```// Copyright (C) 2014  Davis E. King (davis@dlib.net)
#ifndef DLIB_HOUGH_tRANSFORM_Hh_
#define DLIB_HOUGH_tRANSFORM_Hh_

#include "hough_transform_abstract.h"
#include "../image_processing/generic_image.h"
#include "../geometry.h"
#include "../algs.h"
#include "assign_image.h"
#include <limits>

namespace dlib
{

// ----------------------------------------------------------------------------------------

class hough_transform
{

public:
explicit hough_transform (
unsigned long size_
) : _size(size_)
{
DLIB_CASSERT(size_ > 0,
"\t hough_transform::hough_transform(size_)"
<< "\n\t Invalid arguments given to this function."
);

even_size = _size - (_size%2);

const point cent = center(rectangle(0,0,size_-1,size_-1));
xcos_theta.set_size(size_, size_);
ysin_theta.set_size(size_, size_);

std::vector<double> cos_theta(size_), sin_theta(size_);
const double scale = 1<<16;
for (unsigned long t = 0; t < size_; ++t)
{
double theta = t*pi/even_size;

cos_theta[t] = scale*std::cos(theta)/sqrt_2;
sin_theta[t] = scale*std::sin(theta)/sqrt_2;
}
const double offset = scale*even_size/4.0 + 0.5;

for (unsigned long c = 0; c < size_; ++c)
{
const long x = c - cent.x();
for (unsigned long t = 0; t < size_; ++t)
xcos_theta(c,t) = static_cast<int32>(x*cos_theta[t] + offset);
}
for (unsigned long r = 0; r < size_; ++r)
{
const long y = r - cent.y();
for (unsigned long t = 0; t < size_; ++t)
ysin_theta(r,t) = static_cast<int32>(y*sin_theta[t] + offset);
}
}

inline unsigned long size(
) const { return _size; }

long nr(
) const { return _size; }

long nc(
) const { return _size; }

std::pair<dpoint, dpoint> get_line (
const dpoint& p
) const
{
DLIB_ASSERT(rectangle(0,0,size()-1,size()-1).contains(p) == true,
"\t pair<dpoint,dpoint> hough_transform::get_line(dpoint)"
<< "\n\t Invalid arguments given to this function."
<< "\n\t p:      " << p
<< "\n\t size(): " << size()
);

// First we compute the radius measured in pixels from the center and the theta
theta *= pi/180;

// now make a line segment on the line.
const rectangle box = get_rect(*this);
const dpoint cent = center(box);
dpoint v1 = cent + dpoint(size()+1000,0) + dpoint(0,radius);
dpoint v2 = cent - dpoint(size()+1000,0) + dpoint(0,radius);
dpoint p1 = rotate_point(cent, v1, theta);
dpoint p2 = rotate_point(cent, v2, theta);

clip_line_to_rectangle(box, p1, p2);

return std::make_pair(p1,p2);
}

double get_line_angle_in_degrees (
const dpoint& p
) const
{
return angle;
}

void get_line_properties (
const dpoint& p,
double& angle_in_degrees,
) const
{
const dpoint cent = center(get_rect(*this));
double theta = p.x()-cent.x();
angle_in_degrees = 180*theta/even_size;
}

template <
typename image_type
>
point get_best_hough_point (
const point& p,
const image_type& himg_
)
{
const const_image_view<image_type> himg(himg_);

DLIB_ASSERT(himg.nr() == size() && himg.nc() == size() &&
rectangle(0,0,size()-1,size()-1).contains(p) == true,
"\t point hough_transform::get_best_hough_point()"
<< "\n\t Invalid arguments given to this function."
