LSD（line segment detect）基于opencv的代码

博主研究生阶段一直在研究LSD算法，先马出 LSD基于opencv的源代码。

另外链接：http://demo.ipol.im/demo/gjmr_line_segment_detector/

给出了LSD论文的demo和article。

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#include "precomp.hpp"
#include <vector>

/////////////////////////////////////////////////////////////////////////////////////////
// Default LSD parameters
// SIGMA_SCALE 0.6    - Sigma for Gaussian filter is computed as sigma = sigma_scale/scale.
// QUANT       2.0    - Bound to the quantization error on the gradient norm.
// ANG_TH      22.5   - Gradient angle tolerance in degrees.
// LOG_EPS     0.0    - Detection threshold: -log10(NFA) > log_eps
// DENSITY_TH  0.7    - Minimal density of region points in rectangle.
// N_BINS      1024   - Number of bins in pseudo-ordering of gradient modulus.

#define M_3_2_PI    (3 * CV_PI) / 2   // 3/2 pi
#define M_2__PI     (2 * CV_PI)         // 2 pi

#ifndef M_LN10
#define M_LN10      2.30258509299404568402
#endif

#define NOTDEF      double(-1024.0) // Label for pixels with undefined gradient.

#define NOTUSED     0   // Label for pixels not used in yet.
#define USED        1   // Label for pixels already used in detection.

#define RELATIVE_ERROR_FACTOR 100.0

const double DEG_TO_RADS = CV_PI / 180;

#define log_gamma(x) ((x)>15.0?log_gamma_windschitl(x):log_gamma_lanczos(x))

struct edge
{
cv::Point p;
bool taken;
};

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

inline double distSq(const double x1, const double y1,
const double x2, const double y2)
{
return (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1);
}

inline double dist(const double x1, const double y1,
const double x2, const double y2)
{
return sqrt(distSq(x1, y1, x2, y2));
}

// Signed angle difference
inline double angle_diff_signed(const double& a, const double& b)
{
double diff = a - b;
while(diff <= -CV_PI) diff += M_2__PI;
while(diff >   CV_PI) diff -= M_2__PI;
return diff;
}

// Absolute value angle difference
inline double angle_diff(const double& a, const double& b)
{
return std::fabs(angle_diff_signed(a, b));
}

// Compare doubles by relative error.
inline bool double_equal(const double& a, const double& b)
{
// trivial case
if(a == b) return true;

double abs_diff = fabs(a - b);
double aa = fabs(a);
double bb = fabs(b);
double abs_max = (aa > bb)? aa : bb;

if(abs_max < DBL_MIN) abs_max = DBL_MIN;

return (abs_diff / abs_max) <= (RELATIVE_ERROR_FACTOR * DBL_EPSILON);
}

inline bool AsmallerB_XoverY(const edge& a, const edge& b)
{
if (a.p.x == b.p.x) return a.p.y < b.p.y;
else return a.p.x < b.p.x;
}

/**
*   Computes the natural logarithm of the absolute value of
*   the gamma function of x using Windschitl method.
*   See http://www.rskey.org/gamma.htm */
inline double log_gamma_windschitl(const double& x)
{
return 0.918938533204673 + (x-0.5)*log(x) - x
+ 0.5*x*log(x*sinh(1/x) + 1/(810.0*pow(x, 6.0)));
}

/**
*   Computes the natural logarithm of the absolute value of
*   the gamma function of x using the Lanczos approximation.
*   See http://www.rskey.org/gamma.htm */
inline double log_gamma_lanczos(const double& x)
{
static double q[7] = { 75122.6331530, 80916.6278952, 36308.2951477,
8687.24529705, 1168.92649479, 83.8676043424,
2.50662827511 };
double a = (x + 0.5) * log(x + 5.5) - (x + 5.5);
double b = 0;
for(int n = 0; n < 7; ++n)
{
a -= log(x + double(n));
b += q
* pow(x, double(n));
}
return a + log(b);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////

namespace cv{

class LineSegmentDetectorImpl : public LineSegmentDetector
{
public:

/**
* Create a LineSegmentDetectorImpl object. Specifying scale, number of subdivisions for the image, should the lines be refined and other constants as follows:
*
* @param _refine       How should the lines found be refined?
*                      LSD_REFINE_NONE - No refinement applied.
*                      LSD_REFINE_STD  - Standard refinement is applied. E.g. breaking arches into smaller line approximations.
*                      LSD_REFINE_ADV  - Advanced refinement. Number of false alarms is calculated,
*                                    lines are refined through increase of precision, decrement in size, etc.
* @param _scale        The scale of the image that will be used to find the lines. Range (0..1].
* @param _sigma_scale  Sigma for Gaussian filter is computed as sigma = _sigma_scale/_scale.
* @param _quant        Bound to the quantization error on the gradient norm.
* @param _ang_th       Gradient angle tolerance in degrees.
* @param _log_eps      Detection threshold: -log10(NFA) > _log_eps
* @param _density_th   Minimal density of aligned region points in rectangle.
* @param _n_bins       Number of bins in pseudo-ordering of gradient modulus.
*/
LineSegmentDetectorImpl(int _refine = LSD_REFINE_STD, double _scale = 0.8,
double _sigma_scale = 0.6, double _quant = 2.0, double _ang_th = 22.5,
double _log_eps = 0, double _density_th = 0.7, int _n_bins = 1024);

