Principle:Kornia Kornia Geometric Verification

Knowledge Sources	Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography Kornia
Domains	Vision, Geometry, Robust_Estimation
Last Updated	2026-02-09 15:00 GMT

Overview

Technique of robustly estimating geometric models (homographies, fundamental matrices) from noisy feature correspondences while identifying inliers and outliers.

Description

Feature matching inevitably produces outlier (incorrect) correspondences. RANSAC (Random Sample Consensus) robustly estimates a geometric model by: (1) randomly sampling minimal sets of correspondences, (2) fitting a model (e.g., homography from 4 point pairs), (3) scoring the model by counting inlier correspondences (within distance threshold), (4) iterating to find the best model. Local optimization refines the best model using all inliers. The algorithm outputs both the estimated model and an inlier mask for downstream use.

Usage

Use after feature matching to filter outlier matches and estimate geometric transformations between images. Essential for image stitching, visual localization, and multi-view geometry.

Theoretical Basis

RANSAC algorithm:

For i in 1..max_iter:

1. Sample minimal_sample_size points.
2. Fit model M_i.
3. Count inliers: |{j : error(M_i, (p1_j, p2_j)) < threshold}|.
4. If best, polish with all inliers.
5. Early stop if confidence reached: k = log(1 - p) / log(1 - (w^n)), where w = inlier_ratio, n = sample_size, p = confidence.

Related Pages

Implemented By

• Implementation:Kornia_Kornia_RANSAC
• Heuristic:Kornia_Kornia_Numerical_Stability_Patterns