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Count Inliers

Implement a function to count the number of inlier points for a given line model, which is crucial in RANSAC for robust model fitting. The task involves determining how many points in a dataset are well-represented by a line model.

The concept of inliers is essential in model fitting as it distinguishes between points that are close to the model and those that are not, known as outliers. A point is considered an inlier if its perpendicular distance to the line, defined by $y = mx + b$ , is less than a specified threshold. This distance can be calculated using the formula $d = \frac{|mx_i - y_i + b|}{\sqrt{m^2 + 1}}$ .

To count inliers, follow these steps:

Calculate the perpendicular distance from each point to the line.
Compare this distance with the given threshold. The main equation for the distance is

d = \frac{|mx_i - y_i + b|}{\sqrt{m^2 + 1}}

This technique is widely used in computer vision for line detection and model fitting.

Example:

Input:

count_inliers([(0,0), (1,1), (1,3)], 1, 0, 0.5)

Output:

Reasoning:

For each point, calculate the perpendicular distance to the line $y = mx + b$ using $d = \frac{|mx_i - y_i + b|}{\sqrt{m^2 + 1}}$
Point (0,0): $d = \frac{|1(0) - 0 + 0|}{\sqrt{1^2 + 1}} = \frac{0}{\sqrt{2}} \approx 0$ → inlier (0 < 0.5)
Point (1,1): $d = \frac{|1(1) - 1 + 0|}{\sqrt{2}} = \frac{0}{\sqrt{2}} = 0$ → inlier (0 < 0.5)
Point (1,3): $d = \frac{|1(1) - 3 + 0|}{\sqrt{2}} = \frac{2}{\sqrt{2}} \approx 1.41$ → outlier (1.41 > 0.5)
Output: 2 inliers (points that satisfy distance < threshold)

Constraints:

Return count of inliers

Editor

Python 3.13.1

Test Results

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Run code to see test results.