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REVIEW 3 major objections 5 minor 4 references

Evaluation of centroiding algorithms for an autonomous star tracker

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Gaussian least-squares fit wins star-centroid accuracy

desk verdict A transparent Monte Carlo comparison of six standard centroiding algorithms for the AST-INPE star tracker, with a Gaussian least-squares fit winning on accuracy at roughly 35x the cost, but the practical claim is only as strong as the Gaussian PSF assumption. read the letter →

arxiv 2507.17560 v1 pith:MW7NEFUC submitted 2025-07-23 astro-ph.IM physics.ins-det

Marcio Afonso Arimura Fialho This is my paper · ORCID
classification astro-ph.IMphysics.ins-det
keywords startrackercentroidingGaussianpointspreadfunctionMonteCarlosimulationshapefittingcenterofgravitymagnitudeestimationadaptiveoptics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper compares six centroiding algorithms for a star tracker using Monte Carlo simulations of 7x7 pixel synthetic star images with a Gaussian point spread function, shot noise, readout noise, A/D truncation, and saturation. Its central claim is that ALG-6, a least-squares Gaussian shape fit, is the most accurate algorithm both for centroid position and for star magnitude estimation, but also the most expensive, with an average runtime about 36 times larger than the lightweight algorithms. The author shows that thresholding in ALG-1 causes large magnitude errors for dim stars, and that the iteratively weighted algorithms ALG-3, ALG-4, and ALG-5 perform poorly for intermediate magnitudes. The result matters because centroiding accuracy directly limits the attitude accuracy of a star tracker, and dim stars are the most common stars in star tracker images.

What carries the argument

The load-bearing object is the simulated Gaussian PSF with width 0.663 pixels, derived from a single real star image, sampled on a 10x10 sub-grid per pixel to generate realistic star images. Against this model, the paper tests six centroid formulas: thresholded center of gravity (ALG-1), unthresholded center of gravity (ALG-2), iteratively weighted center of gravity using a Gaussian window (ALG-3), intensity-weighted centroiding with exponent q=2 (ALG-4 and ALG-5), and nonlinear least-squares Gaussian shape fitting (ALG-6). The Gaussian shape fit is the mechanism that carries the accuracy advantage: instead of summarizing pixel intensities with moments, it fits the known PSF model directly to the image.

What would settle it

Rerun the Monte Carlo comparison using a measured or otherwise realistic PSF, such as an Airy pattern or a PSF extracted from real star tracker frames, and check whether ALG-6 remains the most accurate centroiding algorithm; a lightweight algorithm winning under a non-Gaussian PSF would refute the paper's central ranking claim.

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Extended reading notes

Core claim

In the simulated conditions, ALG-6 outperformed ALG-1 through ALG-5 in both centroiding error and magnitude estimation error across the tested magnitude range, with the accuracy gap largest for dim stars, where the thresholded algorithms lose signal below the threshold. For stars brighter than magnitude 1.2, saturation of the central pixels degrades every algorithm. The author states this result is conditional on the Gaussian PSF model, and explicitly notes in Section 5.1 that a real PSF that departs significantly from Gaussian could change the ranking, so the claim is best read as: with a Gaussian PSF and the modeled noise, the Gaussian fit is the most accurate choice.

Load-bearing premise

The simulations assume the star's point spread function is Gaussian with a width taken from one real star image; if the actual PSF of the star tracker is significantly non-Gaussian, the ranking of algorithms, and in particular ALG-6's accuracy advantage, could change.

Editorial extensions

If this is right

  • For a star tracker whose PSF is close to Gaussian, switching from the current thresholded center-of-gravity algorithm to ALG-6 would improve both centroid accuracy and dim-star magnitude estimates.
  • The magnitude underestimation in ALG-1 for dim stars is caused by thresholding, so reducing the threshold or using a shape fit could remove the bias without changing the rest of the pipeline.
  • The runtime penalty of ALG-6, about 5.6 ms per star compared with roughly 0.15 ms for the lightweight algorithms, must be absorbed by the onboard computational budget before ALG-6 can be adopted.
  • The same accuracy-versus-cost ranking is likely to transfer to astrometry and adaptive optics applications that use similar centroiding algorithms, where the best algorithm depends on the tolerated computational cost.
  • For bright stars above magnitude 1.2, saturation limits accuracy regardless of algorithm, so no centroiding choice can fix that regime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the true PSF of the star tracker is non-Gaussian, a shape fit matched to that PSF could preserve ALG-6's accuracy advantage, but the paper does not test this; the ranking could also shift toward a lightweight algorithm.
  • A hybrid strategy that runs ALG-6 only on dim stars, where the accuracy gain is largest, and a cheaper algorithm on bright stars could cut the average runtime while retaining most of the benefit.
  • The table's runtimes include image generation, so the true computational gap between ALG-1 and ALG-5 is not yet measured; a standalone benchmark could change the relative cost ranking of the lightweight algorithms.
  • Because magnitude errors follow the same ranking as centroid errors, the paper suggests that a single algorithm can serve both position and brightness estimation, which may simplify star identification logic in an autonomous tracker.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper reports Monte Carlo simulations comparing six centroiding algorithms for the AST-INPE star tracker: five lightweight algorithms (simple thresholded CoG, unthresholded CoG, iteratively weighted CoG, intensity weighted centroiding, and thresholded intensity weighted centroiding) and one Gaussian least-squares shape-fitting algorithm (ALG-6). Synthetic 7x7 pixel images are generated with a Gaussian PSF and include shot noise, readout noise, A/D truncation, and saturation. Centroiding and magnitude-estimation errors are measured against known truth over 10,000 runs per magnitude. The principal finding is that ALG-6 achieves the lowest centroiding and magnitude errors but at a computational cost roughly 35 times that of the light-weight algorithms. The paper explicitly acknowledges that the results depend on the Gaussian PSF assumption and that the ranking could change for other PSFs.

