Robust vs. non-robust estimation
| This documentation was generated with the assistance of AI. Please report any inaccuracies. |
Every geometric quantity irurueta-ar estimates — the fundamental and essential matrices, the image/dual
absolute conic, the dual absolute quadric, radial distortion, triangulated 3D points — follows the same
two-tier pattern:
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A non-robust estimator that computes an exact (or least-mean-squared-error) solution from a fixed, minimal or over-determined set of correspondences, assuming every correspondence is a genuine inlier.
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A family of robust estimators that wrap the non-robust one inside an outlier-rejection loop, so that a correct solution can still be found when a fraction of the input correspondences are mismatches.
This page explains the shared robust-estimation framework once; the domain pages (Fundamental matrix estimation, Self-calibration, etc.) each describe their own non-robust algorithm and reuse this framework for the robust variants.
Why outliers require a different strategy
A plain least-squares fit assumes every measurement’s error follows the same (Gaussian) distribution. Point correspondences produced by automatic matching are not like that: a wrong match is not "a bit noisier", it is arbitrarily wrong, and even a handful of such outliers can pull a least-squares solution far from the correct answer Hartley & Zisserman, 2003. Robust estimators solve a different problem: find the largest subset of correspondences ("inliers") that agrees with some instance of the model, and fit the model to that subset only.
The RANSAC family
irurueta-ar builds its robust estimators on top of com.irurueta.numerical.robust.RobustEstimatorMethod
(from the sibling irurueta-numerical library), which enumerates the sampling/scoring strategy:
| Method | Strategy |
|---|---|
|
Random SAmple Consensus Fischler & Bolles, 1981. Repeatedly draws
a minimal random sample, instantiates the model, and counts inliers (points within a distance threshold |
|
Least Median of Squares. Same random sampling, but scores each candidate model by the median squared residual over all points instead of an inlier count, so no distance threshold needs to be chosen up front. |
|
M-estimator SAmple Consensus. Like RANSAC, but instead of counting inliers it sums a capped residual (inliers contribute their actual residual, outliers contribute a fixed penalty), which produces a smoother, more accurate score surface than a hard inlier count. |
|
PROgressive SAmple Consensus. Like RANSAC, but draws samples preferentially from the highest-quality matches first (given a quality score per correspondence, e.g. a descriptor-matching score), converging faster when scores are informative. |
|
The PROSAC sampling strategy combined with the LMedS median-residual score. |
Every domain in irurueta-ar exposes one concrete class per row above, named
{RANSAC,LMedS,MSAC,PROSAC,PROMedS}<Thing>RobustEstimator (e.g. RANSACFundamentalMatrixRobustEstimator),
plus an abstract <Thing>RobustEstimator base class with a create(…) factory that switches on
RobustEstimatorMethod.
Inlier threshold and iteration count
For threshold-based methods (RANSAC, MSAC, PROSAC), a point is accepted as an inlier when its residual is
below a threshold t. If the measurement error is assumed Gaussian with standard deviation , the
squared residual follows a distribution with m degrees of freedom equal to the codimension of
the model (m = 1 for a fundamental matrix’s point-to-epipolar-line distance), and t can be derived from the
desired inlier probability (typically 0.95) via the inverse cumulative
Hartley & Zisserman, 2003. In practice irurueta-ar
exposes t directly as a tunable threshold property (e.g. RANSACFundamentalMatrixRobustEstimator.DEFAULT_THRESHOLD = 1.0 pixel), since the
right value depends on how the correspondences were produced.
Given a sample size s (the minimum number of correspondences needed to instantiate the model), a desired
confidence p that at least one sample is outlier-free, and an outlier proportion , the
number of random samples N needed is:
irurueta-ar recomputes adaptively as better solutions are found (shrinking N as the
best-known inlier ratio improves) and exposes confidence (default 0.99) and maxIterations (default
5000) as the tunable stopping criteria on every *RobustEstimator class. This matches the RANSAC treatment
in the thesis itself Irurueta, PhD thesis (algorithm 2.2 and algorithm 3.1) and in
Hartley & Zisserman Hartley & Zisserman, 2003.
After the best consensus set is found, every robust estimator can optionally refine the result (refineResult,
default true) by re-fitting the non-robust estimator, or a non-linear (Levenberg-Marquardt) refiner, over all
detected inliers — the numerical machinery for that non-linear refinement follows the same Jacobian-based
least-squares approach described in Numerical Recipes
Press et al., 2007 (chapter 15, "Modeling of Data").
Estimator families in this library
| Domain | Non-robust estimator(s) | Robust family |
|---|---|---|
Fundamental matrix |
|
|
Dual absolute quadric (self-calibration) |
|
|
Image/dual image of the absolute conic |
|
|
Radial distortion |
|
|
3D point triangulation |
|
|
Example
Choosing between a non-robust and a robust estimator for the same problem (fundamental matrix estimation from 8 exact correspondences vs. from a noisy correspondence set):
// Non-robust: exactly 8 correspondences, all assumed correct
var exact = new EightPointsFundamentalMatrixEstimator(leftPoints, rightPoints);
FundamentalMatrix fundamentalMatrix = exact.estimate();
// Robust: many correspondences, some of which may be wrong matches
var robust = (RANSACFundamentalMatrixRobustEstimator)
FundamentalMatrixRobustEstimator.create(leftPoints, rightPoints, RobustEstimatorMethod.RANSAC);
robust.setThreshold(1.0); // pixels
FundamentalMatrix robustFundamentalMatrix = robust.estimate();References
Irurueta, PhD thesis §2.5, §3.2.3
Hartley & Zisserman, 2003 chapter 4 ("Estimation - 2D
Projective Transformations")
Fischler & Bolles, 1981
Press et al., 2007 chapter 15 ("Modeling of Data")