opencv/sources/modules/calib3d/src/calibinit.cpp

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/************************************************************************************\
    This is improved variant of chessboard corner detection algorithm that
    uses a graph of connected quads. It is based on the code contributed
    by Vladimir Vezhnevets and Philip Gruebele.
    Here is the copyright notice from the original Vladimir's code:
    ===============================================================

    The algorithms developed and implemented by Vezhnevets Vladimir
    aka Dead Moroz (vvp@graphics.cs.msu.ru)
    See http://graphics.cs.msu.su/en/research/calibration/opencv.html
    for detailed information.

    Reliability additions and modifications made by Philip Gruebele.
    <a href="mailto:pgruebele@cox.net">pgruebele@cox.net</a>

    Some further improvements for detection of partially occluded boards at non-ideal
    lighting conditions have been made by Alex Bovyrin and Kurt Kolonige

\************************************************************************************/

/************************************************************************************\
  This version adds a new and improved variant of chessboard corner detection
  that works better in poor lighting condition. It is based on work from
  Oliver Schreer and Stefano Masneri. This method works faster than the previous
  one and reverts back to the older method in case no chessboard detection is
  possible. Overall performance improves also because now the method avoids
  performing the same computation multiple times when not necessary.

\************************************************************************************/

#include "precomp.hpp"
#include "circlesgrid.hpp"
#include "opencv2/flann.hpp"

#include <stack>

//#define ENABLE_TRIM_COL_ROW

// Requires CMake flag: DEBUG_opencv_calib3d=ON
//#define DEBUG_CHESSBOARD
#define DEBUG_CHESSBOARD_TIMEOUT 0  // 0 - wait for 'q'

#include <opencv2/core/utils/logger.defines.hpp>
//#undef CV_LOG_STRIP_LEVEL
//#define CV_LOG_STRIP_LEVEL CV_LOG_LEVEL_VERBOSE + 1
#include <opencv2/core/utils/logger.hpp>

#ifdef DEBUG_CHESSBOARD
#include "opencv2/highgui.hpp"
#include "opencv2/imgproc.hpp"
#define DPRINTF(...)  CV_LOG_INFO(NULL, cv::format("calib3d: " __VA_ARGS__))
#else
#define DPRINTF(...)
#endif

namespace cv {

//=====================================================================================
// Implementation for the enhanced calibration object detection
//=====================================================================================

#define MAX_CONTOUR_APPROX  7

struct QuadCountour {
    Point pt[4];
    int parent_contour;

    QuadCountour(const Point pt_[4], int parent_contour_) :
        parent_contour(parent_contour_)
    {
        pt[0] = pt_[0]; pt[1] = pt_[1]; pt[2] = pt_[2]; pt[3] = pt_[3];
    }
};


/** This structure stores information about the chessboard corner.*/
struct ChessBoardCorner
{
    cv::Point2f pt;  // Coordinates of the corner
    int row;         // Board row index
    int count;       // Number of neighbor corners
    struct ChessBoardCorner* neighbors[4]; // Neighbor corners

    ChessBoardCorner(const cv::Point2f& pt_ = cv::Point2f()) :
        pt(pt_), row(0), count(0)
    {
        neighbors[0] = neighbors[1] = neighbors[2] = neighbors[3] = NULL;
    }

    float sumDist(int& n_) const
    {
        float sum = 0;
        int n = 0;
        for (int i = 0; i < 4; ++i)
        {
            if (neighbors[i])
            {
                sum += sqrt(normL2Sqr<float>(neighbors[i]->pt - pt));
                n++;
            }
        }
        n_ = n;
        return sum;
    }
};


/** This structure stores information about the chessboard quadrangle.*/
struct ChessBoardQuad
{
    int count;      // Number of quad neighbors
    int group_idx;  // quad group ID
    int row, col;   // row and column of this quad
    bool ordered;   // true if corners/neighbors are ordered counter-clockwise
    float edge_len; // quad edge len, in pix^2
    // neighbors and corners are synced, i.e., neighbor 0 shares corner 0
    ChessBoardCorner *corners[4]; // Coordinates of quad corners
    struct ChessBoardQuad *neighbors[4]; // Pointers of quad neighbors. M.b. sparse.
    // Each neighbors element corresponds to quad corner, but not just sequential index.

    ChessBoardQuad(int group_idx_ = -1) :
        count(0),
        group_idx(group_idx_),
        row(0), col(0),
        ordered(0),
        edge_len(0)
    {
        corners[0] = corners[1] = corners[2] = corners[3] = NULL;
        neighbors[0] = neighbors[1] = neighbors[2] = neighbors[3] = NULL;
    }
};



#ifdef DEBUG_CHESSBOARD
static void SHOW(const std::string & name, Mat & img)
{
    imshow(name, img);
#if DEBUG_CHESSBOARD_TIMEOUT
    waitKey(DEBUG_CHESSBOARD_TIMEOUT);
#else
    while ((uchar)waitKey(0) != 'q') {}
#endif
}
static void SHOW_QUADS(const std::string & name, const Mat & img_, ChessBoardQuad * quads, int quads_count)
{
    Mat img = img_.clone();
    if (img.channels() == 1)
        cvtColor(img, img, COLOR_GRAY2BGR);
    for (int i = 0; i < quads_count; ++i)
    {
        ChessBoardQuad & quad = quads[i];
        for (int j = 0; j < 4; ++j)
        {
            line(img, quad.corners[j]->pt, quad.corners[(j + 1) & 3]->pt, Scalar(0, 240, 0), 1, LINE_AA);
        }
    }
    imshow(name, img);
#if DEBUG_CHESSBOARD_TIMEOUT
    waitKey(DEBUG_CHESSBOARD_TIMEOUT);
#else
    while ((uchar)waitKey(0) != 'q') {}
#endif
}
#else
#define SHOW(...)
#define SHOW_QUADS(...)
#endif



class ChessBoardDetector
{
public:
    cv::Mat binarized_image;
    Size pattern_size;

    cv::AutoBuffer<ChessBoardQuad> all_quads;
    cv::AutoBuffer<ChessBoardCorner> all_corners;

    int all_quads_count;

    ChessBoardDetector(const Size& pattern_size_) :
        pattern_size(pattern_size_),
        all_quads_count(0)
    {
    }

    void reset()
    {
        all_quads.deallocate();
        all_corners.deallocate();
        all_quads_count = 0;
    }

    void generateQuads(const cv::Mat& image_, int flags, int dilations);

    bool processQuads(std::vector<cv::Point2f>& out_corners, int &prev_sqr_size);

    void findQuadNeighbors();

    void findConnectedQuads(std::vector<ChessBoardQuad*>& out_group, int group_idx);

    int checkQuadGroup(const std::vector<ChessBoardQuad*>& quad_group, std::vector<ChessBoardCorner*>& out_corners);

    int cleanFoundConnectedQuads(std::vector<ChessBoardQuad*>& quad_group);

    int orderFoundConnectedQuads(std::vector<ChessBoardQuad*>& quads);

    void orderQuad(ChessBoardQuad& quad, ChessBoardCorner& corner, int common);

#ifdef ENABLE_TRIM_COL_ROW
    void trimCol(std::vector<ChessBoardQuad*>& quads, int col, int dir);
    void trimRow(std::vector<ChessBoardQuad*>& quads, int row, int dir);
#endif

    int addOuterQuad(ChessBoardQuad& quad, std::vector<ChessBoardQuad*>& quads);

    void removeQuadFromGroup(std::vector<ChessBoardQuad*>& quads, ChessBoardQuad& q0);

    bool checkBoardMonotony(const std::vector<cv::Point2f>& corners);
};