Significance. If the results hold, they provide a useful, transparent benchmark for centroiding-algorithm selection in star tracker development and in related fields such as astrometry and adaptive optics. The Monte Carlo pipeline is clearly documented, the parameter choices are derived from an actual test image, and the comparison of six algorithms under controlled noise conditions is valuable. The computational-cost table, despite its confounds, gives a practical ordering. The main limitation is that the generative model is exactly the model fitted by ALG-6, so the ranking is established only for Gaussian PSFs, and the magnitude-error comparison is incomplete for three of the algorithms. These issues are acknowledged but not resolved within the manuscript.

major comments (3)
  1. [Section 4, Figure 4] The magnitude-error comparison is incomplete: errors for ALG-3, ALG-4, and ALG-5 are omitted, with the statement that they 'should be the same' as those of ALG-2, ALG-2, and ALG-1, respectively. This assertion is not self-evident, particularly for ALG-3, whose brightness estimate A is computed using the iteratively weighted intensity I''(x,y) rather than the unweighted I'(x,y); the weighted sum need not equal ALG-2's sum. Please compute and plot these errors, or provide a rigorous derivation showing that the magnitude estimates coincide.
  2. [Section 5.1] The central claim that ALG-6 is the most accurate algorithm is only demonstrated for a generative model that has the same functional form ALG-6 fits: the simulated PSF is Gaussian (Section 3), and ALG-6 fits a Gaussian shape (Section 2.6). This gives ALG-6 a correctly specified model, and the paper itself concedes in Section 5.1 that the real PSF can depart significantly from Gaussian and that the best algorithm could then differ. Because the practical recommendation for AST-INPE depends on the PSF being nearly Gaussian, the manuscript should include at least one non-Gaussian PSF simulation (e.g., a Moffat profile or an aberrated Gaussian) or a quantitative sensitivity analysis of the ranking to PSF shape.
  3. [Section 3] The PSF width sigma_PSF = 0.663 px is derived from a single bright star image (magnitude 2.65) and used for all simulated magnitudes and all centroid locations. The paper does not discuss how field-dependent or magnitude-dependent PSF variations could affect the conclusions, even though the threshold used by ALG-1 and ALG-5 depends directly on the background noise and the PSF sampling changes with width. A sensitivity scan over a plausible range of sigma_PSF values, or at least a stated justification for treating it as fixed, would strengthen the relevance of the ranking for AST-INPE.
minor comments (5)
  1. [Section 7] There are typos: 'obtanining' should be 'obtaining' and 'couse' should be 'course' in the code availability paragraph.
  2. [Abstract / Notice] The notice contains 'preprin t' with an unintended space; please fix the typo.
  3. [Section 2.3] The IWCoG weighting formula is difficult to read; the exponent '2𝜎𝑠ℎ 2' is ambiguous. Please rewrite it as a standard Gaussian exponent with an explicit denominator, e.g., exp[-( (x-xc)^2 + (y-yc)^2 )/(2 sigma_sh^2)].
  4. [Sections 2.6 and 3] The Gaussian PSF is sampled on a 10x10 sub-grid for image generation (Section 3) but ALG-6 uses a 4x4 sub-grid for fitting (Section 2.6). Please state explicitly that this discretization mismatch is small and does not bias the comparison.
  5. [Table 1] The execution-time measurements include the time to generate the synthetic image, which dominates the runtime of ALG-1 to ALG-5. Since the paper notes that the computational cost of these algorithms 'could not be properly evaluated', consider reporting the incremental algorithm overhead by subtracting the dummy time, so that readers can better compare the algorithms' intrinsic costs.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the Gaussian-PSF scope is explicit, and ALG-6's accuracy is a conditional simulation result rather than a self-referential derivation.

