Opencv 霍夫逆变换

霍夫变换（Hough Transform）／直线检测——第三步：霍夫逆变换

这里是将问题Opencv NMS中得到的极大值进行霍夫逆变换之后画出得到的直线。在这里，已经通过霍夫变换检测出了直线。

算法如下：
1. 极大值点(r,t)通过下式进行逆变换：
y = – \frac{\cos(t)}{\sin(t) } \ x + \frac{r}{\sin(t)}\\
x = – \frac{\sin(t)}{\cos(t) } \ y + \frac{r}{\cos(t)}

2. 对于每个局部最大点，使y = 0-H -1，x = 0-W -1，然后执行1中的逆变换，并在输入图像中绘制检测到的直线。请将线的颜色设置为红色(R,G,B) = (255, 0, 0)。

python实现：

import cv2
import numpy as np
import matplotlib.pyplot as plt

def Canny(img):

    # Gray scale
    def BGR2GRAY(img):
        b = img[:, :, 0].copy()
        g = img[:, :, 1].copy()
        r = img[:, :, 2].copy()

        # Gray scale
        out = 0.2126 * r + 0.7152 * g + 0.0722 * b
        out = out.astype(np.uint8)

        return out


    # Gaussian filter for grayscale
    def gaussian_filter(img, K_size=3, sigma=1.3):

        if len(img.shape) == 3:
            H, W, C = img.shape
            gray = False
        else:
            img = np.expand_dims(img, axis=-1)
            H, W, C = img.shape
            gray = True

        ## Zero padding
        pad = K_size // 2
        out = np.zeros([H + pad * 2, W + pad * 2, C], dtype=np.float)
        out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)

        ## prepare Kernel
        K = np.zeros((K_size, K_size), dtype=np.float)
        for x in range(-pad, -pad + K_size):
            for y in range(-pad, -pad + K_size):
                K[y + pad, x + pad] = np.exp( - (x ** 2 + y ** 2) / (2 * sigma * sigma))
        #K /= (sigma * np.sqrt(2 * np.pi))
        K /= (2 * np.pi * sigma * sigma)
        K /= K.sum()

        tmp = out.copy()

        # filtering
        for y in range(H):
            for x in range(W):
                for c in range(C):
                    out[pad + y, pad + x, c] = np.sum(K * tmp[y : y + K_size, x : x + K_size, c])

        out = np.clip(out, 0, 255)
        out = out[pad : pad + H, pad : pad + W]
        out = out.astype(np.uint8)

        if gray:
            out = out[..., 0]

        return out


    # sobel filter
    def sobel_filter(img, K_size=3):
        if len(img.shape) == 3:
            H, W, C = img.shape
        else:
            H, W = img.shape

        # Zero padding
        pad = K_size // 2
        out = np.zeros((H + pad * 2, W + pad * 2), dtype=np.float)
        out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
        tmp = out.copy()

        out_v = out.copy()
        out_h = out.copy()

        ## Sobel vertical
        Kv = [[1., 2., 1.],[0., 0., 0.], [-1., -2., -1.]]
        ## Sobel horizontal
        Kh = [[1., 0., -1.],[2., 0., -2.],[1., 0., -1.]]

        # filtering
        for y in range(H):
            for x in range(W):
                out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y : y + K_size, x : x + K_size]))
                out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y : y + K_size, x : x + K_size]))

        out_v = np.clip(out_v, 0, 255)
        out_h = np.clip(out_h, 0, 255)

        out_v = out_v[pad : pad + H, pad : pad + W]
        out_v = out_v.astype(np.uint8)
        out_h = out_h[pad : pad + H, pad : pad + W]
        out_h = out_h.astype(np.uint8)

        return out_v, out_h


    def get_edge_angle(fx, fy):
        # get edge strength
        edge = np.sqrt(np.power(fx.astype(np.float32), 2) + np.power(fy.astype(np.float32), 2))
        edge = np.clip(edge, 0, 255)

