Fits a line to a 2D or 3D point set

lin = cv.fitLine(points)
lin = cv.fitLine(points, 'OptionName',optionValue, ...)

Input

• points Input vector of 2D or 3D points. 2D points stored in a cell array of 2-element vectors in the form {[x,y], [x,y], ...} or a Nx2/Nx1x2/1xNx2 numeric array. 3D points stored in a cell array of 3-element vectors in the form {[x,y,z], [x,y,z], ...} or a Nx3/Nx1x3/1xNx3 numeric array.

Output

• lin Output line parameters. In case of 2D fitting, it is a vector of 4-elements vector [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 is a 6-elements vector [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.

Options

• DistType Distance used by the M-estimator (see explanation below). One of: 'L2' (default), 'L1', 'L12', 'Fair', 'Welsch', 'Huber'.
• Param Numerical parameter (C) for some types of distances. If it is 0, an optimal value is chosen. default 0.
• RadiusEps Sufficient accuracy for the radius (distance between the coordinate origin and the line). default 0.01
• AngleEps Sufficient accuracy for the angle. default 0.01

The function fitLine fits a line to a 2D or 3D point set by minimizing \sum_i rho(r_i) where r_i is a distance between the i-th point and the line, and rho(r) is a distance function, one of the following:

• L2

  rho(r) = r^2/2 (the simplest and the fastest least-squares method)

• L1

  rho(r) = r

• L12

  rho(r) = 2 * (sqrt(1+r^2/2) - 1)

• Fair

  rho(r) = C^2 * (r/C - log(1 + r/c)), where C = 1.3998

• Welsch

  rho(r) = C^2/2 * (1 - exp(-(r/c)^2)), where C = 2.9846

• Huber

  | r^2/2 if r<C rho(r) = | , where C = 1.345 | C * (r - C/2) otherwise

The algorithm is based on the M-estimator (http://en.wikipedia.org/wiki/M-estimator) technique that iteratively fits the line using the weighted least-squares algorithm. After each iteration the weights w_i are adjusted to be inversely proportional to rho(r_i).