full rationale

The paper is an empirical Monte Carlo comparison, not a derivation that assumes its own conclusion. Synthetic images are generated from a Gaussian PSF with parameters derived from a real AST-INPE star image (Section 3), and all six algorithms are evaluated on the same known-truth images. ALG-6 is a Gaussian least-squares fit, so the simulation is favorable to it, but this is an openly stated scope condition: Section 5.1 says the PSF can depart significantly from Gaussian and that the best algorithm could then be different. That admission prevents the ranking from being presented as a universal prediction, and it means the Gaussian-on-Gaussian match is a limitation rather than a hidden equivalence. No fitted parameter is renamed as a prediction, no load-bearing self-citation is used, and no uniqueness theorem is imported from the authors' prior work. The only questionable statement is in Section 4, where magnitude errors for ALG-3, ALG-4, and ALG-5 are asserted to equal those of ALG-2, ALG-2, and ALG-1 without computation; this is a reporting gap, not circularity, and it does not change the circularity score.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The central comparison rests on several parameter values extracted from one real star image and on a Gaussian PSF assumption that matches ALG-6's internal model. The algorithm hyperparameters (sigma_sh, q, threshold factor, iteration count) are chosen by hand. No new physical entities are introduced.

free parameters (9)
  • sigma_PSF = 0.663 px
    PSF width derived from a real AST-INPE star image (Fig. 2) and used as the generative model for all synthetic stars; central ranking depends on this width.
  • A_ref = 10046.34 DN
    Zero-magnitude reference digital level derived from the same real star image; used in the mag_est conversion and therefore affects all magnitude error curves.
  • background_level = 56.84 DN
    Mean background level from the real image; input to the synthetic images and to threshold computation.
  • readout_noise_sigma = 108 e-
    Readout noise standard deviation from the real image; one of the modeled noise sources.
  • DN_per_electron = 100 e-/DN
    A/D conversion gain from the real image; converts simulated electron counts to digital levels.
  • sigma_sh for IWCoG = 0.7 px
    Width of the Gaussian weighting window in ALG-3, chosen in the Monte Carlo simulations (Sec. 2.3).
  • q for IWC = 2.0
    Intensity exponent for ALG-4 and ALG-5, chosen in the simulations (Sec. 2.4, 2.5).
  • threshold_factor = 3.5
    Background standard deviation multiplier used to set T in ALG-1 and ALG-5 (Sec. 2.1); chosen, not fitted.
  • IWCoG_iterations = 10
    Number of iterations for ALG-3 (Sec. 2.3); chosen for the simulations.
assumptions (6)
  • domain assumption The star PSF is Gaussian with width sigma_PSF = 0.663 px
    All synthetic images are generated with this model (Sec. 3). Sec. 5.1 acknowledges real PSFs can differ.
  • domain assumption The modeled noise sources (shot, readout, A/D truncation, saturation) capture sensor behavior
    Column non-uniformity and hot/warm pixels are excluded (Sec. 3), so simulated images may miss detector effects.
  • domain assumption Parameters from a single m_V = 2.65 star image are representative
    Fig. 2 provides the values used for all Monte Carlo inputs; no variation across stars, field positions, or time is tested.
  • domain assumption Background level estimated from 24 edge pixels is an unbiased estimate
    Sec. 3 uses edge pixels for b and T; no outlier rejection or robustness analysis is described.
  • standard math lsqnonlin converges to an adequately accurate Gaussian fit
    ALG-6 depends on Matlab's optimizer (Sec. 2.6); initialization, tolerances, and failure cases are not given.
  • domain assumption True centroids are uniformly distributed in the central pixel
    Sec. 3 draws x_t,y_t uniformly in (3,4), which sets the error distribution for all algorithms.

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Cite this review

Pith. "Pith review of Evaluation of centroiding algorithms for an autonomous star tracker." pith.science (2026). https://pith.science/paper/MW7NEFUC

@misc{pith2026250717560,
  author       = {Pith},
  title        = {Pith review of: Evaluation of centroiding algorithms for an autonomous star tracker},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MW7NEFUC}},
  note         = {Machine review of arXiv:2507.17560}
}
read the original abstract

This work presents numerical results of a computer simulation performed with six centroiding algorithms targeting a star tracker in development at INPE, including readout noise and considering a Gaussian point spread function. Five of the tested algorithms are light-weight centroiding algorithms with low computational costs. These were compared to a shape fitting algorithm based on the lsqnonlin function available in Matlab and GNU Octave. The algorithms studied here are also applicable for astrometry and adaptive optics.

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Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

  1. [1]

    Fialho, M. A. A. et al. The Brazilian autonomous star tracker development. Napa,

    work page

  2. [2]

    Zhang, Q. F. et al. A comparison of centring algorithms in the astrometry of Cassini imaging science subsystem images and Anthe’s astrometric reduction. MNRAS 505, 5253–5259 (2021)

    work page 2021

  3. [3]

    B.; Prasad, B

    Vyas, A.; Roopashree, M. B.; Prasad, B. R. Improved Iteratively Weighted Centroiding for accurate spot detection in Laser Guide Star based Shack Hartmann Sensor. Proc. SPIE Vol. 7588, 758806, 2010

    work page 2010

  4. [4]

    B.; Prasad, B

    Vyas, A.; Roopashree, M. B.; Prasad, B. R. Performance of Centroiding Algorithms at Low Light Le vel Conditions in Adaptive Optics. 2009 International Conference on Advances in Recent Technologies in Communication and Computing

    work page 2009

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