<< "\n\t himg.nr(): " << himg.nr()
<< "\n\t himg.nc(): " << himg.nc()
<< "\n\t size():    " << size()
<< "\n\t p:         " << p
);

typedef typename image_traits<image_type>::pixel_type pixel_type;
COMPILE_TIME_ASSERT(pixel_traits<pixel_type>::grayscale == true);
pixel_type best_val = std::numeric_limits<pixel_type>::min();
point best_point;

const long max_n8 = (himg.nc()/8)*8;
const long max_n4 = (himg.nc()/4)*4;
const long r = p.y();
const long c = p.x();

const int32* ysin = &ysin_theta(r,0);
const int32* xcos = &xcos_theta(c,0);
long t = 0;
while(t < max_n8)
{
long rr0 = (*xcos++ + *ysin++)>>16;
long rr1 = (*xcos++ + *ysin++)>>16;
long rr2 = (*xcos++ + *ysin++)>>16;
long rr3 = (*xcos++ + *ysin++)>>16;
long rr4 = (*xcos++ + *ysin++)>>16;
long rr5 = (*xcos++ + *ysin++)>>16;
long rr6 = (*xcos++ + *ysin++)>>16;
long rr7 = (*xcos++ + *ysin++)>>16;

if (himg[rr0][t++] > best_val)
{
best_val = himg[rr0][t-1];
best_point.x() = t-1;
best_point.y() = rr0;
}
if (himg[rr1][t++] > best_val)
{
best_val = himg[rr1][t-1];
best_point.x() = t-1;
best_point.y() = rr1;
}
if (himg[rr2][t++] > best_val)
{
best_val = himg[rr2][t-1];
best_point.x() = t-1;
best_point.y() = rr2;
}
if (himg[rr3][t++] > best_val)
{
best_val = himg[rr3][t-1];
best_point.x() = t-1;
best_point.y() = rr3;
}
if (himg[rr4][t++] > best_val)
{
best_val = himg[rr4][t-1];
best_point.x() = t-1;
best_point.y() = rr4;
}
if (himg[rr5][t++] > best_val)
{
best_val = himg[rr5][t-1];
best_point.x() = t-1;
best_point.y() = rr5;
}
if (himg[rr6][t++] > best_val)
{
best_val = himg[rr6][t-1];
best_point.x() = t-1;
best_point.y() = rr6;
}
if (himg[rr7][t++] > best_val)
{
best_val = himg[rr7][t-1];
best_point.x() = t-1;
best_point.y() = rr7;
}
}
while(t < max_n4)
{
long rr0 = (*xcos++ + *ysin++)>>16;
long rr1 = (*xcos++ + *ysin++)>>16;
long rr2 = (*xcos++ + *ysin++)>>16;
long rr3 = (*xcos++ + *ysin++)>>16;
if (himg[rr0][t++] > best_val)
{
best_val = himg[rr0][t-1];
best_point.x() = t-1;
best_point.y() = rr0;
}
if (himg[rr1][t++] > best_val)
{
best_val = himg[rr1][t-1];
best_point.x() = t-1;
best_point.y() = rr1;
}
if (himg[rr2][t++] > best_val)
{
best_val = himg[rr2][t-1];
best_point.x() = t-1;
best_point.y() = rr2;
}
if (himg[rr3][t++] > best_val)
{
best_val = himg[rr3][t-1];
best_point.x() = t-1;
best_point.y() = rr3;
}
}
while(t < himg.nc())
{
long rr0 = (*xcos++ + *ysin++)>>16;
if (himg[rr0][t++] > best_val)
{
best_val = himg[rr0][t-1];
best_point.x() = t-1;
best_point.y() = rr0;
}
}

return best_point;
}

template <
typename in_image_type,
typename out_image_type
>
void operator() (
const in_image_type& img_,
const rectangle& box,
out_image_type& himg_
) const
{
typedef typename image_traits<in_image_type>::pixel_type in_pixel_type;
typedef typename image_traits<out_image_type>::pixel_type out_pixel_type;

DLIB_CASSERT(box.width() == size() && box.height() == size(),
"\t void hough_transform::operator()"
<< "\n\t Invalid arguments given to this function."