/**
* Detect lines in the input image.
*
* @param _image    A grayscale(CV_8UC1) input image.
*                  If only a roi needs to be selected, use
*                  lsd_ptr->detect(image(roi), ..., lines);
*                  lines += Scalar(roi.x, roi.y, roi.x, roi.y);
* @param _lines    Return: A vector of Vec4i or Vec4f elements specifying the beginning and ending point of a line.
*                          Where Vec4i/Vec4f is (x1, y1, x2, y2), point 1 is the start, point 2 - end.
*                          Returned lines are strictly oriented depending on the gradient.
* @param width     Return: Vector of widths of the regions, where the lines are found. E.g. Width of line.
* @param prec      Return: Vector of precisions with which the lines are found.
* @param nfa       Return: Vector containing number of false alarms in the line region, with precision of 10%.
*                          The bigger the value, logarithmically better the detection.
*                              * -1 corresponds to 10 mean false alarms
*                              * 0 corresponds to 1 mean false alarm
*                              * 1 corresponds to 0.1 mean false alarms
*                          This vector will be calculated _only_ when the objects type is REFINE_ADV
*/
void detect(InputArray _image, OutputArray _lines,
OutputArray width = noArray(), OutputArray prec = noArray(),
OutputArray nfa = noArray());

/**
* Draw lines on the given canvas.
*
* @param image     The image, where lines will be drawn.
*                  Should have the size of the image, where the lines were found
* @param lines     The lines that need to be drawn
*/
void drawSegments(InputOutputArray _image, InputArray lines);

/**
* Draw both vectors on the image canvas. Uses blue for lines 1 and red for lines 2.
*
* @param size      The size of the image, where lines1 and lines2 were found.
* @param lines1    The first lines that need to be drawn. Color - Blue.
* @param lines2    The second lines that need to be drawn. Color - Red.
* @param image     An optional image, where lines will be drawn.
*                  Should have the size of the image, where the lines were found
* @return          The number of mismatching pixels between lines1 and lines2.
*/
int compareSegments(const Size& size, InputArray lines1, InputArray lines2, InputOutputArray _image = noArray());

private:
Mat image;
Mat_<double> scaled_image;
double *scaled_image_data;
Mat_<double> angles;     // in rads
double *angles_data;
Mat_<double> modgrad;
double *modgrad_data;
Mat_<uchar> used;

int img_width;
int img_height;
double LOG_NT;

bool w_needed;
bool p_needed;
bool n_needed;

const double SCALE;
const int doRefine;
const double SIGMA_SCALE;
const double QUANT;
const double ANG_TH;
const double LOG_EPS;
const double DENSITY_TH;
const int N_BINS;

struct RegionPoint {
int x;
int y;
uchar* used;
double angle;
double modgrad;
};

struct coorlist
{
Point2i p;
struct coorlist* next;
};

struct rect
{
double x1, y1, x2, y2;    // first and second point of the line segment
double width;             // rectangle width
double x, y;              // center of the rectangle
double theta;             // angle
double dx,dy;             // (dx,dy) is vector oriented as the line segment
double prec;              // tolerance angle
double p;                 // probability of a point with angle within 'prec'
};

LineSegmentDetectorImpl& operator= (const LineSegmentDetectorImpl&); // to quiet MSVC

/**
* Detect lines in the whole input image.
*
* @param lines         Return: A vector of Vec4f elements specifying the beginning and ending point of a line.
*                              Where Vec4f is (x1, y1, x2, y2), point 1 is the start, point 2 - end.
*                              Returned lines are strictly oriented depending on the gradient.
* @param widths        Return: Vector of widths of the regions, where the lines are found. E.g. Width of line.
* @param precisions    Return: Vector of precisions with which the lines are found.
* @param nfas          Return: Vector containing number of false alarms in the line region, with precision of 10%.
*                              The bigger the value, logarithmically better the detection.
*                                  * -1 corresponds to 10 mean false alarms
*                                  * 0 corresponds to 1 mean false alarm
*                                  * 1 corresponds to 0.1 mean false alarms
*/
void flsd(std::vector<Vec4f>& lines,
std::vector<double>& widths, std::vector<double>& precisions,
std::vector<double>& nfas);

/**
* Finds the angles and the gradients of the image. Generates a list of pseudo ordered points.
*
* @param threshold The minimum value of the angle that is considered defined, otherwise NOTDEF
* @param n_bins    The number of bins with which gradients are ordered by, using bucket sort.
* @param list      Return: Vector of coordinate points that are pseudo ordered by magnitude.
*                  Pixels would be ordered by norm value, up to a precision given by max_grad/n_bins.
*/
void ll_angle(const double& threshold, const unsigned int& n_bins, std::vector<coorlist>& list);