        fx = np.maximum(fx, 1e-10)
        #fx[np.abs(fx) <= 1e-5] = 1e-5

        # get edge angle
        angle = np.arctan(fy / fx)

        return edge, angle


    def angle_quantization(angle):
        angle = angle / np.pi * 180
        angle[angle < -22.5] = 180 + angle[angle < -22.5]
        _angle = np.zeros_like(angle, dtype=np.uint8)
        _angle[np.where(angle <= 22.5)] = 0
        _angle[np.where((angle > 22.5) & (angle <= 67.5))] = 45
        _angle[np.where((angle > 67.5) & (angle <= 112.5))] = 90
        _angle[np.where((angle > 112.5) & (angle <= 157.5))] = 135

        return _angle


    def non_maximum_suppression(angle, edge):
        H, W = angle.shape
        _edge = edge.copy()

        for y in range(H):
            for x in range(W):
                    if angle[y, x] == 0:
                            dx1, dy1, dx2, dy2 = -1, 0, 1, 0
                    elif angle[y, x] == 45:
                            dx1, dy1, dx2, dy2 = -1, 1, 1, -1
                    elif angle[y, x] == 90:
                            dx1, dy1, dx2, dy2 = 0, -1, 0, 1
                    elif angle[y, x] == 135:
                            dx1, dy1, dx2, dy2 = -1, -1, 1, 1
                    if x == 0:
                            dx1 = max(dx1, 0)
                            dx2 = max(dx2, 0)
                    if x == W-1:
                            dx1 = min(dx1, 0)
                            dx2 = min(dx2, 0)
                    if y == 0:
                            dy1 = max(dy1, 0)
                            dy2 = max(dy2, 0)
                    if y == H-1:
                            dy1 = min(dy1, 0)
                            dy2 = min(dy2, 0)
                    if max(max(edge[y, x], edge[y + dy1, x + dx1]), edge[y + dy2, x + dx2]) != edge[y, x]:
                            _edge[y, x] = 0

        return _edge

    def hysterisis(edge, HT=100, LT=30):
        H, W = edge.shape

        # Histeresis threshold
        edge[edge >= HT] = 255
        edge[edge <= LT] = 0

        _edge = np.zeros((H + 2, W + 2), dtype=np.float32)
        _edge[1 : H + 1, 1 : W + 1] = edge

        ## 8 - Nearest neighbor
        nn = np.array(((1., 1., 1.), (1., 0., 1.), (1., 1., 1.)), dtype=np.float32)

        for y in range(1, H+2):
                for x in range(1, W+2):
                        if _edge[y, x] < LT or _edge[y, x] > HT:
                                continue
                        if np.max(_edge[y-1:y+2, x-1:x+2] * nn) >= HT:
                                _edge[y, x] = 255
                        else:
                                _edge[y, x] = 0

        edge = _edge[1:H+1, 1:W+1]

        return edge

    # grayscale
    gray = BGR2GRAY(img)

    # gaussian filtering
    gaussian = gaussian_filter(gray, K_size=5, sigma=1.4)

    # sobel filtering
    fy, fx = sobel_filter(gaussian, K_size=3)

    # get edge strength, angle
    edge, angle = get_edge_angle(fx, fy)

    # angle quantization
    angle = angle_quantization(angle)

    # non maximum suppression
    edge = non_maximum_suppression(angle, edge)

    # hysterisis threshold
    out = hysterisis(edge, 100, 30)

    return out


def Hough_Line(edge, img):
    ## Voting
    def voting(edge):
        H, W = edge.shape

        drho = 1
        dtheta = 1

        # get rho max length
        rho_max = np.ceil(np.sqrt(H ** 2 + W ** 2)).astype(np.int)

        # hough table
        hough = np.zeros((rho_max * 2, 180), dtype=np.int)

        # get index of edge
        ind = np.where(edge == 255)

        ## hough transformation
        for y, x in zip(ind[0], ind[1]):
                for theta in range(0, 180, dtheta):
                        # get polar coordinat4s
                        t = np.pi / 180 * theta
                        rho = int(x * np.cos(t) + y * np.sin(t))

