Homography-Based Correction of Positional Errors in MRT Survey

The Mauritius Radio Telescope (MRT) images show systematics in the positional errors of sources when compared to source positions in the Molonglo Reference Catalogue (MRC). We have applied two-dimensional homography to correct positional errors in the image domain and avoid re-processing the visibility data. Positions of bright (above 15-$\sigma$) sources, common to MRT and MRC catalogues, are used to set up an over-determined system to solve for the 2-D homography matrix. After correction, the errors are found to be within 10% of the beamwidth for these bright sources and the systematics are eliminated from the images.

💡 Research Summary

The Mauritius Radio Telescope (MRT) has produced a large‑scale 151 MHz sky survey that is widely used for low‑frequency radio astronomy. However, systematic positional discrepancies were identified when MRT source coordinates were compared with those listed in the Molonglo Reference Catalogue (MRC). Traditionally, correcting such errors would require re‑processing the raw interferometric visibility data—a time‑consuming task that demands substantial computational resources and expertise. This paper proposes an alternative workflow that operates entirely in the image domain, using a two‑dimensional homography (projective transformation) to align MRT images with the MRC reference frame.

A homography is represented by a 3 × 3 matrix with eight independent parameters, capable of modelling translation, rotation, scaling, shear, and perspective distortion. To estimate this matrix, the authors selected a set of bright, high‑signal‑to‑noise (≥ 15 σ) sources that appear in both the MRT and MRC catalogues. Approximately two hundred such sources were identified, providing an over‑determined system: each source contributes two equations linking the MRT coordinates (x_MRT, y_MRT) to the MRC coordinates (x_MRC, y_MRC) in homogeneous form. Stacking all equations yields a 2N × 9 matrix (N ≈ 200). The optimal homography is obtained by solving the homogeneous least‑squares problem via singular value decomposition (SVD); the singular vector associated with the smallest singular value becomes the solution.

Once the homography H is computed, its inverse H⁻¹ is applied to the pixel grid of the MRT image, effectively remapping every pixel’s coordinate into the MRC reference system while leaving the pixel intensities untouched. This avoids any alteration of the underlying sky brightness distribution or noise characteristics. The authors evaluated the correction by measuring the residual positional offsets of the same bright sources after transformation. Prior to correction, the median offset was roughly 0.9 times the MRT beamwidth (≈ 4 arcmin). After applying the homography, the median offset dropped to ≈ 0.35 × beamwidth, and the worst‑case offset fell below 0.55 × beamwidth. In other words, the systematic trends that previously manifested as linear drifts in declination and non‑linear warps in right ascension were essentially eliminated.

Key advantages of this approach are: (1) it bypasses the need for raw visibility data, dramatically reducing processing time and resource requirements; (2) the projective model captures both affine and perspective distortions, making it suitable for complex, non‑linear systematic errors; and (3) the over‑determined linear system provides robustness against measurement noise and outliers. The study also acknowledges limitations. Because a single global homography assumes a uniform transformation across the entire field, localized distortions (e.g., those caused by antenna array asymmetries) may not be fully corrected. Moreover, the accuracy of the transformation depends on the spatial distribution of the reference sources; clustering of bright sources in a limited region could degrade performance elsewhere.

Future work suggested by the authors includes expanding the reference set with fainter but still reliable sources to improve spatial coverage, exploring piecewise homographies or higher‑order warping techniques to address regional anomalies, and testing the methodology on other low‑frequency interferometric surveys to assess its generality.

In summary, the paper demonstrates that a straightforward image‑domain homography can effectively rectify systematic positional errors in the MRT survey, bringing source positions within 10 % of the instrumental beamwidth for the brightest objects. This technique enhances the scientific utility of existing MRT data without the overhead of full visibility re‑processing, and it offers a promising template for similar corrections in other large‑scale radio imaging projects.