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#include "opencv2/opencv.hpp"
#include <iostream>
#include <vector>
#include <random>
#include <numbers>
std::tuple<int, int, int> GetSample(const int& index_size,
const std::vector<std::tuple<int, int, int>>& sampled_indexes)
{
assert(index_size > 2);
static std::random_device rd;
static std::mt19937_64 gen(rd());
static std::uniform_int_distribution<int> dist(0, index_size - 1);
while (true)
{
std::vector<int> index = { dist(gen),dist(gen),dist(gen) };
if (index[0] == index[1] || index[0] == index[2] || index[1] == index[2]) { continue; }
std::sort(index.begin(), index.end());
bool has_sampled = false;
for (auto& [i, j, k] : sampled_indexes)
{
if (index[0] == i && j == index[1] && k == index[2])
{
has_sampled = true;
break;
}
}
if (has_sampled) { continue; }
else { return { index[0], index[1], index[2]}; }
}
}
void Show(const std::vector<cv::Point2f>& all_pts,
const std::vector<cv::Point2f>& inlier_pts,
const std::vector<cv::Point2f>& sample_pts,
const int windows_size,
const cv::Point2f& center,
const float radius)
{
cv::Mat image = cv::Mat(windows_size, windows_size, CV_8UC3, cv::Scalar::all(255));
for (auto& p : all_pts)
{
if (p.x >= 0 && p.x < windows_size && p.y >= 0 && p.y < windows_size)
{
cv::circle(image, p, 5, { 0, 0, 255 }, -1);
}
}
cv::Point2f p1, p2;
cv::circle(image, center, radius, { 0, 0, 0 }, 2, cv::LINE_AA);
for (auto& p : inlier_pts)
{
if (p.x >= 0 && p.x < windows_size && p.y >= 0 && p.y < windows_size)
{
cv::circle(image, p, 5, { 255, 0, 0 },-1);
}
}
for (auto& p : sample_pts)
{
if (p.x >= 0 && p.x < windows_size && p.y >= 0 && p.y < windows_size)
{
cv::circle(image, p, 5, { 0, 255, 0 }, -1);
}
}
cv::imshow("ransac-line-fit", image);
cv::waitKey(500);
}
void CircleFit(const std::vector<cv::Point2f>& points, cv::Point2f& circleCenter, float& radius)
{
//检查输入参数 | Check input parameters
assert(!points.empty() && points.size());
//构造矩阵 | Construct mat
double XiSum = 0;
double Xi2Sum = 0;
double Xi3Sum = 0;
double YiSum = 0;
double Yi2Sum = 0;
double Yi3Sum = 0;
double XiYiSum = 0;
double Xi2YiSum = 0;
double XiYi2Sum = 0;
double WiSum = 0;
for (size_t i = 0; i < points.size(); i++)
{
XiSum += points.at(i).x;
Xi2Sum += points.at(i).x * points.at(i).x;
Xi3Sum += points.at(i).x * points.at(i).x * points.at(i).x;
YiSum += points.at(i).y ;
Yi2Sum += points.at(i).y * points.at(i).y ;
Yi3Sum += points.at(i).y * points.at(i).y * points.at(i).y;
XiYiSum += points.at(i).x * points.at(i).y ;
Xi2YiSum += points.at(i).x * points.at(i).x * points.at(i).y;
XiYi2Sum += points.at(i).x * points.at(i).y * points.at(i).y;
WiSum += 1;
}
const int N = 3;
cv::Mat A = cv::Mat::zeros(N, N, CV_64FC1);
cv::Mat B = cv::Mat::zeros(N, 1, CV_64FC1);
A.at<double>(0, 0) = Xi2Sum;
A.at<double>(0, 1) = XiYiSum;
A.at<double>(0, 2) = XiSum;
A.at<double>(1, 0) = XiYiSum;
A.at<double>(1, 1) = Yi2Sum;
A.at<double>(1, 2) = YiSum;
A.at<double>(2, 0) = XiSum;
A.at<double>(2, 1) = YiSum;
A.at<double>(2, 2) = WiSum;
B.at<double>(0, 0) = -(Xi3Sum + XiYi2Sum);
B.at<double>(1, 0) = -(Xi2YiSum + Yi3Sum);
B.at<double>(2, 0) = -(Xi2Sum + Yi2Sum);
//解矩阵 | Solve
//求解A*X = B | Solve the A*X = B
cv::Mat X;
cv::solve(A, B, X, cv::DECOMP_LU);
double a = X.at<double>(0, 0);
double b = X.at<double>(1, 0);
double c = X.at<double>(2, 0);
//计算圆心和半径 | Calculate center and radius.
