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References

Every method in Valerian was implemented from the published description below (a paper or a book), or from the plain behaviour that other programs document, such as the names and ranges of a rejection scheme. No code was copied or ported from another program. Where a method is closely related to a program's, the entry says so. The same references are in the # References section at the top of each module's documentation (cargo doc). A reference marked "to verify" could not be checked against the publisher's record at the time of writing.

The pages that explain each step (calibration, stacking, plate solving and so on) say what Valerian does; this page says where the idea comes from.

Calibration, statistics and combining

Master frames, robust statistics and per-pixel rejection (calibrate, stats, combine).

  • Howell, S. B. (2006), Handbook of CCD Astronomy, 2nd ed., Cambridge University Press, doi:10.1017/CBO9780511807909 (bias, dark and flat calibration).
  • Hampel, F. R. (1974), The influence curve and its role in robust estimation, J. Am. Stat. Assoc. 69, 383-393, doi:10.1080/01621459.1974.10482962 (the median absolute deviation).
  • Rousseeuw, P. J. and Croux, C. (1993), Alternatives to the median absolute deviation, J. Am. Stat. Assoc. 88, 1273-1283, doi:10.1080/01621459.1993.10476408 (the 1.4826 factor)
  • Immerkaer, J. (1996), Fast noise variance estimation, Comput. Vis. Image Underst. 64, 300-302, doi:10.1006/cviu.1996.0060 (noise from local differences; here a robust variant on pixel differences).
  • Huber, P. J. (1964), Robust estimation of a location parameter, Ann. Math. Statist. 35, 73-101, doi:10.1214/aoms/1177703732.
  • Huber, P. J. and Ronchetti, E. M. (2009), Robust Statistics, 2nd ed., Wiley, doi:10.1002/9780470434697 (winsorising, and the 1.134 factor for its bias)
  • Sigma clipping, winsorised sigma clipping and linear fit clipping are matched from the behaviour other stackers document (names and ranges), not from their code.

Stars, registration and resampling

Star detection, star-pattern matching and fitting, and resampling (stars, register, transform, warp, debayer).

  • Bertin, E. and Arnouts, S. (1996), SExtractor: software for source extraction, Astron. Astrophys. Suppl. 117, 393-404, doi:10.1051/aas:1996164 (the background mesh and the windowed centroid, implemented from the paper; no SExtractor code is used).
  • Hampel, F. R. (1974), The influence curve and its role in robust estimation, J. Am. Stat. Assoc. 69, 383-393, doi:10.1080/01621459.1974.10482962 (the median absolute deviation).
  • Groth, E. J. (1986), A pattern-matching algorithm for two-dimensional coordinate lists, Astron. J. 91, 1244, doi:10.1086/114099.
  • Valdes, F. G. et al. (1995), FOCAS automatic catalog matching algorithms, Publ. Astron. Soc. Pac. 107, 1119, doi:10.1086/133667.
  • Fischler, M. A. and Bolles, R. C. (1981), Random sample consensus, Commun. ACM 24, 381-395, doi:10.1145/358669.358692.
  • Beroiz, M., Cabral, J. B. and Sanchez, B. (2020), Astroalign: a Python module for astronomical image registration, Astron. Comput. 32, 100384, doi:10.1016/j.ascom.2020.100384 (the same family of method; used as a test oracle only, no code taken).
  • Umeyama, S. (1991), Least-squares estimation of transformation parameters between two point patterns, IEEE Trans. Pattern Anal. Mach. Intell. 13, 376-380, doi:10.1109/34.88573.
  • Umeyama, S. (1991), Least-squares estimation of transformation parameters between two point patterns, IEEE Trans. Pattern Anal. Mach. Intell. 13, 376-380, doi:10.1109/34.88573 (the similarity fit)
  • Hartley, R. I. (1997), In defense of the eight-point algorithm, IEEE Trans. Pattern Anal. Mach. Intell. 19, 580-593, doi:10.1109/34.601246 (point normalisation for the homography fit).
  • Keys, R. G. (1981), Cubic convolution interpolation for digital image processing, IEEE Trans. Acoust. Speech Signal Process. 29, 1153-1160, doi:10.1109/TASSP.1981.1163711 (the bicubic kernel; Catmull-Rom is the a = -0.5 case).
  • Duchon, C. E. (1979), Lanczos filtering in one and two dimensions, J. Appl. Meteorol. 18, 1016-1022, doi:10.1175/1520-0450(1979)018<1016:LFIOAT>2.0.CO;2.
  • Malvar, H. S., He, L.-W. and Cutler, R. (2004), High-quality linear interpolation for demosaicing of Bayer-patterned color images, Proc. IEEE ICASSP 2004, vol. 3, iii-485, doi:10.1109/ICASSP.2004.1326587 (the filter taps).

Stacking and drizzle

Frame weighting and variable-pixel reconstruction (stack, drizzle).

