Plane fitting in a 3d point cloud

Question

I am trying to find planes in a 3d point cloud, using the regression formula Z= aX + bY +C

I implemented least squares and ransac solutions, but the 3 parameters equation limits the plane fitting to 2.5D- the formula can not be applied on planes parallel to the Z-axis.

My question is how can I generalize the plane fitting to full 3d? I want to add the fourth parameter in order to get the full equation aX +bY +c*Z + d how can I avoid the trivial (0,0,0,0) solution?

Thanks!

The Code I'm using:

from sklearn import linear_model

def local_regression_plane_ransac(neighborhood):
    """
    Computes parameters for a local regression plane using RANSAC
    """

    XY = neighborhood[:,:2]
    Z  = neighborhood[:,2]
    ransac = linear_model.RANSACRegressor(
                                          linear_model.LinearRegression(),
                                          residual_threshold=0.1
                                         )
    ransac.fit(XY, Z)

    inlier_mask = ransac.inlier_mask_
    coeff = model_ransac.estimator_.coef_
    intercept = model_ransac.estimator_.intercept_

Answer 1

import pcl
cloud = pcl.PointCloud()
cloud.from_array(points)
seg = cloud.make_segmenter_normals(ksearch=50)
seg.set_optimize_coefficients(True)
seg.set_model_type(pcl.SACMODEL_PLANE)
seg.set_normal_distance_weight(0.05)
seg.set_method_type(pcl.SAC_RANSAC)
seg.set_max_iterations(100)
seg.set_distance_threshold(0.005)
inliers, model = seg.segment()

you need to install python-pcl first. Feel free to play with the parameters. points here is a nx3 numpy array with n 3d points. Model will be [a, b, c, d] such that ax + by + cz + d = 0