/***************************************************************************************************/
//COMPUTE INTENSITY HISTOGRAM OF INPUT IMAGE
template<typename ArrayContainer>
static void icvGetIntensityHistogram256(const Mat& img, ArrayContainer& piHist)
{
    for (int i = 0; i < 256; i++)
        piHist[i] = 0;
    // sum up all pixel in row direction and divide by number of columns
    for (int j = 0; j < img.rows; ++j)
    {
        const uchar* row = img.ptr<uchar>(j);
        for (int i = 0; i < img.cols; i++)
        {
            piHist[row[i]]++;
        }
    }
}
/***************************************************************************************************/
//SMOOTH HISTOGRAM USING WINDOW OF SIZE 2*iWidth+1
template<int iWidth_, typename ArrayContainer>
static void icvSmoothHistogram256(const ArrayContainer& piHist, ArrayContainer& piHistSmooth, int iWidth = 0)
{
    CV_DbgAssert(iWidth_ == 0 || (iWidth == iWidth_ || iWidth == 0));
    iWidth = (iWidth_ != 0) ? iWidth_ : iWidth;
    CV_Assert(iWidth > 0);
    CV_DbgAssert(piHist.size() == 256);
    CV_DbgAssert(piHistSmooth.size() == 256);
    for (int i = 0; i < 256; ++i)
    {
        int iIdx_min = std::max(0, i - iWidth);
        int iIdx_max = std::min(255, i + iWidth);
        int iSmooth = 0;
        for (int iIdx = iIdx_min; iIdx <= iIdx_max; ++iIdx)
        {
            CV_DbgAssert(iIdx >= 0 && iIdx < 256);
            iSmooth += piHist[iIdx];
        }
        piHistSmooth[i] = iSmooth/(iIdx_max-iIdx_min+1);
    }
}
/***************************************************************************************************/
//COMPUTE FAST HISTOGRAM GRADIENT
template<typename ArrayContainer>
static void icvGradientOfHistogram256(const ArrayContainer& piHist, ArrayContainer& piHistGrad)
{
    CV_DbgAssert(piHist.size() == 256);
    CV_DbgAssert(piHistGrad.size() == 256);
    piHistGrad[0] = 0;
    int prev_grad = 0;
    for (int i = 1; i < 255; ++i)
    {
        int grad = piHist[i-1] - piHist[i+1];
        if (std::abs(grad) < 100)
        {
            if (prev_grad == 0)
                grad = -100;
            else
                grad = prev_grad;
        }
        piHistGrad[i] = grad;
        prev_grad = grad;
    }
    piHistGrad[255] = 0;
}
/***************************************************************************************************/
//PERFORM SMART IMAGE THRESHOLDING BASED ON ANALYSIS OF INTENSITY HISTOGRAM
static void icvBinarizationHistogramBased(Mat & img)
{
    CV_Assert(img.channels() == 1 && img.depth() == CV_8U);
    int iCols = img.cols;
    int iRows = img.rows;
    int iMaxPix = iCols*iRows;
    int iMaxPix1 = iMaxPix/100;
    const int iNumBins = 256;
    const int iMaxPos = 20;
    cv::AutoBuffer<int, 256> piHistIntensity(iNumBins);
    cv::AutoBuffer<int, 256> piHistSmooth(iNumBins);
    cv::AutoBuffer<int, 256> piHistGrad(iNumBins);
    cv::AutoBuffer<int> piMaxPos(iMaxPos);

    icvGetIntensityHistogram256(img, piHistIntensity);

#if 0
    // get accumulated sum starting from bright
    cv::AutoBuffer<int, 256> piAccumSum(iNumBins);
    piAccumSum[iNumBins-1] = piHistIntensity[iNumBins-1];
    for (int i = iNumBins - 2; i >= 0; --i)
    {
        piAccumSum[i] = piHistIntensity[i] + piAccumSum[i+1];
    }
#endif

    // first smooth the distribution
    //const int iWidth = 1;
    icvSmoothHistogram256<1>(piHistIntensity, piHistSmooth);

    // compute gradient
    icvGradientOfHistogram256(piHistSmooth, piHistGrad);

    // check for zeros
    unsigned iCntMaxima = 0;
    for (int i = iNumBins-2; (i > 2) && (iCntMaxima < iMaxPos); --i)
    {
        if ((piHistGrad[i-1] < 0) && (piHistGrad[i] > 0))
        {
            int iSumAroundMax = piHistSmooth[i-1] + piHistSmooth[i] + piHistSmooth[i+1];
            if (!(iSumAroundMax < iMaxPix1 && i < 64))
            {
                piMaxPos[iCntMaxima++] = i;
            }
        }
    }

    DPRINTF("HIST: MAXIMA COUNT: %d (%d, %d, %d, ...)", iCntMaxima,
            iCntMaxima > 0 ? piMaxPos[0] : -1,
            iCntMaxima > 1 ? piMaxPos[1] : -1,
            iCntMaxima > 2 ? piMaxPos[2] : -1);

    int iThresh = 0;

    CV_Assert((size_t)iCntMaxima <= piMaxPos.size());

    DPRINTF("HIST: MAXIMA COUNT: %d (%d, %d, %d, ...)", iCntMaxima,
                iCntMaxima > 0 ? piMaxPos[0] : -1,
                iCntMaxima > 1 ? piMaxPos[1] : -1,
                iCntMaxima > 2 ? piMaxPos[2] : -1);

    if (iCntMaxima == 0)
    {
        // no any maxima inside (only 0 and 255 which are not counted above)
        // Does image black-write already?
        const int iMaxPix2 = iMaxPix / 2;
        for (int sum = 0, i = 0; i < 256; ++i) // select mean intensity
        {
            sum += piHistIntensity[i];
            if (sum > iMaxPix2)
            {
                iThresh = i;
                break;
            }
        }
    }
    else if (iCntMaxima == 1)
    {
        iThresh = piMaxPos[0]/2;
    }
    else if (iCntMaxima == 2)
    {
        iThresh = (piMaxPos[0] + piMaxPos[1])/2;
    }
    else // iCntMaxima >= 3
    {
        // CHECKING THRESHOLD FOR WHITE
        int iIdxAccSum = 0, iAccum = 0;
        for (int i = iNumBins - 1; i > 0; --i)
        {
            iAccum += piHistIntensity[i];
            // iMaxPix/18 is about 5,5%, minimum required number of pixels required for white part of chessboard
            if ( iAccum > (iMaxPix/18) )
            {
                iIdxAccSum = i;
                break;
            }
        }

        unsigned iIdxBGMax = 0;
        int iBrightMax = piMaxPos[0];
        // printf("iBrightMax = %d\n", iBrightMax);
        for (unsigned n = 0; n < iCntMaxima - 1; ++n)
        {
            iIdxBGMax = n + 1;
            if ( piMaxPos[n] < iIdxAccSum )
            {
                break;
            }
            iBrightMax = piMaxPos[n];
        }

        // CHECKING THRESHOLD FOR BLACK
        int iMaxVal = piHistIntensity[piMaxPos[iIdxBGMax]];

        //IF TOO CLOSE TO 255, jump to next maximum
        if (piMaxPos[iIdxBGMax] >= 250 && iIdxBGMax + 1 < iCntMaxima)
        {
            iIdxBGMax++;
            iMaxVal = piHistIntensity[piMaxPos[iIdxBGMax]];
        }

        for (unsigned n = iIdxBGMax + 1; n < iCntMaxima; n++)
        {
            if (piHistIntensity[piMaxPos[n]] >= iMaxVal)
            {
                iMaxVal = piHistIntensity[piMaxPos[n]];
                iIdxBGMax = n;
            }
        }

        //SETTING THRESHOLD FOR BINARIZATION
        int iDist2 = (iBrightMax - piMaxPos[iIdxBGMax])/2;
        iThresh = iBrightMax - iDist2;
        DPRINTF("THRESHOLD SELECTED = %d, BRIGHTMAX = %d, DARKMAX = %d", iThresh, iBrightMax, piMaxPos[iIdxBGMax]);
    }

    if (iThresh > 0)
    {
        img = (img >= iThresh);
    }
}

bool findChessboardCorners(InputArray image_, Size pattern_size,
                           OutputArray corners_, int flags)
{
    CV_INSTRUMENT_REGION();

    DPRINTF("==== findChessboardCorners(img=%dx%d, pattern=%dx%d, flags=%d)",
            image_.cols(), image_.rows(), pattern_size.width, pattern_size.height, flags);

    bool found = false;

    const bool is_plain = (flags & CALIB_CB_PLAIN) != 0;

    int type = image_.type(), depth = CV_MAT_DEPTH(type), cn = CV_MAT_CN(type);
    Mat img = image_.getMat();

    CV_CheckType(type, depth == CV_8U && (cn == 1 || cn == 3 || cn == 4),
            "Only 8-bit grayscale or color images are supported");

    if (pattern_size.width <= 2 || pattern_size.height <= 2)
        CV_Error(Error::StsOutOfRange, "Both width and height of the pattern should have bigger than 2");

    if (!corners_.needed())
        CV_Error(Error::StsNullPtr, "Null pointer to corners");

    std::vector<cv::Point2f> out_corners;

    if (is_plain)
      CV_CheckType(type, depth == CV_8U && cn == 1, "Only 8-bit grayscale images are supported whith CALIB_CB_PLAIN flag enable");

    if (img.channels() != 1)
    {
        cvtColor(img, img, COLOR_BGR2GRAY);
    }

    int prev_sqr_size = 0;

    Mat thresh_img_new = img.clone();
    if(!is_plain)
        icvBinarizationHistogramBased(thresh_img_new); // process image in-place
    SHOW("New binarization", thresh_img_new);

    if (flags & CALIB_CB_FAST_CHECK && !is_plain)
    {
        //perform new method for checking chessboard using a binary image.
        //image is binarised using a threshold dependent on the image histogram
        if (checkChessboardBinary(thresh_img_new, pattern_size) <= 0) //fall back to the old method
        {
            if (!checkChessboard(img, pattern_size))
            {
                corners_.release();
                return false;
            }
        }
    }