                        # vote
                        hough[rho + rho_max, theta] += 1

        out = hough.astype(np.uint8)

        return out

    # non maximum suppression
    def non_maximum_suppression(hough):
        rho_max, _ = hough.shape

        ## non maximum suppression
        for y in range(rho_max):
            for x in range(180):
                # get 8 nearest neighbor
                x1 = max(x-1, 0)
                x2 = min(x+2, 180)
                y1 = max(y-1, 0)
                y2 = min(y+2, rho_max-1)
                if np.max(hough[y1:y2, x1:x2]) == hough[y,x] and hough[y, x] != 0:
                    pass
                    #hough[y,x] = 255
                else:
                    hough[y,x] = 0

        return hough

    def inverse_hough(hough, img):
        H, W, _ = img.shape
        rho_max, _ = hough.shape

        out = img.copy()

        # get x, y index of hough table
        ind_x = np.argsort(hough.ravel())[::-1][:20]
        ind_y = ind_x.copy()
        thetas = ind_x % 180
        rhos = ind_y // 180 - rho_max / 2

        # each theta and rho
        for theta, rho in zip(thetas, rhos):
            # theta[radian] -> angle[degree]
            t = np.pi / 180. * theta

            # hough -> (x,y)
            for x in range(W):
                if np.sin(t) != 0:
                    y = - (np.cos(t) / np.sin(t)) * x + (rho) / np.sin(t)
                    y = int(y)
                    if y >= H or y < 0:
                        continue
                    out[y, x] = [0, 0, 255]
            for y in range(H):
                if np.cos(t) != 0:
                    x = - (np.sin(t) / np.cos(t)) * y + (rho) / np.cos(t)
                    x = int(x)
                    if x >= W or x < 0:
                        continue
                    out[y, x] = [0, 0, 255]

        out = out.astype(np.uint8)

        return out


    # voting
    hough = voting(edge)

    # non maximum suppression
    hough = non_maximum_suppression(hough)

    # inverse hough
    out = inverse_hough(hough, img)

    return out


# Read image
img = cv2.imread("thorino.jpg").astype(np.float32)

# Canny
edge = Canny(img)

# Hough
out = Hough_Line(edge, img)

out = out.astype(np.uint8)

# Save result
cv2.imwrite("out.jpg", out)
cv2.imshow("result", out)
cv2.waitKey(0)
cv2.destroyAllWindows()

c++实现：

#include <opencv2/core.hpp>
#include <opencv2/highgui.hpp>
#include <iostream>
#include <math.h>


// RGB to Gray scale
cv::Mat BGR2GRAY(cv::Mat img){
  // get height and width
  int height = img.rows;
  int width = img.cols;
  int channel = img.channels();

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  // BGR -> Gray
  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      out.at<uchar>(y, x) = (int)((float)img.at<cv::Vec3b>(y, x)[0] * 0.0722 + \
                  (float)img.at<cv::Vec3b>(y, x)[1] * 0.7152 + \
                  (float)img.at<cv::Vec3b>(y, x)[2] * 0.2126);
    }
  }
  return out;
}

float clip(float value, float min, float max){
  return fmin(fmax(value, 0), 255);
}

// gaussian filter
cv::Mat gaussian_filter(cv::Mat img, double sigma, int kernel_size){
  int height = img.rows;
  int width = img.cols;
  int channel = img.channels();

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC3);
  if (channel == 1) {
    out = cv::Mat::zeros(height, width, CV_8UC1);
  }

  // prepare kernel
  int pad = floor(kernel_size / 2);
  int _x = 0, _y = 0;
  double kernel_sum = 0;

