Changeset 1070 for trunk/doc/pslib/psLibADD.tex

Timestamp:

Jun 22, 2004, 3:13:17 PM (22 years ago)

Author:

eugene

Message:

clarification of clipped and sample statistics

File:

• trunk/doc/pslib/psLibADD.tex (modified) (4 diffs)

trunk/doc/pslib/psLibADD.tex

@@ -1 @@
-%%% $Id: psLibADD.tex,v 1.18 2004-06-14 21:19:36 price Exp $
+%%% $Id: psLibADD.tex,v 1.19 2004-06-23 01:13:17 eugene Exp $
 \documentclass[panstarrs]{panstarrs}
 
@@ -33 +33 @@
 
 \DocumentsInternal
-PSCD-430-xxx  &   PS-1 Design Reference Mission \\ \hline
-PSCD-430-004  &   Pan-STARRS IPP C Code Conventions \\ \hline
-PSCD-430-005  &   Pan-STARRS IPP SRS \\ \hline
-PSCD-430-006  &   Pan-STARRS IPP ADD \\ \hline
-PSCD-430-008  &   Pan-STARRS IPP Architecture SDR \\ 
+PSDC-430-xxx  &   PS-1 Design Reference Mission \\ \hline
+PSDC-430-004  &   Pan-STARRS IPP C Code Conventions \\ \hline
+PSDC-430-005  &   Pan-STARRS IPP SRS \\ \hline
+PSDC-430-006  &   Pan-STARRS IPP ADD \\ \hline
+PSDC-430-008  &   Pan-STARRS IPP Architecture SDR \\ 
 \DocumentsExternal
 Posix Standard                      & Open Group Based Specifications Issue 6, IEEE Std 1003.1, 2003 \\ \hline
@@ -193 +193 @@
 
 \begin{enumerate}
-\item Compute the sample median. 
+\item Compute the sample median. The number of data points must be
+      limited to 10000; the input dataset must be randomly subsampled
+      if more data points are used.
 \item Compute the sample standard deviation.
 \item Use the sample median as the first estimator of the mean, $\bar{x}$.
@@ -640 +642 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
+\subsubsection{Astronomical Image Manipulations}
+
+\paragraph{Image Cuts and Slices}
+
+Several functions specify operations which manipulate a collection of
+pixels to return a statistic on the pixel collection.  In the simplest
+case, these are trivial to define: if the boundaries of the region of
+interest are specified along integral pixel coordinates, then the
+pixels used to measure the statistic are always an exact integer.
+This is the case for the function \code{psImageSlice} which requires a
+starting coordinate which is an integer and a width in both dimensions
+which is an integer.  For the case of the functions \code{psImageCut}
+and \code{psImageRadialCut}, the situation is a bit more subtle.  In
+both of these cases, the region is unlikely to contain only whole
+pixels and some choices must be made.
+
+One posibility which we reject is to identify the fractional pixels
+which are overlapped by the region of interest and add that fraction
+of the pixel's flux when calculating the statistic of interest.  This
+is computationally intensive, and not necessarily well defined for all
+statistics.  
+
+In PSLib, we instead identify the pixels overlapped by the region, use
+the complete set of pixel values, treating all pixels equally, and
+renormalize as needed.  To perform this, the region of interest is
+laid on top of the image pixels.  Any pixels which overlap the region
+are identified as part of the input sample.  The statistic (ie, sample
+mean, robust mode, etc), is then calculated on this collection of
+pixels.  If the output statistic is an average value, the measured
+value is reported.  If the output statistic is a sum value (sum of
+counts, sum of pixels), then the value is renormalized by the ratio of
+pixels used in the calculation to the pixel area of the region of
+interest.  For example, if the sum within a radial aperture is
+requested, the circle of the specified radius and center is placed on
+the pixel grid.  Any pixels which touch the circle are then placed in
+a list to be analysed.  The statistic of interest is the measured for
+this collection of pixels.  In the case of a circular aperture which
+is centered at the coordinate (2,2) and has a radius of 2, the number
+of pixels which are touched by the circle is 16, while the total pixel
+area of the circle is 12.57 square pixels.  In this case, the pixel
+sum is renormalized by the ratio (12.57/16.00).
+
 \subsubsection{Celestial Coordinate Conversions}