使用C++语言,用RANSAC算法计算最优单映射变换矩阵
时间: 2024-02-06 08:09:59 浏览: 28
RANSAC算法是一种鲁棒的估计方法,用于从数据中找出最优模型。在计算最优单映射变换矩阵时,我们可以采用以下步骤:
1. 随机选择一组匹配点对,计算单映射变换矩阵。
2. 对于剩余的匹配点对,计算它们的变换后的坐标,并计算它们与对应点的距离。
3. 统计距离小于阈值的点对数量,如果数量大于一定比例(例如50%),则认为当前单映射变换矩阵可靠。
4. 重复上述步骤多次,选择一组距离最小的点对对应的单映射变换矩阵作为最优解。
下面是C++代码实现:
```c++
#include <iostream>
#include <vector>
#include <cmath>
#include <random>
using namespace std;
// 定义点的结构体
struct Point {
double x, y;
};
// 计算单映射变换矩阵
vector<vector<double>> calculateHomography(vector<Point>& srcPoints, vector<Point>& dstPoints) {
vector<vector<double>> homography(3, vector<double>(3, 0));
// 构造矩阵A
int numPoints = srcPoints.size();
vector<vector<double>> A(2 * numPoints, vector<double>(9, 0));
for (int i = 0; i < numPoints; i++) {
double x = srcPoints[i].x;
double y = srcPoints[i].y;
double u = dstPoints[i].x;
double v = dstPoints[i].y;
A[2 * i][0] = x;
A[2 * i][1] = y;
A[2 * i][2] = 1;
A[2 * i][6] = -u * x;
A[2 * i][7] = -u * y;
A[2 * i][8] = -u;
A[2 * i + 1][3] = x;
A[2 * i + 1][4] = y;
A[2 * i + 1][5] = 1;
A[2 * i + 1][6] = -v * x;
A[2 * i + 1][7] = -v * y;
A[2 * i + 1][8] = -v;
}
// 求解最小二乘问题Ax=0
vector<vector<double>> U, V;
vector<double> S;
svd(A, U, S, V);
homography[0][0] = V[8][0];
homography[0][1] = V[8][1];
homography[0][2] = V[8][2];
homography[1][0] = V[8][3];
homography[1][1] = V[8][4];
homography[1][2] = V[8][5];
homography[2][0] = V[8][6];
homography[2][1] = V[8][7];
homography[2][2] = V[8][8];
return homography;
}
// 计算两点之间的欧几里得距离
double distance(Point& p1, Point& p2) {
double dx = p2.x - p1.x;
double dy = p2.y - p1.y;
return sqrt(dx * dx + dy * dy);
}
// 计算单映射变换矩阵
vector<vector<double>> calculateHomographyRANSAC(vector<Point>& srcPoints, vector<Point>& dstPoints, double threshold, int maxIterations) {
int numPoints = srcPoints.size();
if (numPoints < 4) {
cout << "At least 4 points are needed!" << endl;
return vector<vector<double>>();
}
int bestInliers = 0;
vector<vector<double>> bestHomography;
random_device rd;
mt19937 gen(rd());
uniform_int_distribution<int> dist(0, numPoints - 1);
// 迭代maxIterations次
for (int i = 0; i < maxIterations; i++) {
// 随机选择4个匹配点对
vector<Point> src(4), dst(4);
for (int j = 0; j < 4; j++) {
int index = dist(gen);
src[j] = srcPoints[index];
dst[j] = dstPoints[index];
}
// 计算单映射变换矩阵
vector<vector<double>> homography = calculateHomography(src, dst);
// 统计距离小于阈值的点对数量
int inliers = 0;
for (int j = 0; j < numPoints; j++) {
Point srcPoint = srcPoints[j];
Point dstPoint = dstPoints[j];
double x = homography[0][0] * srcPoint.x + homography[0][1] * srcPoint.y + homography[0][2];
double y = homography[1][0] * srcPoint.x + homography[1][1] * srcPoint.y + homography[1][2];
double w = homography[2][0] * srcPoint.x + homography[2][1] * srcPoint.y + homography[2][2];
double u = x / w;
double v = y / w;
double d = distance(dstPoint, {u, v});
if (d < threshold) {
inliers++;
}
}
// 更新最优解
if (inliers > bestInliers) {
bestInliers = inliers;
bestHomography = homography;
}
}
return bestHomography;
}
```
其中,`svd()`函数是求解SVD分解的函数,可以通过第三方库(如Eigen)实现。`calculateHomography()`函数计算单映射变换矩阵,`calculateHomographyRANSAC()`函数使用RANSAC算法计算最优单映射变换矩阵。