  // get gaussian kernel
  float kernel[kernel_size][kernel_size];

  for (int y = 0; y < kernel_size; y++){
    for (int x = 0; x < kernel_size; x++){
      _y = y - pad;
      _x = x - pad; 
      kernel[y][x] = 1 / (2 * M_PI * sigma * sigma) * exp( - (_x * _x + _y * _y) / (2 * sigma * sigma));
      kernel_sum += kernel[y][x];
    }
  }

  for (int y = 0; y < kernel_size; y++){
    for (int x = 0; x < kernel_size; x++){
      kernel[y][x] /= kernel_sum;
    }
  }

  // filtering
  double v = 0;

  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      // for BGR
      if (channel == 3){
        for (int c = 0; c < channel; c++){
          v = 0;
          for (int dy = -pad; dy < pad + 1; dy++){
            for (int dx = -pad; dx < pad + 1; dx++){
              if (((x + dx) >= 0) && ((y + dy) >= 0) && ((x + dx) < width) && ((y + dy) < height)){
                v += (double)img.at<cv::Vec3b>(y + dy, x + dx)[c] * kernel[dy + pad][dx + pad];
              }
            }
          }
          out.at<cv::Vec3b>(y, x)[c] = (uchar)clip(v, 0, 255);
        }
      } else {
        // for Gray
        v = 0;
        for (int dy = -pad; dy < pad + 1; dy++){
          for (int dx = -pad; dx < pad + 1; dx++){
            if (((x + dx) >= 0) && ((y + dy) >= 0) && ((x + dx) < width) && ((y + dy) < height)){
              v += (double)img.at<uchar>(y + dy, x + dx) * kernel[dy + pad][dx + pad];
            }
          }
        }
        out.at<uchar>(y, x) = (uchar)clip(v, 0, 255);
      }
    }
  }
  return out;
}

// Sobel filter
cv::Mat sobel_filter(cv::Mat img, int kernel_size, bool horizontal){
  int height = img.rows;
  int width = img.cols;
  int channel = img.channels();

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  // prepare kernel
  double kernel[kernel_size][kernel_size] = {{1, 2, 1}, {0, 0, 0}, {-1, -2, -1}};

  if (horizontal){
    kernel[0][1] = 0;
    kernel[0][2] = -1;
    kernel[1][0] = 2;
    kernel[1][2] = -2;
    kernel[2][0] = 1;
    kernel[2][1] = 0;
  }

  int pad = floor(kernel_size / 2);

  double v = 0;

  // filtering  
  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      v = 0;
      for (int dy = -pad; dy < pad + 1; dy++){
        for (int dx = -pad; dx < pad + 1; dx++){
          if (((y + dy) >= 0) && (( x + dx) >= 0) && ((y + dy) < height) && ((x + dx) < width)){
            v += (double)img.at<uchar>(y + dy, x + dx) * kernel[dy + pad][dx + pad];
          }
        }
      }
      out.at<uchar>(y, x) = (uchar)clip(v, 0, 255);
    }
  }
  return out;
}

// get edge
cv::Mat get_edge(cv::Mat fx, cv::Mat fy){
  // get height and width
  int height = fx.rows;
  int width = fx.cols;

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  double _fx, _fy;

  for(int y = 0; y < height; y++){
    for(int x = 0; x < width; x++){
      _fx = (double)fx.at<uchar>(y, x);
      _fy = (double)fy.at<uchar>(y, x);

      out.at<uchar>(y, x) = (uchar)clip(sqrt(_fx * _fx + _fy * _fy), 0, 255);
    }
  }

  return out;
}

// get angle
cv::Mat get_angle(cv::Mat fx, cv::Mat fy){
  // get height and width
  int height = fx.rows;
  int width = fx.cols;

