OpenCV 线拟合算法

Question

我正在尝试理解 OpenCV fitLine() 算法。

这是来自 OpenCV 的代码片段： icvFitLine2D 函数 - icvFitLine2D

我看到有一些随机函数选择近似点，然后计算点到拟合线的距离（使用选择的点），然后选择其他点并尝试使用选择的 distType 最小化距离。

有人可以澄清this moment 会发生什么，而无需经过严格的数学运算并假设没有出色的统计知识吗？ OpenCV 代码 cmets 和变量名对我理解这段代码没有帮助。

Answer 1

（这是一个老问题，但这个话题激起了我的好奇心）

OpenCV FitLine 实现了两种不同的机制。

如果参数distType 设置为CV_DIST_L2，则使用standard unweighted least squares fit。

如果使用其他distTypes 之一（CV_DIST_L1、CV_DIST_L12、CV_DIST_FAIR、CV_DIST_WELSCH、CV_DIST_HUBER），则该过程是某种RANSAC 适合：

• 最多重复 20 次：
  • 选择 10 个随机点，做一个仅适合它们的最小二乘法
  • 最多重复 30 次：
    • 使用当前找到的线和选择的distType 计算所有点的权重
    • 对所有点进行加权最小二乘拟合
    • （这是Iteratively reweighted least squares fit 或M-Estimator）
• 返回找到的最佳线型

下面是更详细的伪代码描述：

repeat at most 20 times:

    RANSAC (line 371)
     - pick 10 random points, 
     - set their weights to 1, 
     - set all other weights to 0

    least squares weighted fit (fitLine2D_wods, line 381)
     - fit only the 10 picked points to the line, using least-squares

    repeat at most 30 times: (line 382)
     - stop if the difference between the found solution and the previous found solution is less than DELTA  (line 390 - 406)
       (the angle difference must be less than adelta, and the distance beween the line centers must be less than rdelta)
     - stop if the sum of squared distances between the found line and the points is less than EPSILON (line 407)
       (The unweighted sum of squared distances is used here ==> the standard L2 norm)

        re-calculate the weights for *all* points (line 412)
         - using the given norm (CV_DIST_L1 / CV_DIST_L12 / CV_DIST_FAIR / ...)
         - normalize the weights so their sum is 1
         - special case, to catch errors: if for some reason all weights are zero, set all weight to 1

        least squares weighted fit (fitLine2D_wods, line 437)
         - fit *all* points to the line, using weighted least squares

    if the last found solution is better than the current best solution (line 440)
        save it as the new best
        (The unweighted sum of squared distances is used here ==> the standard L2 norm)

        if the distance between the found line and the points is less than EPSILON
             break

return the best solution

权重的计算取决于所选的distType，根据the manual，其公式为weight[Point_i] = 1/ p(distance_between_point_i_and_line)，其中p 为：

distType=CV_DIST_L1

distType=CV_DIST_L12

distType=CV_DIST_FAIR

distType=CV_DIST_WELSCH

distType=CV_DIST_HUBER

不幸的是，我不知道哪个distType 最适合哪种数据，也许其他人可以对此有所了解。

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我注意到一些有趣的事情：选择的范数仅用于迭代重新加权，找到的最佳解决方案总是根据 L2 范数（未加权和最小二乘是最小的）。我不确定这是否正确。