/**
* Grow a region starting from point s with a defined precision,
* returning the containing points size and the angle of the gradients.
*
* @param s         Starting point for the region.
* @param reg       Return: Vector of points, that are part of the region
* @param reg_size  Return: The size of the region.
* @param reg_angle Return: The mean angle of the region.
* @param prec      The precision by which each region angle should be aligned to the mean.
*/
void region_grow(const Point2i& s, std::vector<RegionPoint>& reg,
int& reg_size, double& reg_angle, const double& prec);

/**
* Finds the bounding rotated rectangle of a region.
*
* @param reg       The region of points, from which the rectangle to be constructed from.
* @param reg_size  The number of points in the region.
* @param reg_angle The mean angle of the region.
* @param prec      The precision by which points were found.
* @param p         Probability of a point with angle within 'prec'.
* @param rec       Return: The generated rectangle.
*/
void region2rect(const std::vector<RegionPoint>& reg, const int reg_size, const double reg_angle,
const double prec, const double p, rect& rec) const;

/**
* Compute region's angle as the principal inertia axis of the region.
* @return          Regions angle.
*/
double get_theta(const std::vector<RegionPoint>& reg, const int& reg_size, const double& x,
const double& y, const double& reg_angle, const double& prec) const;

/**
* An estimation of the angle tolerance is performed by the standard deviation of the angle at points
* near the region's starting point. Then, a new region is grown starting from the same point, but using the
* estimated angle tolerance. If this fails to produce a rectangle with the right density of region points,
* 'reduce_region_radius' is called to try to satisfy this condition.
*/
bool refine(std::vector<RegionPoint>& reg, int& reg_size, double reg_angle,
const double prec, double p, rect& rec, const double& density_th);

/**
* Reduce the region size, by elimination the points far from the starting point, until that leads to
* rectangle with the right density of region points or to discard the region if too small.
*/
bool reduce_region_radius(std::vector<RegionPoint>& reg, int& reg_size, double reg_angle,
const double prec, double p, rect& rec, double density, const double& density_th);

/**
* Try some rectangles variations to improve NFA value. Only if the rectangle is not meaningful (i.e., log_nfa <= log_eps).
* @return      The new NFA value.
*/
double rect_improve(rect& rec) const;

/**
* Calculates the number of correctly aligned points within the rectangle.
* @return      The new NFA value.
*/
double rect_nfa(const rect& rec) const;

/**
* Computes the NFA values based on the total number of points, points that agree.
* n, k, p are the binomial parameters.
* @return      The new NFA value.
*/
double nfa(const int& n, const int& k, const double& p) const;

/**
* Is the point at place 'address' aligned to angle theta, up to precision 'prec'?
* @return      Whether the point is aligned.
*/
bool isAligned(const int& address, const double& theta, const double& prec) const;
};

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

CV_EXPORTS Ptr<LineSegmentDetector> createLineSegmentDetector(
int _refine, double _scale, double _sigma_scale, double _quant, double _ang_th,
double _log_eps, double _density_th, int _n_bins)
{
return makePtr<LineSegmentDetectorImpl>(
_refine, _scale, _sigma_scale, _quant, _ang_th,
_log_eps, _density_th, _n_bins);
}

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

LineSegmentDetectorImpl::LineSegmentDetectorImpl(int _refine, double _scale, double _sigma_scale, double _quant,
double _ang_th, double _log_eps, double _density_th, int _n_bins)
:SCALE(_scale), doRefine(_refine), SIGMA_SCALE(_sigma_scale), QUANT(_quant),
ANG_TH(_ang_th), LOG_EPS(_log_eps), DENSITY_TH(_density_th), N_BINS(_n_bins)
{
CV_Assert(_scale > 0 && _sigma_scale > 0 && _quant >= 0 &&
_ang_th > 0 && _ang_th < 180 && _density_th >= 0 && _density_th < 1 &&
_n_bins > 0);
}

void LineSegmentDetectorImpl::detect(InputArray _image, OutputArray _lines,
OutputArray _width, OutputArray _prec, OutputArray _nfa)
{
Mat_<double> img = _image.getMat();
CV_Assert(!img.empty() && img.channels() == 1);

// Convert image to double
img.convertTo(image, CV_64FC1);

std::vector<Vec4f> lines;
std::vector<double> w, p, n;
w_needed = _width.needed();
p_needed = _prec.needed();
if (doRefine < LSD_REFINE_ADV)
n_needed = false;
else
n_needed = _nfa.needed();

flsd(lines, w, p, n);

Mat(lines).copyTo(_lines);
if(w_needed) Mat(w).copyTo(_width);
if(p_needed) Mat(p).copyTo(_prec);
if(n_needed) Mat(n).copyTo(_nfa);
}

void LineSegmentDetectorImpl::flsd(std::vector<Vec4f>& lines,
std::vector<double>& widths, std::vector<double>& precisions,
std::vector<double>& nfas)
{
// Angle tolerance
const double prec = CV_PI * ANG_TH / 180;
const double p = ANG_TH / 180;
const double rho = QUANT / sin(prec);    // gradient magnitude threshold

std::vector<coorlist> list;
if(SCALE != 1)
{
Mat gaussian_img;
const double sigma = (SCALE < 1)?(SIGMA_SCALE / SCALE):(SIGMA_SCALE);
const double sprec = 3;
const unsigned int h =  (unsigned int)(ceil(sigma * sqrt(2 * sprec * log(10.0))));
Size ksize(1 + 2 * h, 1 + 2 * h); // kernel size
GaussianBlur(image, gaussian_img, ksize, sigma);
// Scale image to needed size
resize(gaussian_img, scaled_image, Size(), SCALE, SCALE);
ll_angle(rho, N_BINS, list);
}
else
{
scaled_image = image;
ll_angle(rho, N_BINS, list);
}

