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RANSAC Homography Estimation

Implement RANSAC for homography estimation between two images, a crucial task in computer vision that involves finding the transformation matrix mapping points between planes. A homography $H$ (3×3 matrix) maps points between planes: $\mathbf{p'} = H \mathbf{p}$ .

The Direct Linear Transform (DLT) algorithm estimates $H$ from 4+ correspondences by setting up a linear system $Ah = 0$ and solving using Singular Value Decomposition (SVD).

Set up linear system $Ah = 0$ from point correspondences
Solve using SVD to find $h$ , the last row of $V^T$ RANSAC makes this robust to mismatched correspondences.

H = \begin{bmatrix} h_{11} & h_{12} & h_{13} \\ h_{21} & h_{22} & h_{23} \\ h_{31} & h_{32} & h_{33} \end{bmatrix}

This technique is widely used in image stitching and object recognition.

Example:

Input:

src = [[0,0], [1,0], [1,1], [0,1], [10,10]]
dst = [[0,0], [2,0], [2,2], [0,2], [5,5]]  # 2x scale + outlier
threshold = 1.0

Output:

H ≈ [[2,0,0],[0,2,0],[0,0,1]], 4 inliers

Reasoning:

First 4 point pairs indicate 2× scaling. Last pair [10,10]→[5,5] is inconsistent (would be 0.5× scale).

RANSAC finds the homography explaining 4/5 correspondences.

Constraints:

src_points: Points in first image [[x1,y1], ...]
dst_points: Corresponding points in second image
threshold: Reprojection error threshold
n_iter: RANSAC iterations
Return: Dict with 'H' (3×3 matrix) and 'inliers'

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.

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