  • Naylor, T. (1998), An optimal extraction algorithm for imaging photometry, Mon. Not. R. Astron. Soc. 296, 339-346, doi:10.1046/j.1365-8711.1998.01314.x.
  • King, I. R. (1983), Accuracy of measurement of star images on a pixel array, Publ. Astron. Soc. Pac. 95, 163, doi:10.1086/131139 (why a point source is best weighted by 1/(noise^2 FWHM^2)).
  • Horne, K. (1986), An optimal extraction algorithm for CCD spectroscopy, Publ. Astron. Soc. Pac. 98, 609, doi:10.1086/131801.
  • Fruchter, A. S. and Hook, R. N. (2002), Drizzle: a method for the linear reconstruction of undersampled images, Publ. Astron. Soc. Pac. 114, 144-152, doi:10.1086/338393 (implemented from the paper; none of the STScI drizzle code is used).

Background, stretch and star removal

Gradient removal, tone curves and star removal (background, stretch, starless).

  • Bookstein, F. L. (1989), Principal warps: thin-plate splines and the decomposition of deformations, IEEE Trans. Pattern Anal. Mach. Intell. 11, 567-585, doi:10.1109/34.24792.
  • Duchon, J. (1977), Splines minimizing rotation-invariant semi-norms in Sobolev spaces, Lecture Notes in Mathematics 571, 85-100, doi:10.1007/BFb0086566 (the r^2 ln r kernel).
  • Bertin, E. and Arnouts, S. (1996), SExtractor: software for source extraction, Astron. Astrophys. Suppl. 117, 393-404, doi:10.1051/aas:1996164 (a smooth background from a mesh of medians).
  • Hampel, F. R. (1974), The influence curve and its role in robust estimation, J. Am. Stat. Assoc. 69, 383-393, doi:10.1080/01621459.1974.10482962 (the median absolute deviation).
  • Lupton, R. et al. (2004), Preparing red-green-blue images from CCD data, Publ. Astron. Soc. Pac. 116, 133-137, doi:10.1086/382245 (the arcsinh stretch).
  • Payne, D. and Cranfield, M., Generalised hyperbolic stretch, documented at https://ghsastro.co.uk (implemented from the published formulae; no peer-reviewed paper found, to verify; no GHS script code is used).
  • The midtone transfer function is a standard rational (Moebius) curve; its use as an automatic stretch is matched from the behaviour PixInsight documents, not from code.
  • Moffat, A. F. J. (1969), A theoretical investigation of focal stellar images in the photographic emulsion and application to photographic photometry, Astron. Astrophys. 3, 455 (bibcode 1969A&A.....3..455M; no DOI).
  • Shen, J. and Chan, T. F. (2002), Mathematical models for local nontexture inpaintings, SIAM J. Appl. Math. 62, 1019-1043, doi:10.1137/S0036139900368844 (harmonic inpainting).
  • Young, D. (1954), Iterative methods for solving partial difference equations of elliptic type, Trans. Am. Math. Soc. 76, 92-111, doi:10.1090/S0002-9947-1954-0059635-7 (successive over-relaxation).

Plate solving, world coordinates and colour calibration

The solver, the TAN-SIP world coordinate system, the catalogue and the star-colour calibration (solve, wcs, catalogue, photocal, fits).