LOG_NT = 5 * (log10(double(img_width)) + log10(double(img_height))) / 2 + log10(11.0);
const int min_reg_size = int(-LOG_NT/log10(p)); // minimal number of points in region that can give a meaningful event

// // Initialize region only when needed
// Mat region = Mat::zeros(scaled_image.size(), CV_8UC1);
used = Mat_<uchar>::zeros(scaled_image.size()); // zeros = NOTUSED
std::vector<RegionPoint> reg(img_width * img_height);

// Search for line segments
unsigned int ls_count = 0;
for(size_t i = 0, list_size = list.size(); i < list_size; ++i)
{
unsigned int adx = list[i].p.x + list[i].p.y * img_width;
if((used.ptr()[adx] == NOTUSED) && (angles_data[adx] != NOTDEF))
{
int reg_size;
double reg_angle;
region_grow(list[i].p, reg, reg_size, reg_angle, prec);

// Ignore small regions
if(reg_size < min_reg_size) { continue; }

// Construct rectangular approximation for the region
rect rec;
region2rect(reg, reg_size, reg_angle, prec, p, rec);

double log_nfa = -1;
if(doRefine > LSD_REFINE_NONE)
{
// At least REFINE_STANDARD lvl.
if(!refine(reg, reg_size, reg_angle, prec, p, rec, DENSITY_TH)) { continue; }

if(doRefine >= LSD_REFINE_ADV)
{
// Compute NFA
log_nfa = rect_improve(rec);
if(log_nfa <= LOG_EPS) { continue; }
}
}
// Found new line
++ls_count;

// Add the offset
rec.x1 += 0.5; rec.y1 += 0.5;
rec.x2 += 0.5; rec.y2 += 0.5;

// scale the result values if a sub-sampling was performed
if(SCALE != 1)
{
rec.x1 /= SCALE; rec.y1 /= SCALE;
rec.x2 /= SCALE; rec.y2 /= SCALE;
rec.width /= SCALE;
}

//Store the relevant data
lines.push_back(Vec4f(float(rec.x1), float(rec.y1), float(rec.x2), float(rec.y2)));
if(w_needed) widths.push_back(rec.width);
if(p_needed) precisions.push_back(rec.p);
if(n_needed && doRefine >= LSD_REFINE_ADV) nfas.push_back(log_nfa);

// //Add the linesID to the region on the image
// for(unsigned int el = 0; el < reg_size; el++)
// {
//     region.data[reg[i].x + reg[i].y * width] = ls_count;
// }
}
}
}

void LineSegmentDetectorImpl::ll_angle(const double& threshold,
const unsigned int& n_bins,
std::vector<coorlist>& list)
{
//Initialize data
angles = Mat_<double>(scaled_image.size());
modgrad = Mat_<double>(scaled_image.size());

angles_data = angles.ptr<double>(0);
modgrad_data = modgrad.ptr<double>(0);
scaled_image_data = scaled_image.ptr<double>(0);

img_width = scaled_image.cols;
img_height = scaled_image.rows;

// Undefined the down and right boundaries
angles.row(img_height - 1).setTo(NOTDEF);
angles.col(img_width - 1).setTo(NOTDEF);

// Computing gradient for remaining pixels
CV_Assert(scaled_image.isContinuous() &&
modgrad.isContinuous() &&
angles.isContinuous());   // Accessing image data linearly

double max_grad = -1;
for(int y = 0; y < img_height - 1; ++y)
{
for(int addr = y * img_width, addr_end = addr + img_width - 1; addr < addr_end; ++addr)
{
double DA = scaled_image_data[addr + img_width + 1] - scaled_image_data[addr];
double BC = scaled_image_data[addr + 1] - scaled_image_data[addr + img_width];
double gx = DA + BC;    // gradient x component
double gy = DA - BC;    // gradient y component
double norm = std::sqrt((gx * gx + gy * gy) / 4); // gradient norm

modgrad_data[addr] = norm;    // store gradient

if (norm <= threshold)  // norm too small, gradient no defined
{
angles_data[addr] = NOTDEF;
}
else
{
angles_data[addr] = fastAtan2(float(gx), float(-gy)) * DEG_TO_RADS;  // gradient angle computation
if (norm > max_grad) { max_grad = norm; }
}

}
}

// Compute histogram of gradient values
list = std::vector<coorlist>(img_width * img_height);
std::vector<coorlist*> range_s(n_bins);
std::vector<coorlist*> range_e(n_bins);
unsigned int count = 0;
double bin_coef = (max_grad > 0) ? double(n_bins - 1) / max_grad : 0; // If all image is smooth, max_grad <= 0

for(int y = 0; y < img_height - 1; ++y)
{
const double* norm = modgrad_data + y * img_width;
for(int x = 0; x < img_width - 1; ++x, ++norm)
{
// Store the point in the right bin according to its norm
int i = int((*norm) * bin_coef);
if(!range_e[i])
{
range_e[i] = range_s[i] = &list[count];
++count;
}
else
{
range_e[i]->next = &list[count];
range_e[i] = &list[count];
++count;
}
range_e[i]->p = Point(x, y);
range_e[i]->next = 0;
}
}