    ChessBoardDetector detector(pattern_size);

    const int min_dilations = 0;
    const int max_dilations = is_plain ? 0 : 7;

    // Try our standard "0" and "1" dilations, but if the pattern is not found, iterate the whole procedure with higher dilations.
    // This is necessary because some squares simply do not separate properly without and with a single dilations. However,
    // we want to use the minimum number of dilations possible since dilations cause the squares to become smaller,
    // making it difficult to detect smaller squares.
    for (int dilations = min_dilations; dilations <= max_dilations; dilations++)
    {
        //USE BINARY IMAGE COMPUTED USING icvBinarizationHistogramBased METHOD
        if(!is_plain && dilations > 0)
            dilate( thresh_img_new, thresh_img_new, Mat(), Point(-1, -1), 1 );

        // So we can find rectangles that go to the edge, we draw a white line around the image edge.
        // Otherwise FindContours will miss those clipped rectangle contours.
        // The border color will be the image mean, because otherwise we risk screwing up filters like cvSmooth()...
        rectangle( thresh_img_new, Point(0,0), Point(thresh_img_new.cols-1, thresh_img_new.rows-1), Scalar(255,255,255), 3, LINE_8);

        detector.reset();
        detector.generateQuads(thresh_img_new, flags, dilations);
        DPRINTF("Quad count: %d/%d", detector.all_quads_count, (pattern_size.width/2+1)*(pattern_size.height/2+1));
        SHOW_QUADS("New quads", thresh_img_new, &detector.all_quads[0], detector.all_quads_count);
        if (detector.processQuads(out_corners, prev_sqr_size))
        {
            found = true;
            break;
        }
    }

    DPRINTF("Chessboard detection result 0: %d", (int)found);

    // revert to old, slower, method if detection failed
    if (!found && !is_plain)
    {
        if (flags & CALIB_CB_NORMALIZE_IMAGE)
        {
            img = img.clone();
            equalizeHist(img, img);
        }

        Mat thresh_img;
        prev_sqr_size = 0;

        DPRINTF("Fallback to old algorithm");
        const bool useAdaptive = flags & CALIB_CB_ADAPTIVE_THRESH;
        if (!useAdaptive)
        {
            // empiric threshold level
            // thresholding performed here and not inside the cycle to save processing time
            double mean = cv::mean(img).val[0];
            int thresh_level = std::max(cvRound(mean - 10), 10);
            threshold(img, thresh_img, thresh_level, 255, THRESH_BINARY);
        }
        //if flag CALIB_CB_ADAPTIVE_THRESH is not set it doesn't make sense to iterate over k
        int max_k = useAdaptive ? 6 : 1;
        Mat prev_thresh_img;
        for (int k = 0; k < max_k && !found; k++)
        {
            int prev_block_size = -1;
            for (int dilations = min_dilations; dilations <= max_dilations; dilations++)
            {
                // convert the input grayscale image to binary (black-n-white)
                if (useAdaptive)
                {
                    int block_size = cvRound(prev_sqr_size == 0
                                             ? std::min(img.cols, img.rows) * (k % 2 == 0 ? 0.2 : 0.1)
                                             : prev_sqr_size * 2);
                    block_size = block_size | 1;
                    // convert to binary
                    if (block_size != prev_block_size)
                    {
                        adaptiveThreshold( img, thresh_img, 255, ADAPTIVE_THRESH_MEAN_C, THRESH_BINARY, block_size, (k/2)*5 );
                        dilate( thresh_img, thresh_img, Mat(), Point(-1, -1), dilations );
                        thresh_img.copyTo(prev_thresh_img);
                    }
                    else if (dilations > 0)
                    {
                        dilate( prev_thresh_img, prev_thresh_img, Mat(), Point(-1, -1), 1 );
                        prev_thresh_img.copyTo(thresh_img);
                    }
                    prev_block_size = block_size;
                }
                else
                {
                    if (dilations > 0)
                        dilate( thresh_img, thresh_img, Mat(), Point(-1, -1), 1 );
                }
                SHOW("Old binarization", thresh_img);

                // So we can find rectangles that go to the edge, we draw a white line around the image edge.
                // Otherwise FindContours will miss those clipped rectangle contours.
                // The border color will be the image mean, because otherwise we risk screwing up filters like cvSmooth()...
                rectangle( thresh_img, Point(0,0), Point(thresh_img.cols-1, thresh_img.rows-1), Scalar(255,255,255), 3, LINE_8);

                detector.reset();
                detector.generateQuads(thresh_img, flags, dilations);
                DPRINTF("Quad count: %d/%d", detector.all_quads_count, (pattern_size.width/2+1)*(pattern_size.height/2+1));
                SHOW_QUADS("Old quads", thresh_img, &detector.all_quads[0], detector.all_quads_count);
                if (detector.processQuads(out_corners, prev_sqr_size))
                {
                    found = 1;
                    break;
                }
            }
        }
    }

    DPRINTF("Chessboard detection result 1: %d", (int)found);

    if (found)
        found = detector.checkBoardMonotony(out_corners);

    DPRINTF("Chessboard detection result 2: %d", (int)found);

    // check that none of the found corners is too close to the image boundary
    if (found)
    {
        const int BORDER = 8;
        for (int k = 0; k < pattern_size.width*pattern_size.height; ++k)
        {
            if( out_corners[k].x <= BORDER || out_corners[k].x > img.cols - BORDER ||
                out_corners[k].y <= BORDER || out_corners[k].y > img.rows - BORDER )
            {
                found = false;
                break;
            }
        }
    }

    DPRINTF("Chessboard detection result 3: %d", (int)found);

    if (found)
    {
        if ((pattern_size.height & 1) == 0 && (pattern_size.width & 1) == 0 )
        {
            int last_row = (pattern_size.height-1)*pattern_size.width;
            double dy0 = out_corners[last_row].y - out_corners[0].y;
            if (dy0 < 0)
            {
                int n = pattern_size.width*pattern_size.height;
                for(int i = 0; i < n/2; i++ )
                {
                    std::swap(out_corners[i], out_corners[n-i-1]);
                }
            }
        }
        cv::cornerSubPix(img, out_corners, Size(2, 2), Size(-1,-1),
                         cv::TermCriteria(TermCriteria::EPS + TermCriteria::MAX_ITER, 15, 0.1));
    }

    Mat(out_corners).copyTo(corners_);
    return found;
}

//
// Checks that each board row and column is pretty much monotonous curve:
// It analyzes each row and each column of the chessboard as following:
//    for each corner c lying between end points in the same row/column it checks that
//    the point projection to the line segment (a,b) is lying between projections
//    of the neighbor corners in the same row/column.
//
// This function has been created as temporary workaround for the bug in current implementation
// of cvFindChessboardCorners that produces absolutely unordered sets of corners.
//
bool ChessBoardDetector::checkBoardMonotony(const std::vector<cv::Point2f>& corners)
{
    for (int k = 0; k < 2; ++k)
    {
        int max_i = (k == 0 ? pattern_size.height : pattern_size.width);
        int max_j = (k == 0 ? pattern_size.width: pattern_size.height) - 1;
        for (int i = 0; i < max_i; ++i)
        {
            cv::Point2f a = k == 0 ? corners[i*pattern_size.width] : corners[i];
            cv::Point2f b = k == 0 ? corners[(i+1)*pattern_size.width-1]
                                   : corners[(pattern_size.height-1)*pattern_size.width + i];
            float dx0 = b.x - a.x, dy0 = b.y - a.y;
            if (fabs(dx0) + fabs(dy0) < FLT_EPSILON)
                return false;
            float prevt = 0;
            for (int j = 1; j < max_j; ++j)
            {
                cv::Point2f c = k == 0 ? corners[i*pattern_size.width + j]
                                       : corners[j*pattern_size.width + i];
                float t = ((c.x - a.x)*dx0 + (c.y - a.y)*dy0)/(dx0*dx0 + dy0*dy0);
                if (t < prevt || t > 1)
                    return false;
                prevt = t;
            }
        }
    }
    return true;
}

//
// order a group of connected quads
// order of corners:
//   0 is top left
//   clockwise from there
// note: "top left" is nominal, depends on initial ordering of starting quad
//   but all other quads are ordered consistently
//
// can change the number of quads in the group
// can add quads, so we need to have quad/corner arrays passed in
//
int ChessBoardDetector::orderFoundConnectedQuads(std::vector<ChessBoardQuad*>& quads)
{
    const int max_quad_buf_size = (int)all_quads.size();
    int quad_count = (int)quads.size();

    std::stack<ChessBoardQuad*> stack;

    // first find an interior quad
    ChessBoardQuad *start = NULL;
    for (int i = 0; i < quad_count; i++)
    {
        if (quads[i]->count == 4)
        {
            start = quads[i];
            break;
        }
    }

    if (start == NULL)
        return 0;   // no 4-connected quad

    // start with first one, assign rows/cols
    int row_min = 0, col_min = 0, row_max=0, col_max = 0;

    std::map<int, int> col_hist;
    std::map<int, int> row_hist;

    stack.push(start);
    start->row = 0;
    start->col = 0;
    start->ordered = true;

