)[0] - Point2f(3, 3),
                  currentMarker.ptr< Point2f >(0)[0] + Point2f(3, 3), cornerColor, 1, LINE_AA);

        // draw ID
        if(_ids.total() != 0) {
            Point2f cent(0, 0);
            for(int p = 0; p < 4; p++)
                cent += currentMarker.ptr< Point2f >(0)[p];
            cent = cent / 4.;
            stringstream s;
            s << "id=" << _ids.getMat().ptr< int >(0)[i];
            putText(_image, s.str(), cent, FONT_HERSHEY_SIMPLEX, 0.5, textColor, 2);
        }
    }
}



void drawAxis(InputOutputArray _image, InputArray _cameraMatrix, InputArray _distCoeffs, InputArray _rvec,
              InputArray _tvec, float length)
{
    /* no-op since we're using our own _drawAxis routine */
    /*drawFrameAxes(_image, _cameraMatrix, _distCoeffs, _rvec, _tvec, length, 3);*/
}

void drawMarker(const Ptr<Dictionary> &dictionary, int id, int sidePixels, OutputArray _img, int borderBits) {
    dictionary->drawMarker(id, sidePixels, _img, borderBits);
}



void _drawPlanarBoardImpl(Board *_board, Size outSize, OutputArray _img, int marginSize,
                     int borderBits) {

    /* NOTE: OpenCV v<3.3 does not have .empty() as a Size member */
    CV_Assert(outSize.height > 0 && outSize.width > 0);
    CV_Assert(marginSize >= 0);

    _img.create(outSize, CV_8UC1);
    Mat out = _img.getMat();
    out.setTo(Scalar::all(255));
    out.adjustROI(-marginSize, -marginSize, -marginSize, -marginSize);

    // calculate max and min values in XY plane
    CV_Assert(_board->objPoints.size() > 0);
    float minX, maxX, minY, maxY;
    minX = maxX = _board->objPoints[0][0].x;
    minY = maxY = _board->objPoints[0][0].y;

    for(unsigned int i = 0; i < _board->objPoints.size(); i++) {
        for(int j = 0; j < 4; j++) {
            minX = min(minX, _board->objPoints[i][j].x);
            maxX = max(maxX, _board->objPoints[i][j].x);
            minY = min(minY, _board->objPoints[i][j].y);
            maxY = max(maxY, _board->objPoints[i][j].y);
        }
    }

    float sizeX = maxX - minX;
    float sizeY = maxY - minY;

    // proportion transformations
    float xReduction = sizeX / float(out.cols);
    float yReduction = sizeY / float(out.rows);

    // determine the zone where the markers are placed
    if(xReduction > yReduction) {
        int nRows = int(sizeY / xReduction);
        int rowsMargins = (out.rows - nRows) / 2;
        out.adjustROI(-rowsMargins, -rowsMargins, 0, 0);
    } else {
        int nCols = int(sizeX / yReduction);
        int colsMargins = (out.cols - nCols) / 2;
        out.adjustROI(0, 0, -colsMargins, -colsMargins);
    }

    // now paint each marker
    Dictionary &dictionary = *(_board->dictionary);
    Mat marker;
    Point2f outCorners[3];
    Point2f inCorners[3];
    for(unsigned int m = 0; m < _board->objPoints.size(); m++) {
        // transform corners to markerZone coordinates
        for(int j = 0; j < 3; j++) {
            Point2f pf = Point2f(_board->objPoints[m][j].x, _board->objPoints[m][j].y);
            // move top left to 0, 0
            pf -= Point2f(minX, minY);
            pf.x = pf.x / sizeX * float(out.cols);
            pf.y = (1.0f - pf.y / sizeY) * float(out.rows);
            outCorners[j] = pf;
        }

