WPF -- 一种直线识别方案

本文介绍一种直线的识别方案。

步骤

1. 使用最小二乘法回归直线：

1. 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;
}
}