    // Recursively order the quads so that all position numbers (e.g.,
    // 0,1,2,3) are in the at the same relative corner (e.g., lower right).

    while (!stack.empty())
    {
        ChessBoardQuad* q = stack.top(); stack.pop(); CV_Assert(q);

        int col = q->col;
        int row = q->row;
        col_hist[col]++;
        row_hist[row]++;

        // check min/max
        if (row > row_max) row_max = row;
        if (row < row_min) row_min = row;
        if (col > col_max) col_max = col;
        if (col < col_min) col_min = col;

        for (int i = 0; i < 4; i++)
        {
            CV_DbgAssert(q);
            ChessBoardQuad *neighbor = q->neighbors[i];
            switch(i)   // adjust col, row for this quad
            {           // start at top left, go clockwise
            case 0:
                row--; col--; break;
            case 1:
                col += 2; break;
            case 2:
                row += 2;   break;
            case 3:
                col -= 2; break;
            }

            // just do inside quads
            if (neighbor && neighbor->ordered == false && neighbor->count == 4)
            {
                DPRINTF("col: %d  row: %d", col, row);
                CV_Assert(q->corners[i]);
                orderQuad(*neighbor, *(q->corners[i]), (i+2)&3); // set in order
                neighbor->ordered = true;
                neighbor->row = row;
                neighbor->col = col;
                stack.push(neighbor);
            }
        }
    }

#ifdef DEBUG_CHESSBOARD
    for (int i = col_min; i <= col_max; i++)
        DPRINTF("HIST[%d] = %d", i, col_hist[i]);
#endif

    // analyze inner quad structure
    int w = pattern_size.width - 1;
    int h = pattern_size.height - 1;
    int drow = row_max - row_min + 1;
    int dcol = col_max - col_min + 1;

    // normalize pattern and found quad indices
    if ((w > h && dcol < drow) ||
        (w < h && drow < dcol))
    {
        h = pattern_size.width - 1;
        w = pattern_size.height - 1;
    }

    DPRINTF("Size: %dx%d  Pattern: %dx%d", dcol, drow, w, h);

    // check if there are enough inner quads
    if (dcol < w || drow < h)   // found enough inner quads?
    {
        DPRINTF("Too few inner quad rows/cols");
        return 0;   // no, return
    }
#ifdef ENABLE_TRIM_COL_ROW
    // too many columns, not very common
    if (dcol == w+1)    // too many, trim
    {
        DPRINTF("Trimming cols");
        if (col_hist[col_max] > col_hist[col_min])
        {
            DPRINTF("Trimming left col");
            trimCol(quads, col_min, -1);
        }
        else
        {
            DPRINTF("Trimming right col");
            trimCol(quads, col_max, +1);
        }
    }

    // too many rows, not very common
    if (drow == h+1)    // too many, trim
    {
        DPRINTF("Trimming rows");
        if (row_hist[row_max] > row_hist[row_min])
        {
            DPRINTF("Trimming top row");
            trimRow(quads, row_min, -1);
        }
        else
        {
            DPRINTF("Trimming bottom row");
            trimRow(quads, row_max, +1);
        }
    }

    quad_count = (int)quads.size(); // update after icvTrimCol/icvTrimRow
#endif

    // check edges of inner quads
    // if there is an outer quad missing, fill it in
    // first order all inner quads
    int found = 0;
    for (int i=0; i < quad_count; ++i)
    {
        ChessBoardQuad& q = *quads[i];
        if (q.count != 4)
            continue;

        {   // ok, look at neighbors
            int col = q.col;
            int row = q.row;
            for (int j = 0; j < 4; j++)
            {
                switch(j)   // adjust col, row for this quad
                {           // start at top left, go clockwise
                case 0:
                    row--; col--; break;
                case 1:
                    col += 2; break;
                case 2:
                    row += 2;   break;
                case 3:
                    col -= 2; break;
                }
                ChessBoardQuad *neighbor = q.neighbors[j];
                if (neighbor && !neighbor->ordered && // is it an inner quad?
                    col <= col_max && col >= col_min &&
                    row <= row_max && row >= row_min)
                {
                    // if so, set in order
                    DPRINTF("Adding inner: col: %d  row: %d", col, row);
                    found++;
                    CV_Assert(q.corners[j]);
                    orderQuad(*neighbor, *q.corners[j], (j+2)&3);
                    neighbor->ordered = true;
                    neighbor->row = row;
                    neighbor->col = col;
                }
            }
        }
    }

    // if we have found inner quads, add corresponding outer quads,
    //   which are missing
    if (found > 0)
    {
        DPRINTF("Found %d inner quads not connected to outer quads, repairing", found);
        for (int i = 0; i < quad_count && all_quads_count < max_quad_buf_size; i++)
        {
            ChessBoardQuad& q = *quads[i];
            if (q.count < 4 && q.ordered)
            {
                int added = addOuterQuad(q, quads);
                quad_count += added;
            }
        }

        if (all_quads_count >= max_quad_buf_size)
            return 0;
    }


    // final trimming of outer quads
    if (dcol == w && drow == h) // found correct inner quads
    {
        DPRINTF("Inner bounds ok, check outer quads");
        for (int i = quad_count - 1; i >= 0; i--) // eliminate any quad not connected to an ordered quad
        {
            ChessBoardQuad& q = *quads[i];
            if (q.ordered == false)
            {
                bool outer = false;
                for (int j=0; j<4; j++) // any neighbors that are ordered?
                {
                    if (q.neighbors[j] && q.neighbors[j]->ordered)
                        outer = true;
                }
                if (!outer) // not an outer quad, eliminate
                {
                    DPRINTF("Removing quad %d", i);
                    removeQuadFromGroup(quads, q);
                }
            }

        }
        return (int)quads.size();
    }

    return 0;
}


// add an outer quad
// looks for the neighbor of <quad> that isn't present,
//   tries to add it in.
// <quad> is ordered
int ChessBoardDetector::addOuterQuad(ChessBoardQuad& quad, std::vector<ChessBoardQuad*>& quads)
{
    int added = 0;
    int max_quad_buf_size = (int)all_quads.size();

    for (int i = 0; i < 4 && all_quads_count < max_quad_buf_size; i++) // find no-neighbor corners
    {
        if (!quad.neighbors[i])    // ok, create and add neighbor
        {
            int j = (i+2)&3;
            DPRINTF("Adding quad as neighbor 2");
            int q_index = all_quads_count++;
            ChessBoardQuad& q = all_quads[q_index];
            q = ChessBoardQuad(0);
            added++;
            quads.push_back(&q);

            // set neighbor and group id
            quad.neighbors[i] = &q;
            quad.count += 1;
            q.neighbors[j] = &quad;
            q.group_idx = quad.group_idx;
            q.count = 1;   // number of neighbors
            q.ordered = false;
            q.edge_len = quad.edge_len;

            // make corners of new quad
            // same as neighbor quad, but offset
            const cv::Point2f pt_offset = quad.corners[i]->pt - quad.corners[j]->pt;
            for (int k = 0; k < 4; k++)
            {
                ChessBoardCorner& corner = (ChessBoardCorner&)all_corners[q_index * 4 + k];
                const cv::Point2f& pt = quad.corners[k]->pt;
                corner = ChessBoardCorner(pt);
                q.corners[k] = &corner;
                corner.pt += pt_offset;
            }
            // have to set exact corner
            q.corners[j] = quad.corners[i];

            // now find other neighbor and add it, if possible
            int next_i = (i + 1) & 3;
            int prev_i = (i + 3) & 3; // equal to (j + 1) & 3
            ChessBoardQuad* quad_prev = quad.neighbors[prev_i];
            if (quad_prev &&
                quad_prev->ordered &&
                quad_prev->neighbors[i] &&
                quad_prev->neighbors[i]->ordered )
            {
                ChessBoardQuad* qn = quad_prev->neighbors[i];
                q.count = 2;
                q.neighbors[prev_i] = qn;
                qn->neighbors[next_i] = &q;
                qn->count += 1;
                // have to set exact corner
                q.corners[prev_i] = qn->corners[next_i];
            }
        }
    }
    return added;
}


