RANSAC Line Fitting

Implement RANSAC for robust line fitting to 2D points with outliers. This task involves using the RANSAC algorithm to estimate the parameters of a line that best fits a set of 2D points, some of which may be outliers.

The RANSAC algorithm is a robust estimation technique used to fit models to data with outliers. It works by randomly selecting a minimum number of samples, fitting a model to these samples, and then counting the number of inliers, which are points that are within a certain threshold of the model. The process is repeated for a specified number of iterations, and the model with the most inliers is kept as the best fit. In the case of line fitting, the line can be represented by the equation $ax + by + c = 0$ , where $a^2 + b^2 = 1$ . The distance from a point $(x_0, y_0)$ to the line is given by $d = |ax_0 + by_0 + c|$ .

Here are the steps to follow:

Randomly select a minimum number of samples (2 points for a line)
Fit a line to these samples
Count the number of inliers (points within a threshold of the line)
Repeat for a specified number of iterations

d = |ax_0 + by_0 + c|

This technique is widely used in computer vision applications, such as image processing and feature detection.

Example:

Input:

points = [[0,0], [1,1], [2,2], [3,3], [10,0]]  # Last is outlier
threshold = 0.1
n_iterations = 100

Output:

{'line': [0.707, -0.707, 0], 'inliers': 4}

Reasoning:

Points [0,0], [1,1], [2,2], [3,3] lie on y=x line. Line equation: x - y = 0, normalized: 0.707x - 0.707y = 0

Point [10,0] is far from this line (outlier).

RANSAC finds the line with 4 inliers, ignoring the outlier.

Constraints:

points: List of [x, y] coordinates
threshold: Max distance to be considered inlier
n_iterations: Number of RANSAC iterations
Return: Dict with 'line' [a,b,c] and 'inliers' count

Example:

Constraints:

Test Results