Changeset 1215 for trunk/doc/pslib

Timestamp:

Jul 13, 2004, 11:43:09 AM (22 years ago)

Author:

eugene

Message:

added rotation and interpolation

File:

• trunk/doc/pslib/psLibADD.tex (modified) (3 diffs)

trunk/doc/pslib/psLibADD.tex

@@ -1 @@
-%%% $Id: psLibADD.tex,v 1.21 2004-07-12 22:18:39 eugene Exp $
+%%% $Id: psLibADD.tex,v 1.22 2004-07-13 21:43:09 eugene Exp $
 \documentclass[panstarrs]{panstarrs}
 
@@ -12 +12 @@
 \project{Pan-STARRS Image Processing Pipeline}
 \organization{Institute for Astronomy}
-\version{02}
+\version{03}
 \docnumber{PSDC-430-006}
 
@@ -645 +645 @@
 \subsubsection{Astronomical Image Manipulations}
 
+\paragraph{Interpolation}
+
+Interpolation is needed in various image manipulation operations,
+including rotation and resampling.  We have specified a function to
+perform the interpolation using one of several possible interpolation
+methods, defined below.  It is important in the discussions that
+follow to remember that a pixel with column,row if $i,j$ has
+coordinate at the center of $i+0.5,j+0.5$ and corners with coordinates
+from $i,j$ to $i+1,j+1$.  Thus, the interpolation of a coordinate
+$x,y$ = 5.0,4.0 is a value midway between the four pixels with
+column,row of (5,4), (5,5), (6,4), (6,5).  
+
+\subparagraph{Nearest Pixel Interpolation ({\tt PS\_RESAMPLE\_FLAT})}
+
+In this interpolation, the value of the closest pixel is returned.
+This is equivalent to pixel duplication or replication.
+
+\subparagraph{Bilinear Interpolation ({\tt PS\_RESAMPLE\_BILINEAR})}
+
+In this interpolation, the value at the coordinate is calculated using
+linear interpolation in two dimensions from the four nearest neighbor
+pixels.  The bilinear interpolation value at a coordinate $x,y$
+depends on the four nearest neighbor pixels and the fractional
+distance $fx,fy$ of the given coordinates from the centers of those
+four pixels.  Consider four neighboring pixels at column,row of $i,j$,
+$i+1,j$, $i,j+1$, and $i+1,j+1$ with pixel values $V_{0,0}$,
+$V_{1,0}$, $V_{0,1}$, $V_{1,1}$.  The value at $x,y$ is given by:
+\[ V = (V_{0,0}(1 - f_x) + V_{1,0}f_x)(1 - f_y) + (V_{0,1}(1-f_x) + V_{1,1}f_x)f_y \]
+This expression is more efficiently evaluated by factoring and
+calculating the expresion as:
+\[ r_x = V_{0,0} + (V_{1,0} - V_{0,0})f_x \]
+\[ V = r_x + (V_{0,1} + (V_{1,1} - V_{0,1})f_x - r_x)f_y \]
+
+Note that the values of $f_x$ and $f_y$ require some care.  Given a
+coordinate $x,y$, the value of $f_x$ is calculated as $f_x - 0.5 -
+int(f_x - 0.5)$.  For example, when interpolating the value at
+(5.8.5.2), the relevant neighbor pixels are (5,4), (6,4), (5,5), (6,5)
+and the fractional coordinate values $f_x, f_y = 0.3, 0.7$.  The
+resulting coordinate would be contained within the pixel at column,row
+(5,5).
+
+\subparagraph{Bilinear Interpolation ({\tt PS\_RESAMPLE\_SINC})}
+
+\subparagraph{Bilinear Interpolation ({\tt PS\_RESAMPLE\_LAGRANGE})}
+
 \paragraph{Image Cuts and Slices}