// trimming routines
#ifdef ENABLE_TRIM_COL_ROW
void ChessBoardDetector::trimCol(std::vector<ChessBoardQuad*>& quads, int col, int dir)
{
    std::vector<ChessBoardQuad*> quads_(quads);
    // find the right quad(s)
    for (size_t i = 0; i < quads_.size(); ++i)
    {
        ChessBoardQuad& q = *quads_[i];
#ifdef DEBUG_CHESSBOARD
        if (q.ordered)
            DPRINTF("i: %d  index: %d  cur: %d", (int)i, col, q.col);
#endif
        if (q.ordered && q.col == col)
        {
            if (dir == 1)
            {
                if (q.neighbors[1])
                {
                    removeQuadFromGroup(quads, *q.neighbors[1]);
                }
                if (q.neighbors[2])
                {
                    removeQuadFromGroup(quads, *q.neighbors[2]);
                }
            }
            else
            {
                if (q.neighbors[0])
                {
                    removeQuadFromGroup(quads, *q.neighbors[0]);
                }
                if (q.neighbors[3])
                {
                    removeQuadFromGroup(quads, *q.neighbors[3]);
                }
            }
        }
    }
}

void ChessBoardDetector::trimRow(std::vector<ChessBoardQuad*>& quads, int row, int dir)
{
    std::vector<ChessBoardQuad*> quads_(quads);
    // find the right quad(s)
    for (size_t i = 0; i < quads_.size(); ++i)
    {
        ChessBoardQuad& q = *quads_[i];
#ifdef DEBUG_CHESSBOARD
        if (q.ordered)
            DPRINTF("i: %d  index: %d  cur: %d", (int)i, row, q.row);
#endif
        if (q.ordered && q.row == row)
        {
            if (dir == 1)   // remove from bottom
            {
                if (q.neighbors[2])
                {
                    removeQuadFromGroup(quads, *q.neighbors[2]);
                }
                if (q.neighbors[3])
                {
                    removeQuadFromGroup(quads, *q.neighbors[3]);
                }
            }
            else    // remove from top
            {
                if (q.neighbors[0])
                {
                    removeQuadFromGroup(quads, *q.neighbors[0]);
                }
                if (q.neighbors[1])
                {
                    removeQuadFromGroup(quads, *q.neighbors[1]);
                }
            }

        }
    }
}
#endif

//
// remove quad from quad group
//
void ChessBoardDetector::removeQuadFromGroup(std::vector<ChessBoardQuad*>& quads, ChessBoardQuad& q0)
{
    const int count = (int)quads.size();

    int self_idx = -1;

    // remove any references to this quad as a neighbor
    for (int i = 0; i < count; ++i)
    {
        ChessBoardQuad* q = quads[i];
        if (q == &q0)
            self_idx = i;
        for (int j = 0; j < 4; j++)
        {
            if (q->neighbors[j] == &q0)
            {
                q->neighbors[j] = NULL;
                q->count--;
                for (int k = 0; k < 4; ++k)
                {
                    if (q0.neighbors[k] == q)
                    {
                        q0.neighbors[k] = 0;
                        q0.count--;
#ifndef _DEBUG
                        break;
#endif
                    }
                }
                break;
            }
        }
    }
    CV_Assert(self_idx >= 0); // item itself should be found

    // remove the quad
    if (self_idx != count-1)
        quads[self_idx] = quads[count-1];
    quads.resize(count - 1);
}

//
// put quad into correct order, where <corner> has value <common>
//
void ChessBoardDetector::orderQuad(ChessBoardQuad& quad, ChessBoardCorner& corner, int common)
{
    CV_DbgAssert(common >= 0 && common <= 3);

    // find the corner
    int tc = 0;;
    for (; tc < 4; ++tc)
        if (quad.corners[tc]->pt == corner.pt)
            break;

    // set corner order
    // shift
    while (tc != common)
    {
        // shift by one
        ChessBoardCorner *tempc = quad.corners[3];
        ChessBoardQuad *tempq = quad.neighbors[3];
        for (int i = 3; i > 0; --i)
        {
            quad.corners[i] = quad.corners[i-1];
            quad.neighbors[i] = quad.neighbors[i-1];
        }
        quad.corners[0] = tempc;
        quad.neighbors[0] = tempq;
        tc = (tc + 1) & 3;
    }
}


// if we found too many connect quads, remove those which probably do not belong.
int ChessBoardDetector::cleanFoundConnectedQuads(std::vector<ChessBoardQuad*>& quad_group)
{
    // number of quads this pattern should contain
    int count = ((pattern_size.width + 1)*(pattern_size.height + 1) + 1)/2;

    // if we have more quadrangles than we should,
    // try to eliminate duplicates or ones which don't belong to the pattern rectangle...
    int quad_count = (int)quad_group.size();
    if (quad_count <= count)
        return quad_count;
    CV_DbgAssert(quad_count > 0);

    // create an array of quadrangle centers
    cv::AutoBuffer<cv::Point2f> centers(quad_count);

    cv::Point2f center;
    for (int i = 0; i < quad_count; ++i)
    {
        ChessBoardQuad* q = quad_group[i];

        const cv::Point2f ci = (
                q->corners[0]->pt +
                q->corners[1]->pt +
                q->corners[2]->pt +
                q->corners[3]->pt
            ) * 0.25f;

        centers[i] = ci;
        center += ci;
    }
    center *= (1.0f / quad_count);

    // If we still have more quadrangles than we should,
    // we try to eliminate bad ones based on minimizing the bounding box.
    // We iteratively remove the point which reduces the size of
    // the bounding box of the blobs the most
    // (since we want the rectangle to be as small as possible)
    // remove the quadrangle that causes the biggest reduction
    // in pattern size until we have the correct number
    while (quad_count > count)
    {
        double min_box_area = DBL_MAX;
        int min_box_area_index = -1;

        // For each point, calculate box area without that point
        for (int skip = 0; skip < quad_count; ++skip)
        {
            // get bounding rectangle
            cv::Point2f temp = centers[skip]; // temporarily make index 'skip' the same as
            centers[skip] = center;            // pattern center (so it is not counted for convex hull)
            std::vector<Point2f> hull;
            Mat points(1, quad_count, CV_32FC2, &centers[0]);
            cv::convexHull(points, hull, true);
            centers[skip] = temp;
            double hull_area = contourArea(hull, false);

            // remember smallest box area
            if (hull_area < min_box_area)
            {
                min_box_area = hull_area;
                min_box_area_index = skip;
            }
        }

        ChessBoardQuad *q0 = quad_group[min_box_area_index];

        // remove any references to this quad as a neighbor
        for (int i = 0; i < quad_count; ++i)
        {
            ChessBoardQuad *q = quad_group[i];
            CV_DbgAssert(q);
            for (int j = 0; j < 4; ++j)
            {
                if (q->neighbors[j] == q0)
                {
                    q->neighbors[j] = 0;
                    q->count--;
                    for (int k = 0; k < 4; ++k)
                    {
                        if (q0->neighbors[k] == q)
                        {
                            q0->neighbors[k] = 0;
                            q0->count--;
                            break;
                        }
                    }
                    break;
                }
            }
        }

        // remove the quad
        quad_count--;
        quad_group[min_box_area_index] = quad_group[quad_count];
        centers[min_box_area_index] = centers[quad_count];
    }
    quad_group.resize(quad_count);

    return quad_count;
}



void ChessBoardDetector::findConnectedQuads(std::vector<ChessBoardQuad*>& out_group, int group_idx)
{
    out_group.clear();

    std::stack<ChessBoardQuad*> stack;

    int i = 0;
    for (; i < all_quads_count; i++)
    {
        ChessBoardQuad* q = (ChessBoardQuad*)&all_quads[i];

        // Scan the array for a first unlabeled quad
        if (q->count <= 0 || q->group_idx >= 0) continue;

        // Recursively find a group of connected quads starting from the seed all_quads[i]
        stack.push(q);
        out_group.push_back(q);
        q->group_idx = group_idx;
        q->ordered = false;

        while (!stack.empty())
        {
            q = stack.top(); CV_Assert(q);
            stack.pop();
            for (int k = 0; k < 4; k++ )
            {
                CV_DbgAssert(q);
                ChessBoardQuad *neighbor = q->neighbors[k];
                if (neighbor && neighbor->count > 0 && neighbor->group_idx < 0 )
                {
                    stack.push(neighbor);
                    out_group.push_back(neighbor);
                    neighbor->group_idx = group_idx;
                    neighbor->ordered = false;
                }
            }
        }
        break;
    }
}


int ChessBoardDetector::checkQuadGroup(const std::vector<ChessBoardQuad*>& quad_group, std::vector<ChessBoardCorner*>& out_corners)
{
    const int ROW1 = 1000000;
    const int ROW2 = 2000000;
    const int ROW_ = 3000000;

    int quad_count = (int)quad_group.size();

    std::vector<ChessBoardCorner*> corners(quad_count*4);
    int corner_count = 0;
    int result = 0;

    int width = 0, height = 0;
    int hist[5] = {0,0,0,0,0};
    //ChessBoardCorner* first = 0, *first2 = 0, *right, *cur, *below, *c;

