Correction of Chromatic Aberration from a Single Image Using Keypoints

In this paper, we propose a method to correct for chromatic aberration in a single photograph. Our method replicates what a user would do in a photo editing program to account for this defect. We find matching keypoints in each colour channel then align them as a user would.

💡 Research Summary

The paper presents a practical, calibration‑free method for correcting chromatic aberration (CA) in a single photograph by mimicking the manual channel‑alignment workflow that a user would perform in a photo‑editing program. The authors assume that the most common form of CA can be modeled as a simple uniform scaling and translation of the red and blue channels relative to the green channel, which typically suffers the least shift because it lies in the middle of the visible spectrum.

To quantify how well the three colour channels are aligned, the authors adopt the L‑metric introduced by Bando et al. (2008). For each pixel (x, y) they compute the covariance matrix of the RGB vectors in a local neighbourhood, extract its eigenvalues λ₀, λ₁, λ₂, and combine them with the per‑channel variances σ²_r, σ²_g, σ²_b as

 L(x, y) = (λ₀ · λ₁ · λ₂) / (σ²_r · σ²_g · σ²_b).

L ranges from 0 to 1; lower values indicate that the RGB points are nearly collinear (well aligned), while higher values signal strong colour fringing.

The algorithm proceeds in several stages:

1. Keypoint selection – High‑gradient pixels are randomly sampled because edges provide strong colour contrast and thus reliable L measurements. Optionally, the product of the gradient magnitude and L is thresholded to focus on “high‑L, high‑gradient” locations, while saturated pixels and their neighbours are discarded.

2. Disparity search – For each non‑fixed channel (green and blue when red is the reference, or vice‑versa) the method searches over a limited set of integer translations (dx, dy) and, if necessary, a narrow range of scaling factors σ. The search space is four‑dimensional (dx_g, dy_g, dx_b, dy_b) because the authors typically treat scale differences as negligible; a full scale search could be performed via an image pyramid but was deemed unnecessary for most lenses. For every candidate transformation the L‑metric is recomputed on the keypoint neighbourhoods, and the combination that minimizes the summed L is retained.

3. Pruning – After disparity estimation, each keypoint’s new L value is examined. Only points whose L drops below a preset threshold (indicating successful alignment) are kept. In practice, a handful of well‑behaved points (often five to ten) suffices, and the authors suggest that two points are theoretically enough to solve for the three degrees of freedom (scale, tx, ty) per channel.

4. Transformation estimation – Using the surviving keypoint pairs, a linear similarity transform is solved: