Line 2d robust estimation

Modules demonstrating how to estimate line 2d parameters from a cloud of points containing outliers. More...

Modules demonstrating how to estimate line 2d parameters from a cloud of points containing outliers.

For more informations about parametric estimation features, please see Parametric estimation.

We start by importing all necessary libraries:

import PyIPSDK

Searched 2d line is defined using polar coordinates : and .

We then define input data points as points on previous line with perturbated ordinate :

with :

• a random centered normal noise with unit standard deviation

Coordinates of two points have been manually modified to introduce outliers

# we define a 2d line by its polar coordinates
# rho = 5 and theta = 2pi/3 (roughly 2.094) 
# We then use following sampled points :
# each point is defined has [x; y=(rho-cos(theta)*x)/sin(theta) + N(0, 1)]
# where N(0,1) is a random centered normal noise with unit standard deviation
# Coordinates of two points have been modified to introduce outliers
ptColl = [
    [-10, 1.35403297463199],
    [-9,  0.467545836976205],
    [-8,  -0.46107136900246],
    [-7,  2.88401452309772],
    [-6,  1.35410194806754],
    [-5,  3.42764603498653],
    [-4,  2.73323167279303],
    [-3,  4.22309730303385],
    [-2,  10],                  # outlier !
    [-1,  5.65520168353248],
    [0,   5.91414922631518],
    [1,   5.86675394243645],
    [2,   0],                   # outlier !
    [3,   7.82681999731427],
    [4,   6.99551190321505],
    [5,   8.93195534818365],
    [6,   9.75159614279396],
    [7,   11.116355092464],
    [8,   10.3324851051409],
    [9,   11.8861915791043],
    [10,  10.5877158470975],
]

We then compute robust least square line estimation using following syntax :

# we can then simply compute robust least square line
cfg = PyIPSDK.EstimationConfig()
cfg.initLMS(0.40)
line, res = PyIPSDK.line2dEstimation(ptColl, cfg)

In this case we use Least Mean of Squares (LMS) robust algorithm for computation with an expected outlier ratio set to .

At last we display estimation results

# display results
print("Estimated line :")
print("----------------")
print(line)
print("")
print("Estimation detailed results")
print(res)

See the full source listing