    // build dual graph, which vertices are internal quad corners
    // and two vertices are connected iff they lie on the same quad edge
    for (int i = 0; i < quad_count; ++i)
    {
        ChessBoardQuad* q = quad_group[i];
        /*CvScalar color = q->count == 0 ? cvScalar(0,255,255) :
                         q->count == 1 ? cvScalar(0,0,255) :
                         q->count == 2 ? cvScalar(0,255,0) :
                         q->count == 3 ? cvScalar(255,255,0) :
                                         cvScalar(255,0,0);*/

        for (int j = 0; j < 4; ++j)
        {
            if (q->neighbors[j])
            {
                int next_j = (j + 1) & 3;
                ChessBoardCorner *a = q->corners[j], *b = q->corners[next_j];
                // mark internal corners that belong to:
                //   - a quad with a single neighbor - with ROW1,
                //   - a quad with two neighbors     - with ROW2
                // make the rest of internal corners with ROW_
                int row_flag = q->count == 1 ? ROW1 : q->count == 2 ? ROW2 : ROW_;

                if (a->row == 0)
                {
                    corners[corner_count++] = a;
                    a->row = row_flag;
                }
                else if (a->row > row_flag)
                {
                    a->row = row_flag;
                }

                if (q->neighbors[next_j])
                {
                    if (a->count >= 4 || b->count >= 4)
                        goto finalize;
                    for (int k = 0; k < 4; ++k)
                    {
                        if (a->neighbors[k] == b)
                            goto finalize;
                        if (b->neighbors[k] == a)
                            goto finalize;
                    }
                    a->neighbors[a->count++] = b;
                    b->neighbors[b->count++] = a;
                }
            }
        }
    }

    if (corner_count != pattern_size.width*pattern_size.height)
        goto finalize;

{
    ChessBoardCorner* first = NULL, *first2 = NULL;
    for (int i = 0; i < corner_count; ++i)
    {
        int n = corners[i]->count;
        CV_DbgAssert(0 <= n && n <= 4);
        hist[n]++;
        if (!first && n == 2)
        {
            if (corners[i]->row == ROW1)
                first = corners[i];
            else if (!first2 && corners[i]->row == ROW2)
                first2 = corners[i];
        }
    }

    // start with a corner that belongs to a quad with a single neighbor.
    // if we do not have such, start with a corner of a quad with two neighbors.
    if( !first )
        first = first2;

    if( !first || hist[0] != 0 || hist[1] != 0 || hist[2] != 4 ||
        hist[3] != (pattern_size.width + pattern_size.height)*2 - 8 )
        goto finalize;

    ChessBoardCorner* cur = first;
    ChessBoardCorner* right = NULL;
    ChessBoardCorner* below = NULL;
    out_corners.clear();
    out_corners.push_back(cur);

    for (int k = 0; k < 4; ++k)
    {
        ChessBoardCorner* c = cur->neighbors[k];
        if (c)
        {
            if (!right)
                right = c;
            else if (!below)
                below = c;
        }
    }

    if( !right || (right->count != 2 && right->count != 3) ||
        !below || (below->count != 2 && below->count != 3) )
        goto finalize;

    cur->row = 0;

    first = below; // remember the first corner in the next row

    // find and store the first row (or column)
    while( 1 )
    {
        right->row = 0;
        out_corners.push_back(right);
        if( right->count == 2 )
            break;
        if( right->count != 3 || (int)out_corners.size() >= std::max(pattern_size.width,pattern_size.height) )
            goto finalize;
        cur = right;
        for (int k = 0; k < 4; ++k)
        {
            ChessBoardCorner* c = cur->neighbors[k];
            if (c && c->row > 0)
            {
                int kk = 0;
                for (; kk < 4; ++kk)
                {
                    if (c->neighbors[kk] == below)
                        break;
                }
                if (kk < 4)
                    below = c;
                else
                    right = c;
            }
        }
    }

    width = (int)out_corners.size();
    if (width == pattern_size.width)
        height = pattern_size.height;
    else if (width == pattern_size.height)
        height = pattern_size.width;
    else
        goto finalize;

    // find and store all the other rows
    for (int i = 1; ; ++i)
    {
        if( !first )
            break;
        cur = first;
        first = 0;
        int j = 0;
        for (; ; ++j)
        {
            cur->row = i;
            out_corners.push_back(cur);
            if (cur->count == 2 + (i < height-1) && j > 0)
                break;

            right = 0;

            // find a neighbor that has not been processed yet
            // and that has a neighbor from the previous row
            for (int k = 0; k < 4; ++k)
            {
                ChessBoardCorner* c = cur->neighbors[k];
                if (c && c->row > i)
                {
                    int kk = 0;
                    for (; kk < 4; ++kk)
                    {
                        if (c->neighbors[kk] && c->neighbors[kk]->row == i-1)
                            break;
                    }
                    if(kk < 4)
                    {
                        right = c;
                        if (j > 0)
                            break;
                    }
                    else if (j == 0)
                        first = c;
                }
            }
            if (!right)
                goto finalize;
            cur = right;
        }

        if (j != width - 1)
            goto finalize;
    }

    if ((int)out_corners.size() != corner_count)
        goto finalize;

    // check if we need to transpose the board
    if (width != pattern_size.width)
    {
        std::swap(width, height);

        std::vector<ChessBoardCorner*> tmp(out_corners);
        for (int i = 0; i < height; ++i)
            for (int j = 0; j < width; ++j)
                out_corners[i*width + j] = tmp[j*height + i];
    }

    // check if we need to revert the order in each row
    {
        cv::Point2f p0 = out_corners[0]->pt,
                    p1 = out_corners[pattern_size.width-1]->pt,
                    p2 = out_corners[pattern_size.width]->pt;
        if( (p1.x - p0.x)*(p2.y - p1.y) - (p1.y - p0.y)*(p2.x - p1.x) < 0 )
        {
            if (width % 2 == 0)
            {
                for (int i = 0; i < height; ++i)
                    for (int j = 0; j < width/2; ++j)
                        std::swap(out_corners[i*width+j], out_corners[i*width+width-j-1]);
            }
            else
            {
                for (int j = 0; j < width; ++j)
                    for (int i = 0; i < height/2; ++i)
                        std::swap(out_corners[i*width+j], out_corners[(height - i - 1)*width+j]);
            }
        }
    }

    result = corner_count;
}

finalize:
    if (result <= 0)
    {
        corner_count = std::min(corner_count, pattern_size.area());
        out_corners.resize(corner_count);
        for (int i = 0; i < corner_count; i++)
            out_corners[i] = corners[i];

        result = -corner_count;

        if (result == -pattern_size.area())
            result = -result;
    }

    return result;
}



void ChessBoardDetector::findQuadNeighbors()
{
    const float thresh_scale = 1.f;

    const int all_corners_count = all_quads_count * 4;

    std::vector<Point2f> all_quads_pts;
    all_quads_pts.reserve(all_corners_count);
    for (int idx = 0; idx < all_quads_count; idx++)
    {
        const ChessBoardQuad& cur_quad = (const ChessBoardQuad&)all_quads[idx];
        for (int i = 0; i < 4; i++)
            all_quads_pts.push_back(cur_quad.corners[i]->pt);
    }

    const cvflann::KDTreeSingleIndexParams index_params;
    flann::GenericIndex<flann::L2_Simple<float>> all_quads_pts_index(Mat(all_quads_pts).reshape(1, all_corners_count), index_params);

    // find quad neighbors
    std::vector<int> neighbors_indices(all_corners_count);
    std::vector<float> neighbors_dists(all_corners_count);
    for (int idx = 0; idx < all_quads_count; idx++)
    {
        ChessBoardQuad& cur_quad = (ChessBoardQuad&)all_quads[idx];

        // choose the points of the current quadrangle that are close to
        // some points of the other quadrangles
        // (it can happen for split corners (due to dilation) of the
        // checker board). Search only in other quadrangles!

