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This commit is contained in:
Mauro Torrez
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<html>
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<title>Error</title>
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<style type="text/css">
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TABLE.ba { max-width: 678; text-align: center; padding-bottom: 15; padding-top: 5}
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TD.text_table {padding-left: 2; padding-right: 2; border-width: 1}
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BLOCKQUOTE {padding-right: 400 }
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LI {max-width: 640; clear: left}
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P.footer {max-width: none; width: auto; padding-left: 0}
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P.header {max-width: none; width: auto; padding-left: 0}
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HR.main {max-width: 640; clear: left; padding-left: 0; margin-left: 0}
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HR.footer {clear: both}
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</style>
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</head>
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<body>
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<table align=right valign=top width=160>
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<td valign=top height=600 width=160>
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<a href="http://auricle.dyndns.org/ALE/">
|
||||
<big>ALE</big>
|
||||
<br>
|
||||
Image Processing Software
|
||||
<br>
|
||||
<br>
|
||||
<small>Deblurring, Anti-aliasing, and Superresolution.</small></a>
|
||||
<br><br>
|
||||
<big>
|
||||
Local Operation
|
||||
</big>
|
||||
<hr>
|
||||
localhost<br>
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5393119533<br>
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||||
</table>
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<p><b>[ <a href="../">Up</a> | <a href="mc/">Monte Carlo</a> ]</b></p>
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<h1>Error</h1>
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<p>Error calculations are used to determine whether a transformation is "good"
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or not, and in particular, whether one transformation is better or worse than
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another. A smaller error indicates a better transformation, from the perspective
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of the alignment algorithm.
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<p>ALE defines an error value for each pixel of the alignment reference image, and also
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comprehensive error, which summarizes the error over all pixels.
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<h3>Pre-Alignment Exposure Registration</h3>
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<p>When exposure registration is enabled, ALE performs an exposure registration
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||||
step prior to alignment. The result of this step is dependent on the initial
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alignment (this can be either the default initial alignment or an alignment
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loaded from a transformation data file). See the source for more details.
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<h3>Per-Pixel Error</h3>
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<!-- <p>(Alternatives to normalization exist, including the use of inner products; see
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Steve Mann's paper, available on the website linked in footnote 1, for a
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discussion of alignment approaches.) -->
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<!--
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<p>Based on principle 2, ALE calculates the difference between each alignment reference
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image pixel and the value with which it would be merged given a candidate
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transformation. This latter value is the <i>overlapping value</i>, as
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described in the section on <a href="../../merging/">merging</a>. This difference
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is then raised by the error metric exponent, as specified by the --metric
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option. The exponent defaults to 2.0 for ALE versions 0.1.0 and later, or 1.0
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for version 0.0.0. Hence,
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-->
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<p>The per-pixel error for pixel <i>(i, j)</i> in the alignment reference
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image <i>A</i>, frame <i>B</i>, and transformation <i>T</i>, is:
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<p><blockquote>
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<pre>
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<i>p(i, j, A, B, T) = Abs( A(i, j) - B(T_inverse(i, j)) )<sup>metric_exponent</sup></i>
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</pre>
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</blockquote>
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<p>where <i>Abs()</i> is the absolute value function and <i>B(T_inverse(i,
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j))</i> is determined by bilinear interpolation (unless a different interpolant
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is specified using <code>--afilter</code>). If not specified by the --metric
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option, <i>metric_exponent</i> defaults to 2.
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<p>For coordinates where B(T_inverse(i, j)) is not defined, the error is zero.
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(Feedback from Angelo Pesce led to clarification of this point.)
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<p>In addition to per-pixel error, a per-pixel <i>maximum error
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estimator</i> is calculated, as follows:
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<p><blockquote>
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<pre>
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<i>p_max(i, j, A, B, T) = Max( A(i, j), B(T_inverse(i, j)) )<sup>metric_exponent</sup></i>
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</pre>
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</blockquote>
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<p>For coordinates where B(T_inverse(i, j)) is not defined, the maximum error
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estimator is zero. (Feedback from Angelo Pesce led to clarification of this
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point.)
