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\section{Background estimation}
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\section{Background estimation}
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\label{chap:backest}
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\label{chap:backest}
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The value measured at each pixel is a function of the sum of a ``background''
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The value measured at each pixel is a function of the sum of a ``background''
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signal and light coming from the objects of interest. To be able to detect
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signal and light coming from the objects of interest. To be able to detect
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the faintest of these objects and also to measure accurately their fluxes, one needs
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the faintest of these objects and also to measure accurately their fluxes, one needs
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to have an accurate estimate of the background level in any place of the image,
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to have an accurate estimate of the background level in any place of the \index{image} image,
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a \emph{background map}. Strictly speaking, there should be one background map per
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a \emph{background map}. Strictly speaking, there should be one \index{background map} background map per
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object, that is, what would the image look like if that object was absent.
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object, that is, what would the \index{image} image look like if that object was absent.
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But, at least for detection, we may start by assuming that most discrete sources do not
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But, at least for detection, we may start by assuming that most discrete sources do not
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overlap too severely, which is generally the case for high galactic latitude fields.
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overlap too severely, which is generally the case for high galactic latitude fields.
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To construct the background map, {\sc SExtractor} makes a first pass through the pixel
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To construct the \index{background map} background map, {\sc SExtractor} makes a first pass through the pixel
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data, computing an estimator for the local background in each mesh of a grid
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data, computing an estimator for the \index{local background} local background in each mesh of a grid
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that covers the whole frame.
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that covers the whole frame.
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The background estimator is a combination of $\kappa\,\sigma$ clipping and mode estimation,
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The background estimator is a combination of $\kappa\,\sigma$ clipping and \index{mode} mode estimation,
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similar to the one employed in Stetson's DAOPHOT program (see e.g. Da Costa 1992).
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similar to the one employed in Stetson's \index{DAOPHOT} DAOPHOT program (see e.g. Da Costa 1992).
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Briefly, the local background histogram is clipped iteratively until convergence at
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Briefly, the \index{local background} local background histogram is clipped iteratively until convergence at
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$\pm 3\sigma$ around its median; \gam{Is the factor 3 configurable?} if $\sigma$ is changed by less than 20\% during that process,
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$\pm 3\sigma$ around its \index{median} median; \gam{Is the factor 3 configurable?} if $\sigma$ is changed by less than 20\% during that process,
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we consider that the field is not crowded and we simply take the mean of the clipped histogram
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we consider that the field is not crowded and we simply take the \index{mean} mean of the clipped histogram
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as a value for the background; otherwise we estimate the mode with:
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as a value for the background; otherwise we estimate the \index{mode} mode with:
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\begin{equation}
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\begin{equation}
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\label{eq:mode}
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\label{eq:mode}
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\mbox{Mode} = 2.5 \times \mbox{Median} - 1.5 \times \mbox{Mean}
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\mbox{Mode} = 2.5 \times \mbox{Median} - 1.5 \times \mbox{Mean}
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\end{equation}
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\end{equation}
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This expression is different from the usual approximation
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This expression is different from the usual approximation
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\begin{equation}
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\begin{equation}
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\mbox{Mode} = 3 \times \mbox{Median} - 2 \times \mbox{Mean}
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\mbox{Mode} = 3 \times \mbox{Median} - 2 \times \mbox{Mean}
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\end{equation}
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\end{equation}
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(e.g. Kendall and Stuart 1977), but was found to be more accurate with our clipped
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(e.g. Kendall and Stuart 1977), but was found to be more accurate with our clipped
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distributions, from the simulations we made. Fig. \ref{fig:modevsmean} shows that the expression of
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distributions, from the simulations we made. Fig. \ref{fig:modevsmean} shows that the expression of
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the mode above is considerably less affected\footnote{Obviously in some very unfavorable cases
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the \index{mode} mode above is considerably less affected\footnote{Obviously in some very unfavorable cases
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(like small meshes falling on bright stars), it leads to totally inaccurate results.} by crowding
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(like small meshes falling on bright \index{stars} stars), it leads to totally inaccurate results.} by \index{crowding} crowding
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than a simple clipped mean --- like the one used in FOCAS (Jarvis and Tyson 1981)
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than a simple clipped \index{mean} mean --- like the one used in \index{FOCAS} FOCAS (Jarvis and Tyson 1981)
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or by Infante (1987) --- but is $\approx 30\%$ noisier.
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or by Infante (1987) --- but is $\approx 30\%$ noisier.
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% For this reason
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% For this reason
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This is why
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This is why
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we revert to the clipped
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we revert to the clipped
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mean in non-crowded fields.
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\index{mean} mean in non-crowded fields.
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%---------------------------------- Fig.modevsmean --------------------------------
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%---------------------------------- Fig.modevsmean --------------------------------
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\begin{figure}[htbp]
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\begin{figure}[htbp]
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\centerline{\includegraphics[width=12cm]{ps/modevsmean.ps}}
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\centerline{\includegraphics[width=12cm]{ps/modevsmean.ps}}
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\caption{
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\caption{
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| Line 47... |
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}
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}
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\label{fig:modevsmean}
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\label{fig:modevsmean}
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\end{figure}
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\end{figure}
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Once the grid is set up, a median filter can be applied to suppress possible
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Once the grid is set up, a \index{median} median filter can be applied to suppress possible
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local overestimations due to bright stars. \gam{But sometimes the user will
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local overestimations due to bright \index{stars} stars. \gam{But sometimes the user will
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want to have the bright star be part of the background!} The resulting background map is then simply a (natural)
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want to have the bright star be part of the background!} The resulting \index{background map} background map is then simply a (natural)
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bicubic-spline interpolation between the meshes of the grid.