circleCenter.x = -0.5 * a;
circleCenter.y = -0.5 * b;
radius = 0.5 * std::sqrt(a * a + b * b - 4 * c);
}
void RansacCirclefit(const std::vector<cv::Point2f>& pts,
const float inlier_threshold,
std::vector<int>& inlier_indexes)
{
if (pts.size() <= 3) { return; }
if (inlier_threshold < 1e-6) { return; }
//1. 参数检查，初始化
int iterate_nums = 500; //迭代次数
float sample_points_min_distance = 5.0f; //两个采样点之间最小的距离
std::vector<std::tuple<int, int, int>> sampled_indexes;//已经采样的坐标点
sampled_indexes.reserve(iterate_nums);
std::vector<int> is_inlier(pts.size(), 0);
std::vector<int> is_inlier_tmp(pts.size(), 0);
int max_inlier_num = 0;
int sample_count = 0;
//2. 循环迭代
while (sample_count < iterate_nums)
{
//3. 随机抽取两点(采样）
auto [p1, p2, p3] = GetSample(pts.size(), sampled_indexes);
if (std::abs(pts[p1].x - pts[p2].x) < sample_points_min_distance
&& std::abs(pts[p1].y - pts[p2].y) < sample_points_min_distance
&& std::abs(pts[p2].x - pts[p3].x) < sample_points_min_distance
&& std::abs(pts[p2].y - pts[p3].y) < sample_points_min_distance)
{
continue;
}
else
{
sampled_indexes.push_back({ p1, p2, p2});
}
//4. 圆拟合
float radius = 0.0f;
cv::Point2f center;
CircleFit({ pts[p1], pts[p2], pts[p3]}, center,radius);
//5. 基于拟合的圆区分内外点
int inlier_num = 0;
std::vector<cv::Point2f> inliers;
for (int i = 0; i < pts.size(); i++)
{
auto& p = pts[i];
is_inlier_tmp[i] = 0;
double p_2_center = std::sqrt(std::pow(p.x - center.x, 2) + std::pow(p.y - center.y, 2));
if (std::abs(p_2_center - radius) < inlier_threshold)
{
is_inlier_tmp[i] = 1;
inlier_num++;
inliers.push_back(pts[i]);
}
}
Show(pts, inliers, { { pts[p1], pts[p2], pts[p3]}}, 500, center, radius);
if (inlier_num > max_inlier_num)
{
max_inlier_num = inlier_num;
is_inlier = is_inlier_tmp;
}
//6. 更新迭代的最佳次数
if (inlier_num == 0)
{
iterate_nums = 500;
}
else
{
double epsilon = 1.0 - double(inlier_num) / (double)pts.size(); //野值点比例
double p = 0.99; //所有样本中存在1个好样本的概率
double s = 3.0;
iterate_nums = int(std::log(1.0 - p) / std::log(1.0 - std::pow((1.0 - epsilon), s)));
}
sample_count++;
}
//7. 基于最优的结果所对应的内点做最终拟合
std::vector<cv::Point2f> inliers;
inliers.reserve(max_inlier_num);
for (int i = 0; i < is_inlier.size(); i++)
{
if (1 == is_inlier[i])
{
inliers.push_back(pts[i]);
}
}
float radius = 0.0f;
cv::Point2f center;
CircleFit(inliers, center, radius);
Show(pts, inliers, {}, 500, center, radius);
cv::waitKey(0);
}
int main()
{
std::random_device rd;
std::mt19937_64 gen(rd());
std::uniform_int_distribution<int> dist(0, 360);
std::normal_distribution<double> distr(0, 30);
cv::Point2f center(250, 250);
std::vector<cv::Point2f> pts;
for (int i = 1; i < 150; i ++)
{
float r = 150;
if (i % 2 == 0) { r += distr(gen); }
double theta = dist(gen);
float x = center.x + r * std::cos(theta / 180.0 * std::numbers::pi);
float y = center.y + r * std::sin(theta / 180.0 * std::numbers::pi);
pts.emplace_back(x, y);
}
std::vector<int> inliers_indexes;
RansacCirclefit(pts, 5, inliers_indexes);
return 0;
}
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