// Sort
int idx = n_bins - 1;
for(;idx > 0 && !range_s[idx]; --idx);
coorlist* start = range_s[idx];
coorlist* end = range_e[idx];
if(start)
{
while(idx > 0)
{
--idx;
if(range_s[idx])
{
end->next = range_s[idx];
end = range_e[idx];
}
}
}
}

void LineSegmentDetectorImpl::region_grow(const Point2i& s, std::vector<RegionPoint>& reg,
int& reg_size, double& reg_angle, const double& prec)
{
// Point to this region
reg_size = 1;
reg[0].x = s.x;
reg[0].y = s.y;
int addr = s.x + s.y * img_width;
reg[0].used = used.ptr() + addr;
reg_angle = angles_data[addr];
reg[0].angle = reg_angle;
reg[0].modgrad = modgrad_data[addr];

float sumdx = float(std::cos(reg_angle));
float sumdy = float(std::sin(reg_angle));
*reg[0].used = USED;

//Try neighboring regions
for(int i = 0; i < reg_size; ++i)
{
const RegionPoint& rpoint = reg[i];
int xx_min = std::max(rpoint.x - 1, 0), xx_max = std::min(rpoint.x + 1, img_width - 1);
int yy_min = std::max(rpoint.y - 1, 0), yy_max = std::min(rpoint.y + 1, img_height - 1);
for(int yy = yy_min; yy <= yy_max; ++yy)
{
int c_addr = xx_min + yy * img_width;
for(int xx = xx_min; xx <= xx_max; ++xx, ++c_addr)
{
if((used.ptr()[c_addr] != USED) &&
(isAligned(c_addr, reg_angle, prec)))
{
// Add point
used.ptr()[c_addr] = USED;
RegionPoint& region_point = reg[reg_size];
region_point.x = xx;
region_point.y = yy;
region_point.used = &(used.ptr()[c_addr]);
region_point.modgrad = modgrad_data[c_addr];
const double& angle = angles_data[c_addr];
region_point.angle = angle;
++reg_size;

// Update region's angle
sumdx += cos(float(angle));
sumdy += sin(float(angle));
// reg_angle is used in the isAligned, so it needs to be updates?
reg_angle = fastAtan2(sumdy, sumdx) * DEG_TO_RADS;
}
}
}
}
}

void LineSegmentDetectorImpl::region2rect(const std::vector<RegionPoint>& reg, const int reg_size,
const double reg_angle, const double prec, const double p, rect& rec) const
{
double x = 0, y = 0, sum = 0;
for(int i = 0; i < reg_size; ++i)
{
const RegionPoint& pnt = reg[i];
const double& weight = pnt.modgrad;
x += double(pnt.x) * weight;
y += double(pnt.y) * weight;
sum += weight;
}

// Weighted sum must differ from 0
CV_Assert(sum > 0);

x /= sum;
y /= sum;

double theta = get_theta(reg, reg_size, x, y, reg_angle, prec);

// Find length and width
double dx = cos(theta);
double dy = sin(theta);
double l_min = 0, l_max = 0, w_min = 0, w_max = 0;

for(int i = 0; i < reg_size; ++i)
{
double regdx = double(reg[i].x) - x;
double regdy = double(reg[i].y) - y;

double l = regdx * dx + regdy * dy;
double w = -regdx * dy + regdy * dx;

if(l > l_max) l_max = l;
else if(l < l_min) l_min = l;
if(w > w_max) w_max = w;
else if(w < w_min) w_min = w;
}

// Store values
rec.x1 = x + l_min * dx;
rec.y1 = y + l_min * dy;
rec.x2 = x + l_max * dx;
rec.y2 = y + l_max * dy;
rec.width = w_max - w_min;
rec.x = x;
rec.y = y;
rec.theta = theta;
rec.dx = dx;
rec.dy = dy;
rec.prec = prec;
rec.p = p;

// Min width of 1 pixel
if(rec.width < 1.0) rec.width = 1.0;
}

double LineSegmentDetectorImpl::get_theta(const std::vector<RegionPoint>& reg, const int& reg_size, const double& x,
const double& y, const double& reg_angle, const double& prec) const
{
double Ixx = 0.0;
double Iyy = 0.0;
double Ixy = 0.0;

// Compute inertia matrix
for(int i = 0; i < reg_size; ++i)
{
const double& regx = reg[i].x;
const double& regy = reg[i].y;
const double& weight = reg[i].modgrad;
double dx = regx - x;
double dy = regy - y;
Ixx += dy * dy * weight;
Iyy += dx * dx * weight;
Ixy -= dx * dy * weight;
}

// Check if inertia matrix is null
CV_Assert(!(double_equal(Ixx, 0) && double_equal(Iyy, 0) && double_equal(Ixy, 0)));

