opencv: 线性拟合

opencv提供了fitline函数用于直线拟合，原型为：

C++: void fitLine(InputArray points, OutputArray line, int distType, double param, double reps, double aeps)

Python: cv2.fitLine(points, distType, param, reps, aeps) → line

C: void cvFitLine(const CvArr* points, int distType, double param, double reps, double aeps, float* line)

Python: cv.FitLine(points, distType, param, reps, aeps) → line


Parameters:
points – Input vector of 2D or 3D points, stored in std::vector<> or Mat.
line – Output line parameters. In case of 2D fitting, it should be a vector of 4 elements (like Vec4f) - (vx, vy, x0, y0), where (vx, vy) is a normalized vector collinear to the line and (x0, y0) is a point on the line. In case of 3D fitting, it should be a vector of 6 elements (like Vec6f) - (vx, vy, vz, x0, y0, z0), where (vx, vy, vz) is a normalized vector collinear to the line and (x0, y0, z0) is a point on the line.
distType – Distance used by the M-estimator (see the discussion below).
param – Numerical parameter ( C ) for some types of distances. If it is 0, an optimal value is chosen.
reps – Sufficient accuracy for the radius (distance between the coordinate origin and the line).
aeps – Sufficient accuracy for the angle. 0.01 would be a good default value for reps and aeps.

支持2D,3D的点集拟合，点集使用std::vector<>来存储，如果为3Dpoint，那么line使用Vec6f, 2D points，使用Vec4f;

拟合方式提供了下面几种方法：

distType=CV_DIST_L2 最小二乘法

$ho (r) = r^2/2 quad ext{(the simplest and the fastest least-squares method)}$
distType=CV_DIST_L1

$ho (r) = r$
distType=CV_DIST_L12

$ho (r) = 2 cdot ( sqrt{1 + frac{r^2}{2}} - 1)$
distType=CV_DIST_FAIR

$ho left (r ight ) = C^2 cdot left ( frac{r}{C} - log{left(1 + frac{r}{C} ight)} ight ) quad ext{where} quad C=1.3998$
distType=CV_DIST_WELSCH

$ho left (r ight ) = frac{C^2}{2} cdot left ( 1 - exp{left(-left(frac{r}{C} ight)^2 ight)} ight ) quad ext{where} quad C=2.9846$
distType=CV_DIST_HUBER

$ho (r) = fork{r^2/2}{if $r < C$}{C cdot (r-C/2)}{otherwise} quad ext{where} quad C=1.345$

注：该博文为扩展型；