C# 机器视觉-RANSAC算法拟合圆
我们在开发机器视觉的时候，很多情况下提取到圆的轮廓并不完整。那么我们就需要采取一些手段来将原本不完整的圆拟合成一个完整的圆。下面常用的是RANSAC算法来拟合圆。
static void RANSAC()
{
// 加载图像
Mat image = Cv2.ImRead("path_to_your_image.jpg", ImreadModes.Grayscale);
// 边缘检测
Mat edges = new Mat();
Cv2.Canny(image, edges, 100, 200);
// 寻找边缘点
Point[][] contours;
HierarchyIndex[] hierarchy;
Cv2.FindContours(edges, out contours, out hierarchy, RetrievalModes.External, ContourApproximationModes.ApproxSimple);
// 假设最长的轮廓是我们要拟合圆的边缘
var longestContour = contours.OrderByDescending(c => c.Length).FirstOrDefault();
// RANSAC参数
int iterations = 1000;
double distanceThreshold = 3.0; // 点到圆的最大距离
double bestCircularity = double.MaxValue; // 初始化为最大值
Point2f bestCircleCenter = new Point2f();
float bestCircleRadius = 0;
Random rand = new Random();
for (int i = 0; i < iterations; i++)
{
// 随机选择三个点
Point[] randomPoints = longestContour.OrderBy(x => rand.Next()).Take(3).ToArray();
// 计算这三个点定义的圆
Point2f center;
float radius;
if (TryFitCircleToPoints(randomPoints, out center, out radius))
{
// 计算适合这个圆的点的数量
var inliers = longestContour.Where(p => IsPointNearCircle(p, center, radius, distanceThreshold)).ToList();
int inliersCount = inliers.Count;
// 计算圆度
double circularity = CalculateCircularity(center, radius, inliers);
// 更新最佳圆
if (circularity < bestCircularity)
{
bestCircularity = circularity;
bestCircleCenter = center;
bestCircleRadius = radius;
}
}
}
// 输出最佳拟合圆的结果
Console.WriteLine($"Best circle center: {bestCircleCenter}, radius: {bestCircleRadius}, circularity: {bestCircularity}");
}
// 新增圆度计算方法
static double CalculateCircularity(Point2f center, float radius, List<Point> inliers)
{
double sumSquaredDifferences = inliers.Sum(point =>
{
double distanceToCenter = Math.Sqrt(Math.Pow(point.X - center.X, 2) +Math.Pow(point.Y - center.Y, 2));
return Math.Pow(distanceToCenter - radius, 2);
});
double circularity = Math.Sqrt(sumSquaredDifferences / inliers.Count);
return circularity;
}
static bool TryFitCircleToPoints(Point[] points, out Point2f center, out float radius)
{
// 三点确定一个圆的算法
// 使用三点坐标计算圆心和半径
center = new Point2f();
radius = 0f;
float x1 = points[0].X;
float y1 = points[0].Y;
float x2 = points[1].X;
float y2 = points[1].Y;
float x3 = points[2].X;
float y3 = points[2].Y;
float a = x1 - x2;
float b = y1 - y2;
float c = x1 - x3;
float d = y1 - y3;
float e = ((x1 * x1 - x2 * x2) + (y1 * y1 - y2 * y2)) / 2.0f;
float f = ((x1 * x1 - x3 * x3) + (y1 * y1 - y3 * y3)) / 2.0f;
float det = a * d - b * c;
if (Math.Abs(det) > 1e-6) // 非共线
{
// 计算圆心
center.X = (d * e - b * f) / det;
center.Y = (-c * e + a * f) / det;
// 计算半径
radius = (float)Math.Sqrt((center.X - x1) * (center.X - x1) + (center.Y - y1) * (center.Y - y1));
return true;
}
return false;
}
static bool IsPointNearCircle(Point point, Point2f center, float radius, double threshold)
{
// 计算点到圆的距离，并检查是否小于阈值
double distance = Math.Sqrt(Math.Pow(point.X - center.X, 2) + Math.Pow(point.Y - center.Y, 2)) - radius;
return Math.Abs(distance) <= threshold;
}