        // for each corner of this quadrangle
        for (int i = 0; i < 4; i++)
        {
            if (cur_quad.neighbors[i])
                continue;

            float min_dist = FLT_MAX;
            int closest_neighbor_idx = -1;
            int closest_corner_idx = -1;
            ChessBoardQuad *closest_quad = 0;

            cv::Point2f pt = all_quads_pts[(idx << 2) + i];

            // find the closest corner in all other quadrangles
            std::vector<float> query = Mat(pt);
            float radius = cur_quad.edge_len * thresh_scale + 1;
            const cvflann::SearchParams search_params(-1);
            int neighbors_count = all_quads_pts_index.radiusSearch(query, neighbors_indices, neighbors_dists, radius, search_params);

            for (int neighbor_idx_idx = 0; neighbor_idx_idx < neighbors_count; neighbor_idx_idx++)
            {
                const int neighbor_idx = neighbors_indices[neighbor_idx_idx];
                const int k = neighbor_idx >> 2;
                if (k == idx)
                    continue;

                ChessBoardQuad& q_k = all_quads[k];
                const int j = neighbor_idx & 3;
                if (q_k.neighbors[j])
                    continue;

                const float dist = normL2Sqr<float>(pt - all_quads_pts[neighbor_idx]);
                if (dist <= cur_quad.edge_len * thresh_scale &&
                    dist <= q_k.edge_len * thresh_scale)
                {
                    // check edge lengths, make sure they're compatible
                    // edges that are different by more than 1:4 are rejected.
                    // edge_len is squared edge length, so we compare them
                    // with squared constant 16 = 4^2
                    if (q_k.edge_len > 16 * cur_quad.edge_len ||
                        cur_quad.edge_len > 16 * q_k.edge_len)
                    {
                        DPRINTF("Incompatible edge lengths");
                        continue;
                    }
                    closest_neighbor_idx = neighbor_idx;
                    closest_corner_idx = j;
                    closest_quad = &q_k;
                    min_dist = dist;
                    break;
                }
            }

            // we found a matching corner point?
            if (closest_neighbor_idx >= 0 && closest_corner_idx >= 0 && min_dist < FLT_MAX)
            {
                CV_Assert(closest_quad);

                if (cur_quad.count >= 4 || closest_quad->count >= 4)
                    continue;

                // If another point from our current quad is closer to the found corner
                // than the current one, then we don't count this one after all.
                // This is necessary to support small squares where otherwise the wrong
                // corner will get matched to closest_quad;
                ChessBoardCorner& closest_corner = *closest_quad->corners[closest_corner_idx];
                cv::Point2f closest_corner_pt = all_quads_pts[closest_neighbor_idx];

                int j = 0;
                for (; j < 4; j++)
                {
                    if (cur_quad.neighbors[j] == closest_quad)
                        break;

                    if (normL2Sqr<float>(closest_corner_pt - all_quads_pts[(idx << 2) + j]) < min_dist)
                        break;
                }
                if (j < 4)
                    continue;

                // Check that each corner is a neighbor of different quads
                for(j = 0; j < 4; j++ )
                {
                    if (closest_quad->neighbors[j] == &cur_quad)
                        break;
                }
                if (j < 4)
                    continue;

                // check whether the closest corner to closest_corner is different from pt
                query = Mat(closest_corner_pt);
                radius = min_dist + 1;
                neighbors_count = all_quads_pts_index.radiusSearch(query, neighbors_indices, neighbors_dists, radius, search_params);

                int neighbor_idx_idx = 0;
                for (; neighbor_idx_idx < neighbors_count; neighbor_idx_idx++)
                {
                    const int neighbor_idx = neighbors_indices[neighbor_idx_idx];
                    j = neighbor_idx >> 2;

                    ChessBoardQuad* q = &const_cast<ChessBoardQuad&>(all_quads[j]);
                    if (j == idx || q == closest_quad)
                        continue;

                    const int k = neighbor_idx & 3;
                    CV_DbgAssert(q);
                    if (!q->neighbors[k])
                    {
                        if (normL2Sqr<float>(closest_corner_pt - all_quads_pts[neighbor_idx]) < min_dist)
                            break;
                    }
                }
                if (neighbor_idx_idx < neighbors_count)
                    continue;

                closest_corner.pt = (pt + closest_corner_pt) * 0.5f;

                // We've found one more corner - remember it
                cur_quad.count++;
                cur_quad.neighbors[i] = closest_quad;
                cur_quad.corners[i] = &closest_corner;

                closest_quad->count++;
                closest_quad->neighbors[closest_corner_idx] = &cur_quad;
            }
        }
    }
}


// returns corners in clockwise order
// corners don't necessarily start at same position on quad (e.g.,
//   top left corner)
void ChessBoardDetector::generateQuads(const cv::Mat& image_, int flags, int dilations)
{
    binarized_image = image_;  // save for debug purposes

    int quad_count = 0;

    all_quads.deallocate();
    all_corners.deallocate();

    // empiric bound for minimal allowed area for squares
    const int min_area = 25; //cvRound( image->cols * image->rows * .03 * 0.01 * 0.92 );

    bool filterQuads = (flags & CALIB_CB_FILTER_QUADS) != 0;

    std::vector<std::vector<Point> > contours;
    std::vector<Vec4i> hierarchy;

    cv::findContours(image_, contours, hierarchy, RETR_CCOMP, CHAIN_APPROX_SIMPLE);

    if (contours.empty())
    {
        CV_LOG_DEBUG(NULL, "calib3d(chessboard): cv::findContours() returns no contours");
        return;
    }

    std::vector<int> contour_child_counter(contours.size(), 0);
    int boardIdx = -1;

    std::vector<QuadCountour> contour_quads;

    for (int idx = (int)(contours.size() - 1); idx >= 0; --idx)
    {
        int parentIdx = hierarchy[idx][3];
        if (hierarchy[idx][2] != -1 || parentIdx == -1)  // holes only (no child contours and with parent)
            continue;
        const std::vector<Point>& contour = contours[idx];

        Rect contour_rect = boundingRect(contour);
        if (contour_rect.area() < min_area)
            continue;

        std::vector<Point> approx_contour = contour;

        const int min_approx_level = 1, max_approx_level = MAX_CONTOUR_APPROX;
        for (int approx_level = min_approx_level; approx_contour.size() > 4 && approx_level <= max_approx_level; approx_level++ )
        {
            approxPolyDP(approx_contour, approx_contour, (float)approx_level, true);
        }

        // reject non-quadrangles
        if (approx_contour.size() != 4)
            continue;
        if (!cv::isContourConvex(approx_contour))
            continue;

        cv::Point pt[4];
        for (int i = 0; i < 4; ++i)
            pt[i] = approx_contour[i];
        CV_LOG_VERBOSE(NULL, 9, "... contours(" << contour_quads.size() << " added):" << pt[0] << " " << pt[1] << " " << pt[2] << " " << pt[3]);

        if (filterQuads)
        {
            double p = cv::arcLength(approx_contour, true);
            double area = cv::contourArea(approx_contour, false);

            double d1 = sqrt(normL2Sqr<double>(pt[0] - pt[2]));
            double d2 = sqrt(normL2Sqr<double>(pt[1] - pt[3]));

            // philipg.  Only accept those quadrangles which are more square
            // than rectangular and which are big enough
            double d3 = sqrt(normL2Sqr<double>(pt[0] - pt[1]));
            double d4 = sqrt(normL2Sqr<double>(pt[1] - pt[2]));
            if (!(d3*4 > d4 && d4*4 > d3 && d3*d4 < area*1.5 && area > min_area &&
                d1 >= 0.15 * p && d2 >= 0.15 * p))
                continue;
        }

        contour_child_counter[parentIdx]++;
        if (boardIdx != parentIdx && (boardIdx < 0 || contour_child_counter[boardIdx] < contour_child_counter[parentIdx]))
            boardIdx = parentIdx;

        contour_quads.emplace_back(pt, parentIdx);
    }

    size_t total = contour_quads.size();
    size_t max_quad_buf_size = std::max((size_t)2, total * 3);
    all_quads.allocate(max_quad_buf_size);
    all_corners.allocate(max_quad_buf_size * 4);

    // Create array of quads structures
    for (size_t idx = 0; idx < total; ++idx)
    {
        QuadCountour& qc = contour_quads[idx];
        if (filterQuads && qc.parent_contour != boardIdx)
            continue;

        int quad_idx = quad_count++;
        ChessBoardQuad& q = all_quads[quad_idx];

        // reset group ID
        q = ChessBoardQuad();
        for (int i = 0; i < 4; ++i)
        {
            Point2f pt(qc.pt[i]);
            ChessBoardCorner& corner = all_corners[quad_idx * 4 + i];

            corner = ChessBoardCorner(pt);
            q.corners[i] = &corner;
        }
        q.edge_len = FLT_MAX;
        for (int i = 0; i < 4; ++i)
        {
            float d = normL2Sqr<float>(q.corners[i]->pt - q.corners[(i+1)&3]->pt);
            q.edge_len = std::min(q.edge_len, d);
        }

        const int edge_len_compensation = 2 * dilations;
        q.edge_len += 2 * sqrt(q.edge_len) * edge_len_compensation + edge_len_compensation * edge_len_compensation;
    }

    all_quads_count = quad_count;

    CV_LOG_VERBOSE(NULL, 3, "Total quad contours: " << total);
    CV_LOG_VERBOSE(NULL, 3, "max_quad_buf_size=" << max_quad_buf_size);
    CV_LOG_VERBOSE(NULL, 3, "filtered quad_count=" << quad_count);
}

bool ChessBoardDetector::processQuads(std::vector<cv::Point2f>& out_corners, int &prev_sqr_size)
{
    out_corners.resize(0);
    if (all_quads_count <= 0)
        return false;

    size_t max_quad_buf_size = all_quads.size();

    // Find quad's neighbors
    findQuadNeighbors();

