场景：找到下图中手机的边缘直线。
思路：通过从左到右边缘找点的方法找到边缘点集，再将这些点集拟合成一条直线。
分析：边缘点集容易确定，但是蓝色箭头的异常点会包含在点集中，这时用OpenCV中的fitLine拟合直线会拟合成类似红色那条，可是我们实际想要的直线是绿色那条。
方案：离群（异常）点一般会离拟合后的直线比较远，可以很自然地想到让这些离群点的权重减少后重新拟合一遍；具体原理可参考《机器视觉算法与应用》，对应Halcon中函数fit_line_contour_xld的tukey方法；
效果：下图为迭代10次的效果，随着迭代次数增加颜色变浅，可以看到直线离左上角几个离群点越来越远了。
代码：
void FitLineWeight(vector<Point2f> vecPointInput, vector<float> vWeights, float& fWeight, float& fBias)
{
float x1 = 0;
float x2 = 0;
float y1 = 0;
float x1y1 = 0;
float n = 0;
for (size_t i = 0; i < vecPointInput.size(); i++)
{
float x = vecPointInput[i].x;
float y = vecPointInput[i].y;
float weight = vWeights[i];
x1 += weight * x;
y1 += weight * y;
x2 += weight * x * x;
x1y1 += weight * x * y;
n += weight;
}
Mat matX = (Mat_<float>(2, 2) <<
n, x1, x1, x2);
Mat matY = (Mat_<float>(2, 1) <<
y1, x1y1);
Mat matABC;
solve(matX, matY, matABC);
fBias = matABC.at<float>(0, 0);
fWeight = matABC.at<float>(1, 0);
}
void FitLineItera(vector<Point2f> vecPointInput, int nIteraNum, float& fWeight, float& fBias)
{
vector<float> vWeights(vecPointInput.size(), 1);
FitLineWeight(vecPointInput, vWeights, fWeight, fBias);
if (nIteraNum < 1) nIteraNum = 1;
int nCount = 0;
while (nCount < nIteraNum)//多次迭代
{
vector<float> vWeights;
vector<float> vDist;
for (size_t i = 0; i < vecPointInput.size(); i++)
{
float fDistance;
if (0 == fWeight) fWeight += 0.000001;
PointToLineDistance(vecPointInput[i], fWeight, fBias, fDistance);
vDist.push_back(fDistance);
}
vector<float> vDistCopy;
vDistCopy.assign(vDist.begin(), vDist.end());
sort(vDistCopy.begin(), vDistCopy.end());
double sigma = vDistCopy[vDistCopy.size() / 2] / 0.675;
sigma *= 2;
vWeights.clear();
for (size_t i = 0; i < vDist.size(); i++)
{
double weight;
if (vDist[i] <= sigma)//Tukey
{
double rate = vDist[i] / sigma;
weight = pow((1 - rate * rate), 2);
}
else
{
weight = 0;
}
vWeights.push_back(weight);
}
FitLineWeight(vecPointInput, vWeights, fWeight, fBias);
nCount++;
}
}
bool DrawLine(Mat& imgDraw, float fLineWeight, float fLineBias, const Scalar& color, int thickness, int lineType)
{
vector<Point> vecLine;
int nWidth = imgDraw.cols;
int nHight = imgDraw.rows;
int nTempX;
int nTempY;
nTempX = 0;//直线与矩形左边的交点
nTempY = fLineWeight * nTempX + fLineBias;
if (nTempY > 0 && nTempY < nHight - 1)
vecLine.push_back(Point(nTempX, nTempY));
nTempX = nWidth - 1;//直线与矩形右边的交点
nTempY = fLineWeight * nTempX + fLineBias;
if (nTempY > 0 && nTempY < nHight - 1)
vecLine.push_back(Point(nTempX, nTempY));
nTempY = 0;//直线与矩形上边的交点
nTempX = (nTempY - fLineBias) / fLineWeight;
if (nTempX > 0 && nTempX < nWidth - 1)
vecLine.push_back(Point(nTempX, nTempY));
nTempY = 0;//直线与矩形下边的交点
nTempX = (nTempY - fLineBias) / fLineWeight;
if (nTempX > 0 && nTempX < nWidth - 1)
vecLine.push_back(Point(nTempX, nTempY));
if (2 != vecLine.size())
return false;
line(imgDraw, vecLine[0], vecLine[1], color, thickness, lineType);
return true;
}
int main()
{
vector<Point2f> vecPointInput;
vecPointInput.push_back(Point2f(70.0, 110.0));
vecPointInput.push_back(Point2f(100.0, 180.0));
vecPointInput.push_back(Point2f(220.0, 219.0));
vecPointInput.push_back(Point2f(260.0, 265.0));
vecPointInput.push_back(Point2f(280.0, 278.0));
vecPointInput.push_back(Point2f(320.0, 360.0));
vecPointInput.push_back(Point2f(420.0, 427.0));
vecPointInput.push_back(Point2f(480.0, 477.0));
vecPointInput.push_back(Point2f(520.0, 511.0));
vecPointInput.push_back(Point2f(560.0, 558.0));
vecPointInput.push_back(Point2f(600.0, 601.0));
float fWeight;
float fBias;
Mat imgShow = Mat(Size(1000,1000), CV_8UC3, Scalar(255, 255, 255));
for (size_t i = 0; i < vecPointInput.size(); i++)
drawMarker(imgShow, vecPointInput[i], Scalar(0 ,0, 255), MARKER_CROSS, 10, 1);
for (int i = 0; i < 10; i++)
{
FitLineItera(vecPointInput, i, fWeight, fBias);
DrawLine(imgShow, fWeight, fBias, Scalar(5 + 25 * i, 50 + 20 * i, 0), 2);
}
}
最后：
参考该方法可以很容易实现拟合有离群点的圆，这里不再赘述。
有什么建议可加v讨论：gaoshijue666