public documents.sextractor_doc

\section{Background estimation}

\label{chap:backest}

The value measured at each pixel is a function of the sum of a ``background''

signal and light coming from the objects of interest. To be able to detect

the faintest of these objects and also to measure accurately their fluxes, one needs

to have an accurate estimate of the background level in any place of the \index{image} image,

a \emph{background map}.  Strictly speaking, there should be one \index{background map} background map per

object, that is, what would the \index{image} image look like if that object was absent.

But, at least for detection, we may start by assuming that most discrete sources do not

overlap too severely, which is generally the case for high galactic latitude fields.

To construct the \index{background map} background map, {\sc SExtractor} makes a first pass through the pixel

data, computing an estimator for the \index{local background} local background in each mesh of a grid

that covers the whole frame.

The background estimator is a combination of $\kappa\,\sigma$ clipping and \index{mode} mode estimation,

similar to the one employed in Stetson's \index{DAOPHOT} DAOPHOT program (see e.g. Da Costa 1992).

Briefly, the \index{local background} local background histogram is clipped iteratively until convergence at

$\pm 3\sigma$ around its \index{median} median; \gam{Is the factor 3 configurable?} if $\sigma$ is changed by less than 20\% during that process,

we consider that the field is not crowded and we simply take the \index{mean} mean of the clipped histogram

as a value for the background; otherwise we estimate the \index{mode} mode with:

\begin{equation}

\label{eq:mode}

  \mbox{Mode} = 2.5 \times \mbox{Median} - 1.5 \times \mbox{Mean}

\end{equation}

This expression is different from the usual approximation

\begin{equation}

  \mbox{Mode} = 3 \times \mbox{Median} - 2 \times \mbox{Mean}

\end{equation}

(e.g. Kendall and Stuart 1977), but was found to be more accurate with our clipped

distributions, from the simulations we made. Fig. \ref{fig:modevsmean} shows that the expression of

the \index{mode} mode above is considerably less affected\footnote{Obviously in some very unfavorable cases

(like small meshes falling on bright \index{stars} stars), it leads to totally inaccurate results.} by \index{crowding} crowding

than a simple clipped \index{mean} mean --- like the one used in \index{FOCAS} FOCAS (Jarvis and Tyson 1981)

or by Infante (1987) --- but is $\approx 30\%$ noisier.

% For this reason

This is why

we revert to the clipped

\index{mean} mean in non-crowded fields.

%---------------------------------- Fig.modevsmean  --------------------------------

   \begin{figure}[htbp]

      \centerline{\includegraphics[width=12cm]{ps/modevsmean.ps}}

      \caption{

              Simulations of $32\times32$ pixels background meshes polluted by random Gaussian profiles.

              The true background lies at 0 ADU. While being slightly noisier, the clipped ``Mode''

              gives a more robust estimate than a clipped Mean in crowded regions.

              }

      \label{fig:modevsmean}

   \end{figure}

Once the grid is set up, a \index{median} median filter can be applied to suppress possible

local overestimations due to bright \index{stars} stars. \gam{But sometimes the user will

  want to have the bright star be part of the background!} The resulting \index{background map} background map is then simply a (natural)

bicubic-spline \index{interpolation} interpolation between the meshes of the grid.

In parallel with the making of the \index{background map} background map, an \emph{RMS background map}, that is, a map of the

background noise in the \index{image} image is produced. It will be used if the {\tt WEIGHT\_TYPE} parameter is

set different from {\tt NONE} (see \S\ref{chap:weighttype}).

\subsection{Configuration parameters and tuning}.

The choice of the mesh size ({\tt BACK\_SIZE}) is very important.

If it is too small, the background estimation is affected by the presence of objects and

random noise. Most importantly, part of the flux of the most extended

objects can be absorbed into the \index{background map} background map. If the mesh size is too large,

it cannot reproduce the small scale variations of the background. Therefore

a good compromise has to be found by the user. Typically, for reasonably

sampled \index{image} images, a width\footnote{{\sc SExtractor} offers the

possibility of rectangular background meshes; but it is advised to use

square ones, except in some very special cases (rapidly varying background

in one direction for example).} of 32 to 256 pixels works well. The user has

some control over the \index{background map} background map by specifying the size

of the \index{median} median filter ({\tt BACK\_FILTERSIZE}). A width

and height of 1 \index{mean} means that no filtering will be

applied to the background grid. Usually a size of $3\times3$ is enough, but it

may be necessary to use larger dimensions, especially to compensate, in part, for

small background mesh sizes, or in the case of large artefacts in the \index{image} images.

Median filtering also helps reducing possible \index{ringing} ringing effects of the bicubic-spline

around bright features. In some specific cases it might be desirable to \index{median} median-filter

only background meshes whose original values exceed some \index{threshold} threshold above the filtered-value.

This differential \index{threshold} threshold is set by the {\tt BACK\_FILTERTHRESH} parameter, in ADUs.

It is important to note that all {\tt BACK\_} configuration parameters also affect the

background-RMS map.

By default, the computed \index{background map} background map is automatically subtracted

from the input \index{image} image.  But there are some situations where it is more

appropriate to subtract a {\em constant} from the \index{image} image (e.g., images

where the background noise distribution is strongly skewed).  The {\tt

BACK\_TYPE} configuration parameter (set by default to ``AUTO'') can

be switched to {\tt MANUAL} to allow for the value specified by the

{\tt BACK\_VALUE} parameter to be subtracted from the input

\index{image} image. The default value is 0.

\gam{Describe {\tt MINIBACK}}

\label{chap:miniback}

\subsection{CPU cost}.

The background estimation operation can take a considerable time on the largest \index{image} images,

e.g. a few minutes minutes for a $32000\times32000$ frame on a 2GHz

processor.

\gam{Update time?}