  // prepare output
  cv::Mat out = cv::Mat::zeros(height, width, CV_8UC1);

  double _fx, _fy;
  double angle;

  for(int y = 0; y < height; y++){
    for(int x = 0; x < width; x++){
      _fx = fmax((double)fx.at<uchar>(y, x), 0.000001);
      _fy = (double)fy.at<uchar>(y, x);

      angle = atan2(_fy, _fx);
      angle = angle / M_PI * 180;

      if(angle < -22.5){
        angle = 180 + angle;
      } else if (angle >= 157.5) {
        angle = angle - 180;
      }

      // quantization
      if (angle <= 22.5){
        out.at<uchar>(y, x) = 0;
      } else if (angle <= 67.5){
        out.at<uchar>(y, x) = 45;
      } else if (angle <= 112.5){
        out.at<uchar>(y, x) = 90;
      } else {
        out.at<uchar>(y, x) = 135;
      }
    }
  }

  return out;
}


// non maximum suppression
cv::Mat non_maximum_suppression(cv::Mat angle, cv::Mat edge){
  int height = angle.rows;
  int width = angle.cols;
  int channel = angle.channels();

  int dx1, dx2, dy1, dy2;
  int now_angle;

  // prepare output
  cv::Mat _edge = cv::Mat::zeros(height, width, CV_8UC1);

  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      now_angle = angle.at<uchar>(y, x);
      // angle condition
      if (now_angle == 0){
        dx1 = -1;
        dy1 = 0;
        dx2 = 1;
        dy2 = 0;
      } else if(now_angle == 45) {
        dx1 = -1;
        dy1 = 1;
        dx2 = 1;
        dy2 = -1;
      } else if(now_angle == 90){
        dx1 = 0;
        dy1 = -1;
        dx2 = 0;
        dy2 = 1;
      } else {
        dx1 = -1;
        dy1 = -1;
        dx2 = 1;
        dy2 = 1;
      }

      if (x == 0){
        dx1 = fmax(dx1, 0);
        dx2 = fmax(dx2, 0);
      }
      if (x == (width - 1)){
        dx1 = fmin(dx1, 0);
        dx2 = fmin(dx2, 0);
      }
      if (y == 0){
        dy1 = fmax(dy1, 0);
        dy2 = fmax(dy2, 0);
      }
      if (y == (height - 1)){
        dy1 = fmin(dy1, 0);
        dy2 = fmin(dy2, 0);
      }

      // if pixel is max among adjuscent pixels, pixel is kept
      if (fmax(fmax(edge.at<uchar>(y, x), edge.at<uchar>(y + dy1, x + dx1)), edge.at<uchar>(y + dy2, x + dx2)) == edge.at<uchar>(y, x)) {
        _edge.at<uchar>(y, x) = edge.at<uchar>(y, x);
      }
    }
  }

  return _edge;
}

// histerisis
cv::Mat histerisis(cv::Mat edge, int HT, int LT){
  int height = edge.rows;
  int width = edge.cols;
  int channle = edge.channels();

  // prepare output
  cv::Mat _edge = cv::Mat::zeros(height, width, CV_8UC1);

  int now_pixel;

  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){
      // get pixel
      now_pixel = edge.at<uchar>(y, x);

      // if pixel >= HT
      if (now_pixel >= HT){
        _edge.at<uchar>(y, x) = 255;
      } 
      // if LT < pixel < HT
      else if (now_pixel > LT) {
        for (int dy = -1; dy < 2; dy++){
          for (int dx = -1; dx < 2; dx++){
            // if 8 nearest neighbor pixel >= HT
            if (edge.at<uchar>(fmin(fmax(y + dy, 0), 255), fmin(fmax(x + dx, 0), 255)) >= HT){
              _edge.at<uchar>(y, x) = 255;
            }
          }
        }
      }
    }
  }
  return _edge;
}


// Canny
cv::Mat Canny(cv::Mat img){
  // BGR -> Gray
  cv::Mat gray = BGR2GRAY(img);