// Compute smallest eigenvalue
double lambda = 0.5 * (Ixx + Iyy - sqrt((Ixx - Iyy) * (Ixx - Iyy) + 4.0 * Ixy * Ixy));

// Compute angle
double theta = (fabs(Ixx)>fabs(Iyy))?
double(fastAtan2(float(lambda - Ixx), float(Ixy))):
double(fastAtan2(float(Ixy), float(lambda - Iyy))); // in degs
theta *= DEG_TO_RADS;

// Correct angle by 180 deg if necessary
if(angle_diff(theta, reg_angle) > prec) { theta += CV_PI; }

return theta;
}

bool LineSegmentDetectorImpl::refine(std::vector<RegionPoint>& reg, int& reg_size, double reg_angle,
const double prec, double p, rect& rec, const double& density_th)
{
double density = double(reg_size) / (dist(rec.x1, rec.y1, rec.x2, rec.y2) * rec.width);

if (density >= density_th) { return true; }

// Try to reduce angle tolerance
double xc = double(reg[0].x);
double yc = double(reg[0].y);
const double& ang_c = reg[0].angle;
double sum = 0, s_sum = 0;
int n = 0;

for (int i = 0; i < reg_size; ++i)
{
*(reg[i].used) = NOTUSED;
if (dist(xc, yc, reg[i].x, reg[i].y) < rec.width)
{
const double& angle = reg[i].angle;
double ang_d = angle_diff_signed(angle, ang_c);
sum += ang_d;
s_sum += ang_d * ang_d;
++n;
}
}
double mean_angle = sum / double(n);
// 2 * standard deviation
double tau = 2.0 * sqrt((s_sum - 2.0 * mean_angle * sum) / double(n) + mean_angle * mean_angle);

// Try new region
region_grow(Point(reg[0].x, reg[0].y), reg, reg_size, reg_angle, tau);

if (reg_size < 2) { return false; }

region2rect(reg, reg_size, reg_angle, prec, p, rec);
density = double(reg_size) / (dist(rec.x1, rec.y1, rec.x2, rec.y2) * rec.width);

if (density < density_th)
{
return reduce_region_radius(reg, reg_size, reg_angle, prec, p, rec, density, density_th);
}
else
{
return true;
}
}

bool LineSegmentDetectorImpl::reduce_region_radius(std::vector<RegionPoint>& reg, int& reg_size, double reg_angle,
const double prec, double p, rect& rec, double density, const double& density_th)
{
// Compute region's radius
double xc = double(reg[0].x);
double yc = double(reg[0].y);
double radSq1 = distSq(xc, yc, rec.x1, rec.y1);
double radSq2 = distSq(xc, yc, rec.x2, rec.y2);
double radSq = radSq1 > radSq2 ? radSq1 : radSq2;

while(density < density_th)
{
radSq *= 0.75*0.75; // Reduce region's radius to 75% of its value
// Remove points from the region and update 'used' map
for(int i = 0; i < reg_size; ++i)
{
if(distSq(xc, yc, double(reg[i].x), double(reg[i].y)) > radSq)
{
// Remove point from the region
*(reg[i].used) = NOTUSED;
std::swap(reg[i], reg[reg_size - 1]);
--reg_size;
--i; // To avoid skipping one point
}
}

if(reg_size < 2) { return false; }

// Re-compute rectangle
region2rect(reg, reg_size ,reg_angle, prec, p, rec);

// Re-compute region points density
density = double(reg_size) /
(dist(rec.x1, rec.y1, rec.x2, rec.y2) * rec.width);
}

return true;
}

double LineSegmentDetectorImpl::rect_improve(rect& rec) const
{
double delta = 0.5;
double delta_2 = delta / 2.0;

double log_nfa = rect_nfa(rec);

if(log_nfa > LOG_EPS) return log_nfa; // Good rectangle

// Try to improve
// Finer precision
rect r = rect(rec); // Copy
for(int n = 0; n < 5; ++n)
{
r.p /= 2;
r.prec = r.p * CV_PI;
double log_nfa_new = rect_nfa(r);
if(log_nfa_new > log_nfa)
{
log_nfa = log_nfa_new;
rec = rect(r);
}
}
if(log_nfa > LOG_EPS) return log_nfa;

// Try to reduce width
r = rect(rec);
for(unsigned int n = 0; n < 5; ++n)
{
if((r.width - delta) >= 0.5)
{
r.width -= delta;
double log_nfa_new = rect_nfa(r);
if(log_nfa_new > log_nfa)
{
rec = rect(r);
log_nfa = log_nfa_new;
}
}
}
if(log_nfa > LOG_EPS) return log_nfa;

// Try to reduce one side of rectangle
r = rect(rec);
for(unsigned int n = 0; n < 5; ++n)
{
if((r.width - delta) >= 0.5)
{
r.x1 += -r.dy * delta_2;
r.y1 +=  r.dx * delta_2;
r.x2 += -r.dy * delta_2;
r.y2 +=  r.dx * delta_2;
r.width -= delta;
double log_nfa_new = rect_nfa(r);
if(log_nfa_new > log_nfa)
{
rec = rect(r);
log_nfa = log_nfa_new;
}
}
}
if(log_nfa > LOG_EPS) return log_nfa;