    // allocate extra for adding in orderFoundQuads
    std::vector<ChessBoardQuad*> quad_group;
    std::vector<ChessBoardCorner*> corner_group; corner_group.reserve(max_quad_buf_size * 4);

    for (int group_idx = 0; ; group_idx++)
    {
        findConnectedQuads(quad_group, group_idx);
        if (quad_group.empty())
            break;

        int count = (int)quad_group.size();

        // order the quad corners globally
        // maybe delete or add some
        DPRINTF("Starting ordering of inner quads (%d)", count);
        count = orderFoundConnectedQuads(quad_group);
        DPRINTF("Finished ordering of inner quads (%d)", count);

        if (count == 0)
            continue;       // haven't found inner quads

        // If count is more than it should be, this will remove those quads
        // which cause maximum deviation from a nice square pattern.
        count = cleanFoundConnectedQuads(quad_group);
        DPRINTF("Connected group: %d, count: %d", group_idx, count);

        count = checkQuadGroup(quad_group, corner_group);
        DPRINTF("Connected group: %d, count: %d", group_idx, count);

        int n = count > 0 ? pattern_size.width * pattern_size.height : -count;
        n = std::min(n, pattern_size.width * pattern_size.height);
        float sum_dist = 0;
        int total = 0;

        for(int i = 0; i < n; i++ )
        {
            int ni = 0;
            float sum = corner_group[i]->sumDist(ni);
            sum_dist += sum;
            total += ni;
        }
        prev_sqr_size = cvRound(sum_dist/std::max(total, 1));

        if (count > 0 || (-count > (int)out_corners.size()))
        {
            // copy corners to output array
            out_corners.clear();
            out_corners.reserve(n);
            for (int i = 0; i < n; ++i)
                out_corners.push_back(corner_group[i]->pt);

            if (count == pattern_size.width*pattern_size.height
                    && checkBoardMonotony(out_corners))
            {
                return true;
            }
        }
    }

    return false;
}



void drawChessboardCorners( InputOutputArray image, Size patternSize,
                                InputArray _corners,
                                bool patternWasFound )
{
    CV_INSTRUMENT_REGION();

    int type = image.type();
    int cn = CV_MAT_CN(type);
    CV_CheckType(type, cn == 1 || cn == 3 || cn == 4,
            "Number of channels must be 1, 3 or 4" );

    int depth = CV_MAT_DEPTH(type);
    CV_CheckType(type, depth == CV_8U || depth == CV_16U || depth == CV_32F,
            "Only 8-bit, 16-bit or floating-point 32-bit images are supported");

    if (_corners.empty())
        return;
    Mat corners = _corners.getMat();
    const Point2f* corners_data = corners.ptr<Point2f>(0);
    CV_DbgAssert(corners_data);
    int nelems = corners.checkVector(2, CV_32F, true);
    CV_Assert(nelems >= 0);

    const int shift = 0;
    const int radius = 4;
    const int r = radius*(1 << shift);

    double scale = 1;
    switch (depth)
    {
    case CV_8U:
        scale = 1;
        break;
    case CV_16U:
        scale = 256;
        break;
    case CV_32F:
        scale = 1./255;
        break;
    }

    int line_type = (type == CV_8UC1 || type == CV_8UC3) ? LINE_AA : LINE_8;

    if (!patternWasFound)
    {
        Scalar color(0,0,255,0);
        if (cn == 1)
            color = Scalar::all(200);
        color *= scale;

        for (int i = 0; i < nelems; i++ )
        {
            cv::Point2i pt(
                    cvRound(corners_data[i].x*(1 << shift)),
                    cvRound(corners_data[i].y*(1 << shift))
            );
            line(image, Point(pt.x - r, pt.y - r), Point( pt.x + r, pt.y + r), color, 1, line_type, shift);
            line(image, Point(pt.x - r, pt.y + r), Point( pt.x + r, pt.y - r), color, 1, line_type, shift);
            circle(image, pt, r+(1<<shift), color, 1, line_type, shift);
        }
    }
    else
    {
        const int line_max = 7;
        static const int line_colors[line_max][4] =
        {
            {0,0,255,0},
            {0,128,255,0},
            {0,200,200,0},
            {0,255,0,0},
            {200,200,0,0},
            {255,0,0,0},
            {255,0,255,0}
        };

        cv::Point2i prev_pt;
        for (int y = 0, i = 0; y < patternSize.height; y++)
        {
            const int* line_color = &line_colors[y % line_max][0];
            Scalar color(line_color[0], line_color[1], line_color[2], line_color[3]);
            if (cn == 1)
                color = Scalar::all(200);
            color *= scale;

            for (int x = 0; x < patternSize.width; x++, i++)
            {
                cv::Point2i pt(
                        cvRound(corners_data[i].x*(1 << shift)),
                        cvRound(corners_data[i].y*(1 << shift))
                );

                if (i != 0)
                    line(image, prev_pt, pt, color, 1, line_type, shift);

                line(image, Point(pt.x - r, pt.y - r), Point( pt.x + r, pt.y + r), color, 1, line_type, shift);
                line(image, Point(pt.x - r, pt.y + r), Point( pt.x + r, pt.y - r), color, 1, line_type, shift);
                circle(image, pt, r+(1<<shift), color, 1, line_type, shift);
                prev_pt = pt;
            }
        }
    }
}

bool findCirclesGrid( InputArray _image, Size patternSize,
                          OutputArray _centers, int flags, const Ptr<FeatureDetector> &blobDetector,
                          const CirclesGridFinderParameters& parameters_)
{
    CV_INSTRUMENT_REGION();

    CirclesGridFinderParameters parameters = parameters_; // parameters.gridType is amended below

    bool isAsymmetricGrid = (flags & CALIB_CB_ASYMMETRIC_GRID) ? true : false;
    bool isSymmetricGrid  = (flags & CALIB_CB_SYMMETRIC_GRID ) ? true : false;
    CV_Assert(isAsymmetricGrid ^ isSymmetricGrid);

    std::vector<Point2f> centers;

    std::vector<Point2f> points;
    if (blobDetector)
    {
        std::vector<KeyPoint> keypoints;
        blobDetector->detect(_image, keypoints);
        for (size_t i = 0; i < keypoints.size(); i++)
        {
            points.push_back(keypoints[i].pt);
        }
    }
    else
    {
        CV_CheckTypeEQ(_image.type(), CV_32FC2, "blobDetector must be provided or image must contains Point2f array (std::vector<Point2f>) with candidates");
        _image.copyTo(points);
    }

    if(flags & CALIB_CB_ASYMMETRIC_GRID)
      parameters.gridType = CirclesGridFinderParameters::ASYMMETRIC_GRID;
    if(flags & CALIB_CB_SYMMETRIC_GRID)
      parameters.gridType = CirclesGridFinderParameters::SYMMETRIC_GRID;

    if(flags & CALIB_CB_CLUSTERING)
    {
      CirclesGridClusterFinder circlesGridClusterFinder(parameters);
      circlesGridClusterFinder.findGrid(points, patternSize, centers);
      Mat(centers).copyTo(_centers);
      return !centers.empty();
    }

    bool isValid = false;
    const int attempts = 2;
    const size_t minHomographyPoints = 4;
    Mat H;
    for (int i = 0; i < attempts; i++)
    {
        centers.clear();
        CirclesGridFinder boxFinder(patternSize, points, parameters);
        try
        {
            bool isFound = boxFinder.findHoles();
            if (isFound)
            {
                switch(parameters.gridType)
                {
                case CirclesGridFinderParameters::SYMMETRIC_GRID:
                    boxFinder.getHoles(centers);
                    break;
                case CirclesGridFinderParameters::ASYMMETRIC_GRID:
                    boxFinder.getAsymmetricHoles(centers);
                    break;
                default:
                    CV_Error(Error::StsBadArg, "Unknown pattern type");
                }

                isValid = true;
                break;  // done, return result
            }
        }
        catch (const cv::Exception& e)
        {
            CV_UNUSED(e);
            CV_LOG_DEBUG(NULL, "findCirclesGrid2: attempt=" << i << ": " << e.what());
            // nothing, next attempt
        }

        boxFinder.getHoles(centers);
        if (i != attempts - 1)
        {
            if (centers.size() < minHomographyPoints)
                break;
            H = CirclesGridFinder::rectifyGrid(boxFinder.getDetectedGridSize(), centers, points, points);
        }
    }

    if (!centers.empty() && !H.empty())  // undone rectification
    {
        Mat orgPointsMat;
        transform(centers, orgPointsMat, H.inv());
        convertPointsFromHomogeneous(orgPointsMat, centers);
    }
    Mat(centers).copyTo(_centers);
    return isValid;
}

bool findCirclesGrid(InputArray _image, Size patternSize,
                     OutputArray _centers, int flags, const Ptr<FeatureDetector> &blobDetector)
{
    return cv::findCirclesGrid(_image, patternSize, _centers, flags, blobDetector, CirclesGridFinderParameters());
}

} // namespace
/* End of file. */