  // gaussian filter
  cv::Mat gaussian = gaussian_filter(gray, 1.4, 5);

  // sobel filter (vertical)
  cv::Mat fy = sobel_filter(gaussian, 3, false);

  // sobel filter (horizontal)
  cv::Mat fx = sobel_filter(gaussian, 3, true);

  // get edge
  cv::Mat edge = get_edge(fx, fy);

  // get angle
  cv::Mat angle = get_angle(fx, fy);

  // edge non-maximum suppression
  edge = non_maximum_suppression(angle, edge);

  // histerisis
  edge = histerisis(edge, 100, 30);

  return edge;
}



//------
// hough

const int ANGLE_T = 180;
const int RHO_MAX = 320;

// hough table
struct struct_hough_table {
  int table[RHO_MAX * 2][ANGLE_T];
};

// hough vote
struct_hough_table Hough_vote(struct_hough_table hough_table, cv::Mat img){
  int height = img.rows;
  int width = img.cols;
  int rho = 0;
  double angle = 0;

  for (int y = 0; y < height; y++){
    for (int x = 0; x < width; x++){

      // if not edge, skip
      if (img.at<uchar>(y, x) != 255){
        continue;
      }

      // 0 <= angle t < 180
      for (int t = 0; t < ANGLE_T; t++){
        angle = M_PI / 180 * t;
        rho = (int)(x * cos(angle) + y * sin(angle));
        hough_table.table[rho + RHO_MAX][t] ++;
      }
    }
  }

  return hough_table;
}

// hough nms
struct_hough_table Hough_NMS(struct_hough_table hough_table){
  // output hough table
  struct_hough_table output_hough_table;

  // initialize 0
  for (int rho = 0; rho < RHO_MAX * 2; rho++){
    for (int t = 0; t < ANGLE_T; t++){ 
      output_hough_table.table[rho][t] = 0;
    }
  }


  // top N x, y
  int N = 30;
  int top_N_rho[N], top_N_t[N], top_N_vote[N];
  int tmp_rho, tmp_t, tmp_vote, tmp_rho2, tmp_t2, tmp_vote2;
  int rho, t;

  for (int n = 0; n < N; n++){
    top_N_rho[n] = -1;
    top_N_t[n] = -1;
    top_N_vote[n] = -1;
  }

  for (int rho = 0; rho < RHO_MAX * 2; rho++){
    for (int t = 0; t < ANGLE_T; t++){
      if (hough_table.table[rho][t] == 0){
        continue;
      }

      // compare to left top
      if (((t - 1) >= 0) && ((rho - 1) >= 0)){
        if (hough_table.table[rho][t] < hough_table.table[rho - 1][t - 1]){
          continue;
        }
      }

      // comparet to top
      if ((rho - 1) >= 0){
        if (hough_table.table[rho][t] < hough_table.table[rho - 1][t]){
          continue;
        }
      }

      // compare to left top
      if (((t + 1) < ANGLE_T) && ((rho - 1) >= 0)){
        if (hough_table.table[rho][t] < hough_table.table[rho - 1][t + 1]){
          continue;
        }
      }

      // compare to left
      if ((t - 1) >= 0){
        if (hough_table.table[rho][t] < hough_table.table[rho][t - 1]){
          continue;
        }
      }

      // compare to right
      if ((t + 1) < ANGLE_T){
        if (hough_table.table[rho][t] < hough_table.table[rho][t + 1]){
          continue;
        }
      }

      // compare to left bottom
      if (((t - 1) >= 0) && ((rho + 1) < RHO_MAX * 2)){
        if (hough_table.table[rho][t] < hough_table.table[rho + 1][t - 1]){
          continue;
        }
      }

      // compare to bottom
      if ((rho + 1) < RHO_MAX * 2){
        if (hough_table.table[rho][t] < hough_table.table[rho + 1][t]){
          continue;
        }
      }

