Abstract
Exponential, de Vaucouleurs, and Sérsic profiles are simple and successful models for fitting twodimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or correlation) of the models with the telescope point-spread function (PSF); these operations are slow, and easy to get slightly wrong at small radii. Here we exploit the realization that these models can be approximated to arbitrary accuracy with a mixture (linear superposition) of two-dimensional Gaussians (MoGs). MoGs are fast to render and fast to affine-transform. Most importantly, if you have a MoG model for the pixel-convolved PSF, the PSF-convolved, affine-transformed galaxy models are themselves MoGs and therefore very fast to compute, integrate, and render precisely. We present worked examples that can be directly used in image fitting; we are using them ourselves. The MoG profiles we provide can be swapped in to replace the standard models in any image-fitting code; they sped up model fitting in our projects by an order of magnitude; they ought to make any code faster at essentially no cost in precision.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 719-730 |
| Number of pages | 12 |
| Journal | Publications of the Astronomical Society of the Pacific |
| Volume | 125 |
| Issue number | 928 |
| DOIs | |
| State | Published - Jun 2013 |
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ASJC Scopus subject areas
- Astronomy and Astrophysics
- Space and Planetary Science
Cite this
Replacing standard galaxy profiles with mixtures of Gaussians. / Hogg, David W.; Lang, Dustin.
In: Publications of the Astronomical Society of the Pacific, Vol. 125, No. 928, 06.2013, p. 719-730.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Replacing standard galaxy profiles with mixtures of Gaussians
AU - Hogg, David W.
AU - Lang, Dustin
PY - 2013/6
Y1 - 2013/6
N2 - Exponential, de Vaucouleurs, and Sérsic profiles are simple and successful models for fitting twodimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or correlation) of the models with the telescope point-spread function (PSF); these operations are slow, and easy to get slightly wrong at small radii. Here we exploit the realization that these models can be approximated to arbitrary accuracy with a mixture (linear superposition) of two-dimensional Gaussians (MoGs). MoGs are fast to render and fast to affine-transform. Most importantly, if you have a MoG model for the pixel-convolved PSF, the PSF-convolved, affine-transformed galaxy models are themselves MoGs and therefore very fast to compute, integrate, and render precisely. We present worked examples that can be directly used in image fitting; we are using them ourselves. The MoG profiles we provide can be swapped in to replace the standard models in any image-fitting code; they sped up model fitting in our projects by an order of magnitude; they ought to make any code faster at essentially no cost in precision.
AB - Exponential, de Vaucouleurs, and Sérsic profiles are simple and successful models for fitting twodimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or correlation) of the models with the telescope point-spread function (PSF); these operations are slow, and easy to get slightly wrong at small radii. Here we exploit the realization that these models can be approximated to arbitrary accuracy with a mixture (linear superposition) of two-dimensional Gaussians (MoGs). MoGs are fast to render and fast to affine-transform. Most importantly, if you have a MoG model for the pixel-convolved PSF, the PSF-convolved, affine-transformed galaxy models are themselves MoGs and therefore very fast to compute, integrate, and render precisely. We present worked examples that can be directly used in image fitting; we are using them ourselves. The MoG profiles we provide can be swapped in to replace the standard models in any image-fitting code; they sped up model fitting in our projects by an order of magnitude; they ought to make any code faster at essentially no cost in precision.
UR - http://www.scopus.com/inward/record.url?scp=84879471727&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879471727&partnerID=8YFLogxK
U2 - 10.1086/671228
DO - 10.1086/671228
M3 - Article
VL - 125
SP - 719
EP - 730
JO - Publications of the Astronomical Society of the Pacific
JF - Publications of the Astronomical Society of the Pacific
SN - 0004-6280
IS - 928
ER -