# How to fit a line using RANSAC in Cartesian coordinates?

I spent some time trying different things and manage with relative ease to get the following result. The thought i had was:

1. Divide points into section.
2. Use RANSAC on each section to get a line estimate.

The dividing part was done quite trivialt by comparing distance between incrementing measurements. Not that this is the part that needs to be worked more on, you can see it's flaws on the "yellow part" where two lines are estimated as one section.

The result I got was the following (note that chaning parameters will improve the result):

This is the code (note that I am not a professional programmer):

import matplotlib.pyplot as plt
import numpy as np
from sklearn import linear_model, datasets
from skimage.measure import LineModelND, ransac
import pandas as pd
import math

angle = df.values[:,0]
distance = df.values[:,1]
cartesian = [(r*math.cos(phi*math.pi/180), r*math.sin(phi*math.pi/180)) for r, phi in zip(distance, angle)]
x, y = map(list, zip(*cartesian))

# coverting this into 2d array
x_data =  np.array(x)
y_data =  np.array(y)

def plot_ransac(segment_data_x, segment_data_y):
data = np.column_stack([segment_data_x, segment_data_y])

# fit line using all data
model = LineModelND()
model.estimate(data)

# robustly fit line only using inlier data with RANSAC algorithm
model_robust, inliers = ransac(data, LineModelND, min_samples=2,
residual_threshold=5, max_trials=1000)
outliers = inliers == False

# generate coordinates of estimated models
line_x = np.array([segment_data_x.min(), segment_data_x.max()])
line_y = model.predict_y(line_x)
line_y_robust = model_robust.predict_y(line_x)
k = (line_y_robust[1] - line_y_robust[0])/(line_x[1]- line_x[0])
m = line_y_robust[0] - k*line_x[0]
x0 = (segment_data_y.min() - m)/k
x1 = (segment_data_y.max() - m)/k
line_x_y = np.array([x0, x1])
line_y_robust_y = model_robust.predict_y(line_x_y)
if (distance(line_x[0], line_y_robust[0], line_x[1], line_y_robust[1]) <
distance(line_x_y[0], line_y_robust_y[0], line_x_y[1], line_y_robust_y[1])):
plt.plot(line_x, line_y_robust, '-b', label='Robust line model')
else:
plt.plot(line_x_y, line_y_robust_y, '-b', label='Robust line model')

x_segments = []
y_segments = []

def distance(x1,y1,x2,y2):
return np.sqrt((x1-x2)**2 + (y1-y2)**2)

start = 0
distances = []
for i in range(len(x_data)-1):
distance_to_point = distance(x_data[i], y_data[i], x_data[i+1], y_data[i+1])
distances.append(distance_to_point)
if distance_to_point > 200:
if i-start>10:
x_segments.append(x_data[start:i])
y_segments.append(y_data[start:i])
start = i+1
if i == len(x_data)-2:
if i-start>10:
x_segments.append(x_data[start:i])
y_segments.append(y_data[start:i])

plt.plot(x_data, y_data, '.', color = 'grey')
for x_seg, y_seg in zip(x_segments, y_segments):
plt.plot(x_seg, y_seg,'.', markersize = 10)
plot_ransac(x_seg, y_seg)
print('Line is:', distance(x_seg[0], y_seg[0],x_seg[1], y_seg[1]), 'units long')

plt.axis('equal')
plt.show()


Hope this is somewhat helpful for you.

I could not find the solution for sklearn, But thankfully there is another library from sci-image. And Ski-image detects the line properly. Here is the solution that I was looking for.

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from skimage.measure import ransac, LineModelND, CircleModel
import math

angle = df.values[:,0]
distance = df.values[:,1]

x= angle
y= distance

cartesian = [(r*math.cos(phi*math.pi/180), r*math.sin(phi*math.pi/180)) for r,
phi in zip(distance, angle)]

x, y = map(list, zip(*cartesian))

# converting this into 2d array
x=  np.array(x)
y=  np.array(y)

x=x.reshape(-1, 1)
y=y.reshape(-1, 1)

data = np.column_stack([x, y])

model = LineModelND()
model.estimate(data)
# robustly fit line only using inlier data with RANSAC algorithm
model_robust, inliers = ransac(data, LineModelND, min_samples=2,
residual_threshold=10, max_trials=1000)
outliers = inliers == False

# generate coordinates of estimated models
line_x = np.arange(x.min(),x.max())  #[:, np.newaxis]
line_y = model.predict_y(line_x)
line_y_robust = model_robust.predict_y(line_x)

fig, ax = plt.subplots()
ax.plot(data[outliers, 0], data[outliers, 1], '.r', alpha=0.6,
label='Outlier data')
ax.plot(data[inliers, 0], data[inliers, 1], '.b', alpha=0.6,
label='Inlier data')
print("data: ", data)
print(data[inliers, 0], data[inliers, 1])
#ax.plot(line_x, line_y, '-k', label='Line model from all data')
#ax.plot(line_x, line_y_robust, '-b', label='Robust line model')
#ax.legend(loc='lower left')
plt.show()


And here is the resulting image that I am getting:

You are most welcome to modify or edit this answer. I would love to get a different answer.