      // compare to right bottom
      if (((t + 1) < ANGLE_T) && ((rho + 1) < RHO_MAX * 2)){
        if (hough_table.table[rho][t] < hough_table.table[rho + 1][t + 1]){
          continue;
        }
      }

      // Select top N votes
      for (int n = 0; n < N; n++){
        if (top_N_vote[n] <= hough_table.table[rho][t]){
          tmp_vote = top_N_vote[n];
          tmp_rho = top_N_rho[n];
          tmp_t = top_N_t[n];
          top_N_vote[n] = hough_table.table[rho][t];
          top_N_rho[n] = rho;
          top_N_t[n] = t;

          for (int m = n + 1; m < N - 1; m++){
            tmp_vote2 = top_N_vote[m];
            tmp_rho2 = top_N_rho[m];
            tmp_t2 = top_N_t[m];
            top_N_vote[m] = tmp_vote;
            top_N_rho[m] = tmp_rho;
            top_N_t[m] = tmp_t;
            tmp_vote = tmp_vote2;
            tmp_rho = tmp_rho2;
            tmp_t = tmp_t2;
          }

          top_N_vote[N - 1] = tmp_vote;
          top_N_rho[N - 1] = tmp_rho;
          top_N_t[N - 1] = tmp_t;
          break;
        }
      }
    }
  }

  // get pixel for top N votes
  for (int n = 0; n < N; n++){
    if (top_N_rho[n] == -1){
      break;
    }
    rho = top_N_rho[n];
    t = top_N_t[n];
    output_hough_table.table[rho][t] = hough_table.table[rho][t];
  }

  return output_hough_table;
}

// Inverse hough transformation
cv::Mat Hough_inverse(struct_hough_table hough_table, cv::Mat img){
  int height = img.rows;
  int width = img.cols;

  double _cos, _sin;
  int y, x;

  for (int rho = 0; rho < RHO_MAX * 2; rho++){
    for (int t = 0; t < ANGLE_T; t++){
      // if not vote, skip
      if (hough_table.table[rho][t] < 1){
        continue;
      }

      _cos = cos(t * M_PI / 180);
      _sin = sin(t * M_PI / 180);

      if ((_sin == 0) || (_cos == 0)){
        continue;
      }

      for (int x = 0; x < width; x++){
        y = (int)(- _cos / _sin * x + (rho - RHO_MAX) / _sin);

        if ((y >= 0) && (y < height)){
          img.at<cv::Vec3b>(y, x) = cv::Vec3b(0, 0, 255);
        }
      }

      for (int y = 0; y < height; y++){
        x = (int)(- _sin / _cos * y + (rho - RHO_MAX) / _cos);

        if ((x >= 0) && (x < width)){
          img.at<cv::Vec3b>(y, x) = cv::Vec3b(0, 0, 255);
        }
      }
    }
  }

  return img;
}

// hough line detection
cv::Mat Hough_line(cv::Mat img){
  // get edge by canny
  cv::Mat edge = Canny(img);

  // hough
  struct_hough_table hough_table;

  // initialize 0
  for (int rho = 0; rho < RHO_MAX * 2; rho++){
    for (int t = 0; t < ANGLE_T; t++){
      hough_table.table[rho][t] = 0;
    }
  }

  // hough vote
  hough_table = Hough_vote(hough_table, edge);

  // hough NMS
  hough_table = Hough_NMS(hough_table);

  // hough inverse
  cv::Mat out = Hough_inverse(hough_table, img);

  return out;
}


int main(int argc, const char* argv[]){
  // read image
  cv::Mat img = cv::imread("thorino.jpg", cv::IMREAD_COLOR);

  // Hough line detection
  cv::Mat hough = Hough_line(img);

  //cv::imwrite("out.jpg", out);
  cv::imshow("answer(hough)", hough);
  cv::waitKey(0);
  cv::destroyAllWindows();

  return 0;
}

输入：

输出：