使用RANSAC的直线拟合算法

RANSAC 算法

简介

随机样本共识（RANSAC）是一种迭代方法，可从一组包含离群值的观察数据中估算数学模型的参数，当不对离群值施加影响时，离群值不受影响。因此，它也可以解释为异常检测方法。[1]从某种意义上说，它是非确定性算法，它仅以一定的概率产生合理的结果，并且随着允许更多的迭代，这种概率会增加。该算法由Fischler和Bolles于1981年在SRI International上首次发布。他们使用RANSAC解决了位置确定问题（LDP），其目的是确定空间上的点，这些点投射到图像上并成为一组地标。已知位置。

一个基本的假设是，数据由“内部”组成，即尽管分布可能受噪声影响，但可以通过某些模型参数集解释其分布的数据，以及不适合模型的数据“外部”。异常值可能来自例如噪声的极值，错误的测量结果或关于数据解释的错误假设。 RANSAC还假定，给定（通常是很小）一组inlier，存在一种可以估算模型参数的程序，该模型可以最佳地解释或拟合该数据。

RANSAC 思想伪代码

Given:
    data – 数据集
    model – 目标生成模型
    n – Minimum number of data points required to estimate model parameters.
    k – 最大迭代次数
    t – 判断模型足够好的阈值
    d – 最少的邻近点数量

Return:
    bestFit – 最好的模型（或者因为没有结果而返回NULL）

iterations = 0
bestFit = nul
bestErr = something really large

while iterations < k do
    maybeInliers := n randomly selected values from data
    maybeModel := model parameters fitted to maybeInliers
    alsoInliers := empty set
    for every point in data not in maybeInliers do
        if point fits maybeModel with an error smaller than t
             add point to alsoInliers
    end for
    if the number of elements in alsoInliers is > d then
        // 这个if并表明我们或许得到了一个好模型
        // 现在看看有多好
        betterModel := model parameters fitted to all points in maybeInliers and alsoInliers
        thisErr := a measure of how well betterModel fits these points
        if thisErr < bestErr then
            bestFit := betterModel
            bestErr := thisErr
        end if
    end if
    increment iterations
end while

return bestFit

[引用] 以上两部分完全摘自 维基百科： 只是为了阅读方便，进行了翻译并且粘贴在此

使用RANSAC的直线拟合算法

def ransacLine(points, iter=100, good_len=300, sample_points=10):
    '''
    ransacLine is to make robust prediction of a straight line out of a point set
    the algorithm is referred on wikipedia, check it out!

    [Input]
    points: 2-D points list
    
    [Parameters]
    iterations: more iterations might come out better model at the expense of more time consumption
    good_len: how many points around do you think is good enough to further
    sample point: how many points randomly choose at first
    
    Author: penway from cnblogs.com/penway
    '''

    bestLoss = 99999999999

    for i in range(0, iter):
        # choose maybeInliners
        maybeInliners = random.sample(points, sample_points)

        # make maybeModel
        maybeModel = cv.fitLine(np.asanyarray(maybeInliners), 1, 0.1, 0.01, 0.01).tolist()
        # maybeModel: [dx, dy, x0, y0]
        # maybeFunc = ax + by + c = [a, b, c] = [dy, -dx, dx*y0 - dy*x0]
        maybeFunc = [maybeModel[1][0], -maybeModel[0][0], maybeModel[0][0]*maybeModel[3][0] - maybeModel[1][0]*maybeModel[2][0]]

        alsoInliners = []
        for i in points:
            if not i in maybeInliners:
                # judge if near the line
                if i[0]*maybeFunc[0] + i[1]*maybeFunc[1] + maybeFunc[2] < 4:
                    alsoInliners.append(i)

        if len(alsoInliners) > good_len:
            # This implies that we may have found a good model, now test how good it is
            maybeInliners.extend(alsoInliners)
            betterModel = cv.fitLine(np.asanyarray(maybeInliners), 1, 0.1, 0.01, 0.01).tolist()
            betterFunc = [betterModel[1][0], -betterModel[0][0], betterModel[0][0]*betterModel[3][0] - betterModel[1][0]*betterModel[2][0]]
            thisLoss = 0
            for i in maybeInliners:  # use L2 as the loss function
                thisLoss += (i[0]*betterFunc[0] + i[1]*betterFunc[1] + betterFunc[2]) * (i[0]*betterFunc[0] + i[1]*betterFunc[1] + betterFunc[2])
            if thisLoss <= bestLoss:
                bestModel = betterModel
                bestFunc = betterFunc
                bestLoss = thisLoss

    return bestModel