        // get marker
        Size dst_sz(outCorners[2] - outCorners[0]); // assuming CCW order
        dst_sz.width = dst_sz.height = std::min(dst_sz.width, dst_sz.height); //marker should be square
        dictionary.drawMarker(_board->ids[m], dst_sz.width, marker, borderBits);

        if((outCorners[0].y == outCorners[1].y) && (outCorners[1].x == outCorners[2].x)) {
            // marker is aligned to image axes
            marker.copyTo(out(Rect(outCorners[0], dst_sz)));
            continue;
        }

        // interpolate tiny marker to marker position in markerZone
        inCorners[0] = Point2f(-0.5f, -0.5f);
        inCorners[1] = Point2f(marker.cols - 0.5f, -0.5f);
        inCorners[2] = Point2f(marker.cols - 0.5f, marker.rows - 0.5f);

        // remove perspective
        Mat transformation = getAffineTransform(inCorners, outCorners);
        warpAffine(marker, out, transformation, out.size(), INTER_LINEAR,
                        BORDER_TRANSPARENT);
    }
}



void drawPlanarBoard(const Ptr<Board> &_board, Size outSize, OutputArray _img, int marginSize,
                     int borderBits) {
    _drawPlanarBoardImpl(_board, outSize, _img, marginSize, borderBits);
}



double calibrateCameraAruco(InputArrayOfArrays _corners, InputArray _ids, InputArray _counter,
                            const Ptr<Board> &board, Size imageSize, InputOutputArray _cameraMatrix,
                            InputOutputArray _distCoeffs, OutputArrayOfArrays _rvecs,
                            OutputArrayOfArrays _tvecs,
                            OutputArray _stdDeviationsIntrinsics,
                            OutputArray _stdDeviationsExtrinsics,
                            OutputArray _perViewErrors,
                            int flags, TermCriteria criteria) {

    // for each frame, get properly processed imagePoints and objectPoints for the calibrateCamera
    // function
    vector< Mat > processedObjectPoints, processedImagePoints;
    size_t nFrames = _counter.total();
    int markerCounter = 0;
    for(size_t frame = 0; frame < nFrames; frame++) {
        int nMarkersInThisFrame =  _counter.getMat().ptr< int >()[frame];
        vector< Mat > thisFrameCorners;
        vector< int > thisFrameIds;

        CV_Assert(nMarkersInThisFrame > 0);

        thisFrameCorners.reserve((size_t) nMarkersInThisFrame);
        thisFrameIds.reserve((size_t) nMarkersInThisFrame);
        for(int j = markerCounter; j < markerCounter + nMarkersInThisFrame; j++) {
            thisFrameCorners.push_back(_corners.getMat(j));
            thisFrameIds.push_back(_ids.getMat().ptr< int >()[j]);
        }
        markerCounter += nMarkersInThisFrame;
        Mat currentImgPoints, currentObjPoints;
        getBoardObjectAndImagePoints(board, thisFrameCorners, thisFrameIds, currentObjPoints,
            currentImgPoints);
        if(currentImgPoints.total() > 0 && currentObjPoints.total() > 0) {
            processedImagePoints.push_back(currentImgPoints);
            processedObjectPoints.push_back(currentObjPoints);
        }
    }

    return calibrateCamera(processedObjectPoints, processedImagePoints, imageSize, _cameraMatrix,
                           _distCoeffs, _rvecs, _tvecs, _stdDeviationsIntrinsics, _stdDeviationsExtrinsics,
                           _perViewErrors, flags, criteria);
}



double calibrateCameraAruco(InputArrayOfArrays _corners, InputArray _ids, InputArray _counter,
  const Ptr<Board> &board, Size imageSize, InputOutputArray _cameraMatrix,
  InputOutputArray _distCoeffs, OutputArrayOfArrays _rvecs,
  OutputArrayOfArrays _tvecs, int flags, TermCriteria criteria) {
    return calibrateCameraAruco(_corners, _ids, _counter, board, imageSize, _cameraMatrix, _distCoeffs, _rvecs, _tvecs,
      noArray(), noArray(), noArray(), flags, criteria);
}



}
}