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bicubic-spline \index{interpolation} interpolation between the meshes of the grid.
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In parallel with the making of the background map, an \emph{RMS background map}, that is, a map of the
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In parallel with the making of the \index{background map} background map, an \emph{RMS background map}, that is, a map of the
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background noise in the image is produced. It will be used if the {\tt WEIGHT\_TYPE} parameter is
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background noise in the \index{image} image is produced. It will be used if the {\tt WEIGHT\_TYPE} parameter is
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set different from {\tt NONE} (see \S\ref{chap:weighttype}).
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set different from {\tt NONE} (see \S\ref{chap:weighttype}).
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\subsection{Configuration parameters and tuning}.
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\subsection{Configuration parameters and tuning}.
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The choice of the mesh size ({\tt BACK\_SIZE}) is very important.
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The choice of the mesh size ({\tt BACK\_SIZE}) is very important.
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If it is too small, the background estimation is affected by the presence of objects and
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If it is too small, the background estimation is affected by the presence of objects and
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random noise. Most importantly, part of the flux of the most extended
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random noise. Most importantly, part of the flux of the most extended
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objects can be absorbed into the background map. If the mesh size is too large,
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objects can be absorbed into the \index{background map} background map. If the mesh size is too large,
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it cannot reproduce the small scale variations of the background. Therefore
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it cannot reproduce the small scale variations of the background. Therefore
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a good compromise has to be found by the user. Typically, for reasonably
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a good compromise has to be found by the user. Typically, for reasonably
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sampled images, a width\footnote{{\sc SExtractor} offers the
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sampled \index{image} images, a width\footnote{{\sc SExtractor} offers the
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possibility of rectangular background meshes; but it is advised to use
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possibility of rectangular background meshes; but it is advised to use
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square ones, except in some very special cases (rapidly varying background
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square ones, except in some very special cases (rapidly varying background
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in one direction for example).} of 32 to 256 pixels works well. The user has
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in one direction for example).} of 32 to 256 pixels works well. The user has
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some control over the background map by specifying the size
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some control over the \index{background map} background map by specifying the size
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of the median filter ({\tt BACK\_FILTERSIZE}). A width
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of the \index{median} median filter ({\tt BACK\_FILTERSIZE}). A width
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and height of 1 means that no filtering will be
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and height of 1 \index{mean} means that no filtering will be
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applied to the background grid. Usually a size of $3\times3$ is enough, but it
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applied to the background grid. Usually a size of $3\times3$ is enough, but it
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may be necessary to use larger dimensions, especially to compensate, in part, for
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may be necessary to use larger dimensions, especially to compensate, in part, for
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small background mesh sizes, or in the case of large artefacts in the images.
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small background mesh sizes, or in the case of large artefacts in the \index{image} images.
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Median filtering also helps reducing possible ringing effects of the bicubic-spline
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Median filtering also helps reducing possible \index{ringing} ringing effects of the bicubic-spline
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around bright features. In some specific cases it might be desirable to median-filter
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around bright features. In some specific cases it might be desirable to \index{median} median-filter
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only background meshes whose original values exceed some threshold above the filtered-value.
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only background meshes whose original values exceed some \index{threshold} threshold above the filtered-value.
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This differential threshold is set by the {\tt BACK\_FILTERTHRESH} parameter, in ADUs.
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This differential \index{threshold} threshold is set by the {\tt BACK\_FILTERTHRESH} parameter, in ADUs.
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It is important to note that all {\tt BACK\_} configuration parameters also affect the
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It is important to note that all {\tt BACK\_} configuration parameters also affect the
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background-RMS map.
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background-RMS map.
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By default, the computed background map is automatically subtracted
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By default, the computed \index{background map} background map is automatically subtracted
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from the input image. But there are some situations where it is more
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from the input \index{image} image. But there are some situations where it is more
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appropriate to subtract a {\em constant} from the image (e.g., images
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appropriate to subtract a {\em constant} from the \index{image} image (e.g., images
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where the background noise distribution is strongly skewed). The {\tt
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where the background noise distribution is strongly skewed). The {\tt
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BACK\_TYPE} configuration parameter (set by default to ``AUTO'') can
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BACK\_TYPE} configuration parameter (set by default to ``AUTO'') can
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be switched to {\tt MANUAL} to allow for the value specified by the
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be switched to {\tt MANUAL} to allow for the value specified by the
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{\tt BACK\_VALUE} parameter to be subtracted from the input
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{\tt BACK\_VALUE} parameter to be subtracted from the input
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image. The default value is 0.
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\index{image} image. The default value is 0.
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\gam{Describe {\tt MINIBACK}}
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\gam{Describe {\tt MINIBACK}}
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\label{chap:miniback}
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\label{chap:miniback}
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\subsection{CPU cost}.
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\subsection{CPU cost}.
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The background estimation operation can take a considerable time on the largest images,
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The background estimation operation can take a considerable time on the largest \index{image} images,
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e.g. a few minutes minutes for a $32000\times32000$ frame on a 2GHz
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e.g. a few minutes minutes for a $32000\times32000$ frame on a 2GHz
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processor.
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processor.
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\gam{Update time?}
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\gam{Update time?}
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