// Try to reduce other side of rectangle
r = rect(rec);
for(unsigned int n = 0; n < 5; ++n)
{
if((r.width - delta) >= 0.5)
{
r.x1 -= -r.dy * delta_2;
r.y1 -=  r.dx * delta_2;
r.x2 -= -r.dy * delta_2;
r.y2 -=  r.dx * delta_2;
r.width -= delta;
double log_nfa_new = rect_nfa(r);
if(log_nfa_new > log_nfa)
{
rec = rect(r);
log_nfa = log_nfa_new;
}
}
}
if(log_nfa > LOG_EPS) return log_nfa;

// Try finer precision
r = rect(rec);
for(unsigned int n = 0; n < 5; ++n)
{
if((r.width - delta) >= 0.5)
{
r.p /= 2;
r.prec = r.p * CV_PI;
double log_nfa_new = rect_nfa(r);
if(log_nfa_new > log_nfa)
{
rec = rect(r);
log_nfa = log_nfa_new;
}
}
}

return log_nfa;
}

double LineSegmentDetectorImpl::rect_nfa(const rect& rec) const
{
int total_pts = 0, alg_pts = 0;
double half_width = rec.width / 2.0;
double dyhw = rec.dy * half_width;
double dxhw = rec.dx * half_width;

std::vector<edge> ordered_x(4);
edge* min_y = &ordered_x[0];
edge* max_y = &ordered_x[0]; // Will be used for loop range

ordered_x[0].p.x = int(rec.x1 - dyhw); ordered_x[0].p.y = int(rec.y1 + dxhw); ordered_x[0].taken = false;
ordered_x[1].p.x = int(rec.x2 - dyhw); ordered_x[1].p.y = int(rec.y2 + dxhw); ordered_x[1].taken = false;
ordered_x[2].p.x = int(rec.x2 + dyhw); ordered_x[2].p.y = int(rec.y2 - dxhw); ordered_x[2].taken = false;
ordered_x[3].p.x = int(rec.x1 + dyhw); ordered_x[3].p.y = int(rec.y1 - dxhw); ordered_x[3].taken = false;

std::sort(ordered_x.begin(), ordered_x.end(), AsmallerB_XoverY);

// Find min y. And mark as taken. find max y.
for(unsigned int i = 1; i < 4; ++i)
{
if(min_y->p.y > ordered_x[i].p.y) {min_y = &ordered_x[i]; }
if(max_y->p.y < ordered_x[i].p.y) {max_y = &ordered_x[i]; }
}
min_y->taken = true;

// Find leftmost untaken point;
edge* leftmost = 0;
for(unsigned int i = 0; i < 4; ++i)
{
if(!ordered_x[i].taken)
{
if(!leftmost) // if uninitialized
{
leftmost = &ordered_x[i];
}
else if (leftmost->p.x > ordered_x[i].p.x)
{
leftmost = &ordered_x[i];
}
}
}
leftmost->taken = true;

// Find rightmost untaken point;
edge* rightmost = 0;
for(unsigned int i = 0; i < 4; ++i)
{
if(!ordered_x[i].taken)
{
if(!rightmost) // if uninitialized
{
rightmost = &ordered_x[i];
}
else if (rightmost->p.x < ordered_x[i].p.x)
{
rightmost = &ordered_x[i];
}
}
}
rightmost->taken = true;

// Find last untaken point;
edge* tailp = 0;
for(unsigned int i = 0; i < 4; ++i)
{
if(!ordered_x[i].taken)
{
if(!tailp) // if uninitialized
{
tailp = &ordered_x[i];
}
else if (tailp->p.x > ordered_x[i].p.x)
{
tailp = &ordered_x[i];
}
}
}
tailp->taken = true;

double flstep = (min_y->p.y != leftmost->p.y) ?
(min_y->p.x - leftmost->p.x) / (min_y->p.y - leftmost->p.y) : 0; //first left step
double slstep = (leftmost->p.y != tailp->p.x) ?
(leftmost->p.x - tailp->p.x) / (leftmost->p.y - tailp->p.x) : 0; //second left step

double frstep = (min_y->p.y != rightmost->p.y) ?
(min_y->p.x - rightmost->p.x) / (min_y->p.y - rightmost->p.y) : 0; //first right step
double srstep = (rightmost->p.y != tailp->p.x) ?
(rightmost->p.x - tailp->p.x) / (rightmost->p.y - tailp->p.x) : 0; //second right step

double lstep = flstep, rstep = frstep;

double left_x = min_y->p.x, right_x = min_y->p.x;

// Loop around all points in the region and count those that are aligned.
int min_iter = min_y->p.y;
int max_iter = max_y->p.y;
for(int y = min_iter; y <= max_iter; ++y)
{
if (y < 0 || y >= img_height) continue;

int adx = y * img_width + int(left_x);
for(int x = int(left_x); x <= int(right_x); ++x, ++adx)
{
if (x < 0 || x >= img_width) continue;