  • Lang, D., Hogg, D. W., Mierle, K., Blanton, M. and Roweis, S. (2010), Astrometry.net: blind astrometric calibration of arbitrary astronomical images, Astron. J. 139, 1782-1800, doi:10.1088/0004-6256/139/5/1782 (the idea of blind solving by matching star patterns; Valerian matches triangles, not quads, and uses none of that project's code).
  • Groth, E. J. (1986), A pattern-matching algorithm for two-dimensional coordinate lists, Astron. J. 91, 1244, doi:10.1086/114099.
  • Valdes, F. G. et al. (1995), FOCAS automatic catalog matching algorithms, Publ. Astron. Soc. Pac. 107, 1119, doi:10.1086/133667.
  • Calabretta, M. R. and Greisen, E. W. (2002), Representations of celestial coordinates in FITS, Astron. Astrophys. 395, 1077-1122, doi:10.1051/0004-6361:20021327 (the TAN projection).
  • Shupe, D. L. et al. (2005), The SIP convention for representing distortion in FITS image headers, ASP Conf. Ser. 347, 491 (no DOI; to verify).
  • Shupe, D. L. et al. (2012), More flexibility in representing geometric distortion in astronomical images, Proc. SPIE 8451, 84511M, doi:10.1117/12.925460.
  • Gaia Collaboration, Prusti, T. et al. (2016), The Gaia mission, Astron. Astrophys. 595, A1, doi:10.1051/0004-6361/201629272.
  • Gaia Collaboration, Vallenari, A. et al. (2023), Gaia Data Release 3: summary of the content and survey properties, Astron. Astrophys. 674, A1, doi:10.1051/0004-6361/202243940.
  • Greisen, E. W. and Calabretta, M. R. (2002), Representations of world coordinates in FITS, Astron. Astrophys. 395, 1061-1075, doi:10.1051/0004-6361:20021326.
  • Pence, W. D. et al. (2010), Definition of the Flexible Image Transport System (FITS), version 3.0, Astron. Astrophys. 524, A42, doi:10.1051/0004-6361/201015362.
  • Lindegren, L. et al. (2021), Gaia Early Data Release 3: the astrometric solution, Astron. Astrophys. 649, A2, doi:10.1051/0004-6361/202039709 (Gaia DR3 astrometry is that of EDR3).
  • Data: ESA/Gaia/DPAC. ESA states the licence is CC BY-NC 3.0 IGO (https://www.cosmos.esa.int/web/gaia-users/license): see docs/LEGAL-AUDIT.md.
  • Riello, M. et al. (2021), Gaia Early Data Release 3: photometric content and validation, Astron. Astrophys. 649, A3, doi:10.1051/0004-6361/202039587 (the BP and RP photometry; DR3 photometry is that of EDR3).
  • Casagrande, L. and VandenBerg, D. A. (2018), On the use of Gaia magnitudes and new tables of bolometric corrections, Mon. Not. R. Astron. Soc. 479, L102-L107, doi:10.1093/mnrasl/sly104 (the solar BP-RP colour of 0.82; value to verify against the paper).
  • Theil, H. (1950), reprinted in Henri Theil's Contributions to Economics and Econometrics, Springer (1992), doi:10.1007/978-94-011-2546-8_20, and Sen, P. K. (1968), Estimates of the regression coefficient based on Kendall's tau, J. Am. Stat. Assoc. 63, 1379-1389, doi:10.1080/01621459.1968.10480934 (the Theil-Sen line).
  • Huber, P. J. (1964), Robust estimation of a location parameter, Ann. Math. Statist. 35, 73-101, doi:10.1214/aoms/1177703732.
  • Stetson, P. B. (2000), Homogeneous photometry for star clusters and resolved galaxies. II. Photometric standard stars, Publ. Astron. Soc. Pac. 112, 925-931, doi:10.1086/316595 (DOI to verify; the colour equation behind the zero point and colour term of photocal --report and plot zeropoint).
  • Howell, S. B. (1989), Two-dimensional aperture photometry: signal-to-noise ratio of point-source observations and optimal data-extraction techniques, Publ. Astron. Soc. Pac. 101, 616-622, doi:10.1086/132477 (DOI to verify; the aperture signal-to-noise and magnitude error of the calibrated star catalogue).
  • Merline, W. J. and Howell, S. B. (1995), A realistic model for point-sources imaged on array detectors: the model and initial results, Exp. Astron. 6, 163-210, doi:10.1007/BF00421131 (DOI to verify; the same).
  • Newberry, M. V. (1991), Signal-to-noise considerations for sky-subtracted CCD data, Publ. Astron. Soc. Pac. 103, 122-130, doi:10.1086/132802 (DOI to verify; the point-source limiting magnitude at a signal-to-noise ratio).

Mosaics

Placing panes on one canvas, matching their levels and blending the seams (mosaic).

  • Burt, P. J. and Adelson, E. H. (1983), A multiresolution spline with application to image mosaics, ACM Trans. Graph. 2, 217-236, doi:10.1145/245.247.
  • Szeliski, R. (2006), Image alignment and stitching: a tutorial, Found. Trends Comput. Graph. Vis. 2, 1-104, doi:10.1561/0600000009.
  • Brown, M. and Lowe, D. G. (2007), Automatic panoramic image stitching using invariant features, Int. J. Comput. Vis. 74, 59-73, doi:10.1007/s11263-006-0002-3.

Viewing

The image pyramid the viewer draws from (pyramid).

  • Williams, L. (1983), Pyramidal parametrics, ACM SIGGRAPH Computer Graphics 17(3), 1-11, doi:10.1145/964967.801126 (the mip-map).
  • Burt, P. J. and Adelson, E. H. (1983), The Laplacian pyramid as a compact image code, IEEE Trans. Commun. 31, 532-540, doi:10.1109/TCOM.1983.1095851.

Data

  • Gaia Data Release 3 star positions, G magnitudes and BP-RP colours (gaia-dr3-g11.vcat): (c) ESA/Gaia/DPAC. See Credits and trademarks for the acknowledgement and the licence.

Programs used only to check Valerian

The parity scripts in scripts/ run these Python libraries as independent references on the developer's machine. They are not part of Valerian, not shipped and not linked: numpy, scipy, astropy, photutils, scikit-image, sep and astroalign (see the list in Credits and trademarks).