本文介绍一种直线的辨认计划。
步骤
- 应用最小二乘法回归直线：
$$\begin{cases}\frac{\sum_{i=1}^N(x_i,\overline{x})(y_i,\overline{y})}{\sum_{i=1}^N(x_i,\overline{x})^2}\\b=\overline{y}-k\overline{x}\end{cases}$$
- 失去直线方程
y=kx+b后，计算所有点到直线的间隔，若在阈值范畴内，认为是直线。
实现
/// <summary>/// 最小二乘法求回归直线方程/// </summary>/// <param name="points">输出数据</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：个别直线</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; //点到拟合直线间隔过大 } return true;}/// <summary>/// 计算点到直线的间隔/// </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：个别直线</param>/// <returns>间隔</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; }}