一種直線識別方案

本文介紹一種直線的識別方案。

步驟

1. 使用最小二乘法迴歸直線：

$$\begin{cases}\frac{\sum_{i=1}^N(x_i,\overline{x})(y_i,\overline{y})}{\sum_{i=1}^N(x_i,\overline{x})^2}\\b=\overline{y}-k\overline{x}\end{cases}$$

1. 獲得直線方程y=kx+b後，計算全部點到直線的距離，若在閾值範圍內，認爲是直線。

實現

/// <summary>
/// 最小二乘法求迴歸直線方程
/// </summary>
/// <param name="points">輸入數據</param>
/// <param name="k">直線斜率</param>
/// <param name="b">直線截距</param>
/// <param name="type">直線類型 1：水平線 2：垂直線 3：通常直線</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) //平行於X軸爲水平線，返回縱座標平均值
    {
        b = averageY;
        type = 1;
    }
    else if (denominator == 0)//平行於Y軸爲垂直線，返回橫座標平均值
    {
        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; //點到擬合直線距離過大
    }

    return true;
}

/// <summary>
/// 計算點到直線的距離
/// </summary>
/// <param name="p">待計算點</param>
/// <param name="k">直線斜率</param>
/// <param name="b">直線截距</param>
/// <param name="type">直線類型 1：水平線 2：垂直線 3：通常直線</param>
/// <returns>距離</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;
    }
}