doc/localhost/ALE/download/ale-0.6.0-tech/iterative/index.html

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  25 <a href="http://auricle.dyndns.org/ALE/">
  26 <big>ALE</big>
  27 <br>
  28 Image Processing Software
  29 <br>
  30 <br>
  31 <small>Deblurring, Anti-aliasing, and Superresolution.</small></a>
  32 <br><br>
  33 <big>
  34 Local Operation
  35 </big>
  36 <hr>
  37 localhost<br>
  38 5393119533<br>
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  40
  41
  42
  43 <p><b>[ <a href="../">Up</a> ]</b></p>
  44 <h1>Irani-Peleg Renderer</h1>
  45
  46 <p>ALE implements an iterative image reconstruction algorithm based on Michal
  47 Irani and Shmuel Peleg's paper "Improving Resolution by Image Registration",
  48 published in <i>Graphical Models and Image Processing</i>, Vol. 53, No. 3, May,
  49 pp. 231-239, 1991, or available at:
  50
  51 <p><a href="http://www.wisdom.weizmann.ac.il/~irani/abstracts/superResolution.html">http://www.wisdom.weizmann.ac.il/~irani/abstracts/superResolution.html</a>
  52
  53 <p>This algorithm iteratively performs two steps: first, an
  54 approximation of <b>T</b> is projected, based on a filter approximating
  55 <b>d<sub>j</sub></b>, and data collected during <a
  56 href="../alignment/">alignment</a>, to create a set of simulated input frames;
  57 second, the per-pixel error -- between these simulated input frames and the
  58 actual input frames -- is calculated, backprojected, and subtracted from the
  59 approximation of <b>T</b>, resulting in a new approximation of <b>T</b>.
  60
  61 <h2>Initial Image Approximation</h2>
  62
  63 <p>ALE uses the results of previous rendering steps as the initial image
  64 approximation.</p>
  65
  66 <h2>Projection and Back-projection filters</h2>
  67
  68 ALE provides command-line options for selecting forward-projection filters,
  69 including box filters (release 0.4.2 and later) and custom filters (release
  70 0.4.7 and later).  The back-projection filters are constructed from the
  71 forward-projection filters in such a way that condition (9) from Theorem 4.1
  72 in the source paper is satisfied.
  73
  74 <h2>Transformation details</h2>
  75
  76 <p>ALE's method of transforming pixel areas between coordinate systems
  77 approximates transformed pixel boundaries with axis-aligned rectangular
  78 regions.  Since boundaries are transformed into the coordinate systems of the
  79 input frames, this approximation can be improved by using larger scale factors
  80 (and hence reducing the size of transformed pixels).</p>
  81
  82 <h2>Multi-level operation</h2>
  83
  84 <p>The following is an edited excerpt from the comment headers for the source
  85 file <code>d2/render/ipc.h</code>.  For more information about ALE's
  86 implementation of multi-level operation, see the relevant source files.
  87
  88 <pre>
  89  * The algorithm in the source paper looks something like this (PSF' is the
  90  * backprojection kernel, and corresponds to what the authors of the paper call
  91  * AUX):
  92  *
  93  * ===============================================================
  94  *    Forward         Backward           Binary Operators
  95  * ---------------------------------------------------------------
  96  *
  97  *    scene(n) ------> scene(n+1)        <--- summation
  98  *
  99  *      |                 ^
 100  *      |                 |
 101  *     PSF               PSF'
 102  *      |                 |
 103  *      |        ---------+              <--- difference
 104  *      V       /         |
 105  *
 106  *   simulated(n)       real
 107  *
 108  * ===============================================================
 109  *
 110  * This assumes a single colorspace representation.  However, consumer cameras
 111  * sometimes perform sharpening in non-linear colorspace, whereas lens and
 112  * sensor blurring occurs in linear colorspace.  Hence, there can be two
 113  * colorspaces involved; ALE accounts for this with linear and non-linear
 114  * colorspace PSFs.  Hence, the algorithm we use looks something like:
 115  *
 116  * ===============================================================
 117  *    Forward         Backward            Binary Operators
 118  * ---------------------------------------------------------------
 119  *
 120  *    scene(n) -----> scene(n+1)          <--- summation
 121  *
 122  *      |                 ^
 123  *      |                 |
 124  *    LPSF              LPSF'
 125  *      |                 |
 126  *      |       ----------+               <--- difference,
 127  *      V      /          |                    exposure
 128  *                                             re-estimation
 129  *  lsimulated(n)      lreal(n)
 130  *
 131  *      |                 ^
 132  *      |                 |
 133  *   unlinearize       linearize
 134  *      |                 |
 135  *      V                 |
 136  *
 137  *  lsim_nl(n) -----> lreal_nl(n)         <--- summation
 138  *
 139  *      |                 ^
 140  *      |                 |
 141  *    NLPSF             NLPSF'
 142  *      |                 |
 143  *      |       ----------+               <--- difference
 144  *      V      /          |
 145  *
 146  *  nlsimulated(n)     real_nl
 147  *
 148  *                        ^
 149  *                        |
 150  *                    unlinearize
 151  *                        |
 152  *                        |
 153  *
 154  *                      real
 155  *
 156  * ===============================================================
 157 </pre>
 158
 159
 160 <hr>
 161 <i>Copyright 2003, 2004 <a href="mailto:dhilvert@auricle.dyndns.org">David Hilvert</a></i>
 162 <p>Verbatim copying and distribution of this entire article is permitted in any medium, provided this notice is preserved.
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