c# 圆形识别方案和直线识别方案的参考示例

圆形识别方案

识别流程

• 判断是否为封闭图形；
• 根据圆的方程，取输入点集中的1/6、3/6、5/6处的三个点，求得圆的方程，获取圆心及半径；
• 取点集中的部分点，计算点到圆心的距离与半径的比例，与设定的阈值比较，得出结果。~~~~

实现

public static bool IsCircle(List<Point> points, out Point center, out double radius)
{
 int len = points.Count;
 center = new Point();
 radius = 0;

 // 判断是否为封闭图形
 if (!IsClosedFigure(points))
 return false;

 int judgePointNum = len * 50 / 100;
 if (len < judgePointNum)
 return false;

 // 取链表上三个点作为判断圆的根据
 Point p1 = points[len / 6];
 Point p2 = points[len / 2];
 Point p3 = points[len * 5 / 6];
 if ((Math.Abs(p1.X - p2.X) < 100 && Math.Abs(p1.Y - p2.Y) < 100)
 || (Math.Abs(p1.X - p3.X) < 100 && Math.Abs(p1.Y - p3.Y) < 100)
 || (Math.Abs(p2.X - p3.X) < 100 && Math.Abs(p2.Y - p3.Y) < 100))
 return false;

 // 三个点确定圆的方程，获取圆心坐标及半径
 GetCircle(p1, p2, p3, out center, out radius);

 // 获取圆上平均分部的多个点，判断其到圆心的距离与半径之差是否在精度内
 for (int i = 0; i < judgePointNum; ++i)
 {
 // 获取圆上点
 Point p = points[len * i / judgePointNum];
 double deviation = Math.Abs(GetDistance(center, p) - radius);

 // 点在圆上的偏移量与半径的比值若大于固定值，则不为圆
 if (deviation/radius > MaxRatio)
  return false;
 }

 return true;
}

直线识别方案

步骤

1.使用最小二乘法回归直线：

2.得到直线方程y=kx+b后，计算所有点到直线的距离，若在阈值范围内，认为是直线。

实现

/// <summary>
/// 最小二乘法求回归直线方程
/// </summary>
/// <param name="points">输入数据</param>
/// <param name="k">直线斜率</param>
/// <param name="b">直线截距</param>
/// <param name="type">直线类型 1：水平线 2：垂直线 3：一般直线</param>
/// <returns></returns>
public static bool IsLine(List<Point> points, out double k, out double b, out int type)
{
 k = 0;
 b = 0;
 type = 0;

 if (points.Count < 2) return false;

 double averageX = 0, averageY = 0, n = 0;
 n = points.Count;
 foreach (Point p in points)
 {
 averageX += p.X;
 averageY += p.Y;
 }
 averageX /= n;
 averageY /= n;

 double numerator = 0, denominator = 0;
 foreach (Point p in points)
 {
 numerator += (p.X - averageX) * (p.Y - averageY);
 denominator += (p.X - averageX) * (p.X - averageX);
 }

 if (numerator == 0) //平行于X轴为水平线，返回纵坐标平均值
 {
 b = averageY;
 type = 1;
 }
 else if (denominator == 0)//平行于Y轴为垂直线，返回横坐标平均值
 {
 b = averageX;
 type = 2;
 }
 else
 {
 type = 3;
 }

 k = numerator / denominator;
 b = averageY - k * averageX;

 foreach (Point p in points)
 {
 dis = GetPoint2LineDistance(p, k, b, type);
 if (dis > MAX_POINT_LINE_DIS) return false; //点到拟合直线距离过大
 }

 return true;
}

/// <summary>
/// 计算点到直线的距离
/// </summary>
/// <param name="p">待计算点</param>
/// <param name="k">直线斜率</param>
/// <param name="b">直线截距</param>
/// <param name="type">直线类型 1：水平线 2：垂直线 3：一般直线</param>
/// <returns>距离</returns>
private static double GetPoint2LineDistance(Point p, double k, double b, int type)
{
 if (type == 1)
 {
 return Math.Abs(p.Y - b);
 }
 else if (type == 2)
 {
 return Math.Abs(p.X - b);
 }
 else
 {
 double numerator = 0, denominator = 0;
 numerator = Math.Abs(k * p.X - p.Y + b);
 denominator = Math.Sqrt(k * k + 1);
 return numerator / denominator;
 }
}

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