<< "\n\t box.width():  " << box.width()
<< "\n\t box.height(): " << box.height()
<< "\n\t size():       " << size()
);

COMPILE_TIME_ASSERT(pixel_traits<in_pixel_type>::grayscale == true);
COMPILE_TIME_ASSERT(pixel_traits<out_pixel_type>::grayscale == true);

const_image_view<in_image_type> img(img_);
image_view<out_image_type> himg(himg_);

himg.set_size(size(), size());
assign_all_pixels(himg, 0);

auto record_hit = [&](const point& hough_point, const point& /*img_point*/, const in_pixel_type& val)
{
himg[hough_point.y()][hough_point.x()] += val;
};
perform_generic_hough_transform(img_, box, record_hit);
}

template <
typename in_image_type,
typename out_image_type
>
void operator() (
const in_image_type& img_,
out_image_type& himg_
) const
{
rectangle box(0,0, num_columns(img_)-1, num_rows(img_)-1);
(*this)(img_, box, himg_);
}

template <
typename in_image_type
>
std::vector<std::vector<point>> find_pixels_voting_for_lines (
const in_image_type& img,
const rectangle& box,
const std::vector<point>& hough_points,
const unsigned long angle_window_size = 1,
const unsigned long radius_window_size = 1
) const
{

typedef typename image_traits<in_image_type>::pixel_type in_pixel_type;

DLIB_CASSERT(angle_window_size >= 1);
DLIB_CASSERT(box.width() == size() && box.height() == size(),
"\t std::vector<std::vector<point>> hough_transform::find_pixels_voting_for_lines()"
<< "\n\t Invalid arguments given to this function."
<< "\n\t box.width():  " << box.width()
<< "\n\t box.height(): " << box.height()
<< "\n\t size():       " << size()
);
#ifdef ENABLE_ASSERTS
for (auto& p : hough_points)
DLIB_CASSERT(get_rect(*this).contains(p),
"You gave a hough_points that isn't actually in the Hough space of this object."
<< "\n\t get_rect(*this): "<< get_rect(*this)
<< "\n\t p: "<< p
);
#endif

std::vector<std::vector<point>> constituent_points(hough_points.size());

// make a map that lets us look up in constant time if a hough point is in the
// constituent_points output and if so where.
matrix<uint32> hmap(size(),size());
hmap = hough_points.size();
for (size_t i = 0; i < hough_points.size(); ++i)
{
for (long r = area.top(); r <= area.bottom(); ++r)
{
for (long c = area.left(); c <= area.right(); ++c)
{
hmap(r,c) = i;
}
}
}

// record that this image point voted for this Hough point
auto record_hit = [&](const point& hough_point, const point& img_point, in_pixel_type)
{
auto idx = hmap(hough_point.y(), hough_point.x());
if (idx < constituent_points.size())
{
if (constituent_points[idx].size() == 0 || constituent_points[idx].back() != img_point)
constituent_points[idx].push_back(img_point);
}
};

perform_generic_hough_transform(img, box, record_hit);

return constituent_points;
}

template <
typename in_image_type
>
std::vector<std::vector<point>> find_pixels_voting_for_lines (
const in_image_type& img,
const std::vector<point>& hough_points,
const unsigned long angle_window_size = 1,
const unsigned long radius_window_size = 1
) const
{
rectangle box(0,0, num_columns(img)-1, num_rows(img)-1);
return find_pixels_voting_for_lines(img, box, hough_points, angle_window_size, radius_window_size);
}

template <
typename image_type,
typename thresh_type
>
std::vector<point> find_strong_hough_points(
const image_type& himg_,
const thresh_type hough_count_threshold,
const double angle_nms_thresh,
)
{
const_image_view<image_type> himg(himg_);

DLIB_CASSERT(himg.nr() == size());
DLIB_CASSERT(himg.nc() == size());
DLIB_CASSERT(angle_nms_thresh >= 0)

std::vector<std::pair<double,point>> initial_lines;
for (long r = 0; r < himg.nr(); ++r)
{
for (long c = 0; c < himg.nc(); ++c)
{
if (himg[r][c] >= hough_count_threshold)
initial_lines.emplace_back(himg[r][c], point(c,r));
}
}

std::vector<point> final_lines;

// Now do non-max suppression.  First, sort the initial_lines so the best lines come first.
std::sort(initial_lines.rbegin(), initial_lines.rend(),
[](const std::pair<double,point>& a, const std::pair<double,point>& b){ return a.first<b.first;});
for (auto& r : initial_lines)
{

// check if anything in final_lines is too close to r.second.  If
// something is found then discard r.second.
auto too_close = false;
{
auto& ref_angle = ref.first;

// We need to check for wrap around in angle since, for instance, a
// line with angle and radius of 90 and 10 is the same line as one with
// angle -90 and radius -10.