++total_pts;
if(isAligned(adx, rec.theta, rec.prec))
{
++alg_pts;
}
}

if(y >= leftmost->p.y) { lstep = slstep; }
if(y >= rightmost->p.y) { rstep = srstep; }

left_x += lstep;
right_x += rstep;
}

return nfa(total_pts, alg_pts, rec.p);
}

double LineSegmentDetectorImpl::nfa(const int& n, const int& k, const double& p) const
{
// Trivial cases
if(n == 0 || k == 0) { return -LOG_NT; }
if(n == k) { return -LOG_NT - double(n) * log10(p); }

double p_term = p / (1 - p);

double log1term = (double(n) + 1) - log_gamma(double(k) + 1)
- log_gamma(double(n-k) + 1)
+ double(k) * log(p) + double(n-k) * log(1.0 - p);
double term = exp(log1term);

if(double_equal(term, 0))
{
if(k > n * p) return -log1term / M_LN10 - LOG_NT;
else return -LOG_NT;
}

// Compute more terms if needed
double bin_tail = term;
double tolerance = 0.1; // an error of 10% in the result is accepted
for(int i = k + 1; i <= n; ++i)
{
double bin_term = double(n - i + 1) / double(i);
double mult_term = bin_term * p_term;
term *= mult_term;
bin_tail += term;
if(bin_term < 1)
{
double err = term * ((1 - pow(mult_term, double(n-i+1))) / (1 - mult_term) - 1);
if(err < tolerance * fabs(-log10(bin_tail) - LOG_NT) * bin_tail) break;
}

}
return -log10(bin_tail) - LOG_NT;
}

inline bool LineSegmentDetectorImpl::isAligned(const int& address, const double& theta, const double& prec) const
{
if(address < 0) { return false; }
const double& a = angles_data[address];
if(a == NOTDEF) { return false; }

// It is assumed that 'theta' and 'a' are in the range [-pi,pi]
double n_theta = theta - a;
if(n_theta < 0) { n_theta = -n_theta; }
if(n_theta > M_3_2_PI)
{
n_theta -= M_2__PI;
if(n_theta < 0) n_theta = -n_theta;
}

return n_theta <= prec;
}

void LineSegmentDetectorImpl::drawSegments(InputOutputArray _image, InputArray lines)
{
CV_Assert(!_image.empty() && (_image.channels() == 1 || _image.channels() == 3));

Mat gray;
if (_image.channels() == 1)
{
gray = _image.getMatRef();
}
else if (_image.channels() == 3)
{
cvtColor(_image, gray, CV_BGR2GRAY);
}

// Create a 3 channel image in order to draw colored lines
std::vector<Mat> planes;
planes.push_back(gray);
planes.push_back(gray);
planes.push_back(gray);

merge(planes, _image);

Mat _lines;
_lines = lines.getMat();
int N = _lines.checkVector(4);

// Draw segments
for(int i = 0; i < N; ++i)
{
const Vec4f& v = _lines.at<Vec4f>(i);
Point2f b(v[0], v[1]);
Point2f e(v[2], v[3]);
line(_image.getMatRef(), b, e, Scalar(0, 0, 255), 1);
}
}

int LineSegmentDetectorImpl::compareSegments(const Size& size, InputArray lines1, InputArray lines2, InputOutputArray _image)
{
Size sz = size;
if (_image.needed() && _image.size() != size) sz = _image.size();
CV_Assert(sz.area());

Mat_<uchar> I1 = Mat_<uchar>::zeros(sz);
Mat_<uchar> I2 = Mat_<uchar>::zeros(sz);

Mat _lines1;
Mat _lines2;
_lines1 = lines1.getMat();
_lines2 = lines2.getMat();
int N1 = _lines1.checkVector(4);
int N2 = _lines2.checkVector(4);

// Draw segments
for(int i = 0; i < N1; ++i)
{
Point2f b(_lines1.at<Vec4f>(i)[0], _lines1.at<Vec4f>(i)[1]);
Point2f e(_lines1.at<Vec4f>(i)[2], _lines1.at<Vec4f>(i)[3]);
line(I1, b, e, Scalar::all(255), 1);
}
for(int i = 0; i < N2; ++i)
{
Point2f b(_lines2.at<Vec4f>(i)[0], _lines2.at<Vec4f>(i)[1]);
Point2f e(_lines2.at<Vec4f>(i)[2], _lines2.at<Vec4f>(i)[3]);
line(I2, b, e, Scalar::all(255), 1);
}

// Count the pixels that don't agree
Mat Ixor;
bitwise_xor(I1, I2, Ixor);
int N = countNonZero(Ixor);

if (_image.needed())
{
CV_Assert(_image.channels() == 3);
Mat img = _image.getMatRef();
CV_Assert(img.isContinuous() && I1.isContinuous() && I2.isContinuous());

for (unsigned int i = 0; i < I1.total(); ++i)
{
uchar i1 = I1.ptr()[i];
uchar i2 = I2.ptr()[i];
if (i1 || i2)
{
unsigned int base_idx = i * 3;
if (i1) img.ptr()[base_idx] = 255;
else img.ptr()[base_idx] = 0;
img.ptr()[base_idx + 1] = 0;
if (i2) img.ptr()[base_idx + 2] = 255;
else img.ptr()[base_idx + 2] = 0;
}
}
}

return N;
}

} // namespace cv