{
too_close = true;
break;
}
}

if (!too_close)
{
final_lines.emplace_back(r.second);
}
}

return final_lines;
}

template <
typename in_image_type,
typename record_hit_function_type
>
void perform_generic_hough_transform (
const in_image_type& img_,
const rectangle& box,
record_hit_function_type record_hit
) const
{

typedef typename image_traits<in_image_type>::pixel_type in_pixel_type;

DLIB_ASSERT(box.width() == size() && box.height() == size(),
"\t void hough_transform::perform_generic_hough_transform()"
<< "\n\t Invalid arguments given to this function."
<< "\n\t box.width():  " << box.width()
<< "\n\t box.height(): " << box.height()
<< "\n\t size():       " << size()
);

COMPILE_TIME_ASSERT(pixel_traits<in_pixel_type>::grayscale == true);

const_image_view<in_image_type> img(img_);

const rectangle area = box.intersect(get_rect(img));

const long max_n8 = (size()/8)*8;
const long max_n4 = (size()/4)*4;
for (long r = area.top(); r <= area.bottom(); ++r)
{
const int32* ysin_base = &ysin_theta(r-box.top(),0);
for (long c = area.left(); c <= area.right(); ++c)
{
const auto val = img[r][c];
if (val != 0)
{
/*
// The code in this comment is equivalent to the more complex but
// faster code below.  We keep this simple version of the Hough
// transform implementation here just to document what it's doing
// more clearly.
const point cent = center(box);
const long x = c - cent.x();
const long y = r - cent.y();
for (long t = 0; t < size(); ++t)
{
double theta = t*pi/even_size;
double radius = (x*std::cos(theta) + y*std::sin(theta))/sqrt_2 + even_size/2 + 0.5;

record_hit(point(t,rr), point(c,r), val);
}
continue;
*/

// Run the speed optimized version of the code in the above
// comment.
const int32* ysin = ysin_base;
const int32* xcos = &xcos_theta(c-box.left(),0);
long t = 0;
while(t < max_n8)
{
long rr0 = (*xcos++ + *ysin++)>>16;
long rr1 = (*xcos++ + *ysin++)>>16;
long rr2 = (*xcos++ + *ysin++)>>16;
long rr3 = (*xcos++ + *ysin++)>>16;
long rr4 = (*xcos++ + *ysin++)>>16;
long rr5 = (*xcos++ + *ysin++)>>16;
long rr6 = (*xcos++ + *ysin++)>>16;
long rr7 = (*xcos++ + *ysin++)>>16;

record_hit(point(t++,rr0), point(c,r), val);
record_hit(point(t++,rr1), point(c,r), val);
record_hit(point(t++,rr2), point(c,r), val);
record_hit(point(t++,rr3), point(c,r), val);
record_hit(point(t++,rr4), point(c,r), val);
record_hit(point(t++,rr5), point(c,r), val);
record_hit(point(t++,rr6), point(c,r), val);
record_hit(point(t++,rr7), point(c,r), val);
}
while(t < max_n4)
{
long rr0 = (*xcos++ + *ysin++)>>16;
long rr1 = (*xcos++ + *ysin++)>>16;
long rr2 = (*xcos++ + *ysin++)>>16;
long rr3 = (*xcos++ + *ysin++)>>16;
record_hit(point(t++,rr0), point(c,r), val);
record_hit(point(t++,rr1), point(c,r), val);
record_hit(point(t++,rr2), point(c,r), val);
record_hit(point(t++,rr3), point(c,r), val);
}
while(t < (long)size())
{
long rr0 = (*xcos++ + *ysin++)>>16;
record_hit(point(t++,rr0), point(c,r), val);
}
}
}
}
}

template <
typename in_image_type,
typename record_hit_function_type
>
void perform_generic_hough_transform (
const in_image_type& img_,
record_hit_function_type record_hit
) const
{
rectangle box(0,0, num_columns(img_)-1, num_rows(img_)-1);
perform_generic_hough_transform(img_, box, record_hit);
}

private:

unsigned long _size;
unsigned long even_size; // equal to _size if _size is even, otherwise equal to _size-1.
matrix<int32> xcos_theta, ysin_theta;
};
}

#endif // DLIB_HOUGH_tRANSFORM_Hh_

```