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|
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|
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<h3>Comprehensive Error</h3>
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<p>There are two varieties of comprehensive error used by ALE: <i>exhaustive</i>
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error (enabled by <code>--no-mc</code>) and <a
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href="mc/"><i>Monte Carlo</i></a> error (enabled by <code>--mc</code>).
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Whereas the exhaustive approach evaluates the error for each pixel in the
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alignment reference image, the <a href="mc/">Monte Carlo</a> approach evaluates
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only a subset of pixels.
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<p>If we consider <i>Sum[]</i> to provide the sum over whatever subset of
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pixels we are sampling (including possibly the set of all pixels), then the
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comprehensive error function, for alignment reference image <i>A</i>, frame
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<i>B</i>, and transformation <i>T</i>, is:
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||||
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<p><blockquote>
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<pre>
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<i>E(A, B, T) = (Sum [ p(i, j, A, B, T) ] / Sum [ p_max(i, j, A, B, T) ])<sup>(1/metric_exponent)</sup></i>
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</pre>
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</blockquote>
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<br><br>
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<hr>
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<i>Copyright 2002, 2003, 2004 <a href="mailto:dhilvert@auricle.dyndns.org">David Hilvert</a></i>
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<p>Verbatim copying and distribution of this entire article is permitted in any
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||||
medium, provided this notice is preserved.
|
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</body>
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</html>
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@@ -0,0 +1,160 @@
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<html>
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<title>Monte Carlo Error</title>
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<style type="text/css">
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TABLE.ba { max-width: 678; text-align: center; padding-bottom: 15; padding-top: 5}
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TABLE.inline { padding-right: 300; clear: left}
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TD.text_table {padding-left: 2; padding-right: 2; border-width: 1}
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H2 {clear: left}
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P {max-width: none; padding-right: 300; clear: left}
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BLOCKQUOTE {padding-right: 400 }
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LI {max-width: 640; clear: left}
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P.footer {max-width: none; width: auto; padding-left: 0}
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P.header {max-width: none; width: auto; padding-left: 0}
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HR.main {max-width: 640; clear: left; padding-left: 0; margin-left: 0}
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HR.footer {clear: both}
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</style>
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</head>
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<body>
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<table align=right valign=top width=160>
|
||||
<td valign=top height=600 width=160>
|
||||
<a href="http://auricle.dyndns.org/ALE/">
|
||||
<big>ALE</big>
|
||||
<br>
|
||||
Image Processing Software
|
||||
<br>
|
||||
<br>
|
||||
<small>Deblurring, Anti-aliasing, and Superresolution.</small></a>
|
||||
<br><br>
|
||||
<big>
|
||||
Local Operation
|
||||
</big>
|
||||
<hr>
|
||||
localhost<br>
|
||||
5393119533<br>
|
||||
</table>
|
||||
|
||||
|
||||
|
||||
|
||||
<p><b>[ <a href="../">Up</a> ]</b></p>
|
||||
<h1>Monte Carlo Error</h1>
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||||
|
||||
<p>Use of Monte Carlo error can decrease the time required to align large images,
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||||
since performing coordinate transformations and memory accesses at every pixel
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||||
can be expensive. Sections in this page describe the motivation for Monte
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||||
Carlo alignment, the ratio calculations used, the sampling algorithm, cache
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behavior for the algorithm, randomization approaches, typical deviations from
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the specified ratios, special handling of level-of-detail, and practical
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observations regarding the use of Monte Carlo error.
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<h2>Motivation</h2>
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<p>Performing large numbers of coordinate transformations and memory accesses in
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||||
order to determine alignment error can be computationally expensive. One
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||||
approach to mitigating this expense is to use reduced level-of-detail.
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However, using reduced level-of-detail can also reduce alignment precision. In
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particular, reducing the level of detail by a factor of two can make impossible
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the task of precisely aligning a horizontal line one pixel high. However, if
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||||
just a few pixels from the line are sampled at full detail, exact alignment is
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||||
possible.
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||||
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||||
<h2>Ratio Calculations</h2>
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||||
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||||
<p>In Monte Carlo alignment, a ratio
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<blockquote>
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||||
<i>s = (expected # of pixel
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samples) / (# of total pixels in the accumulated image)</i>
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||||
</blockquote>
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||||
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||||
is specified. From this ratio, a new ratio
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||||
|
||||
<blockquote>
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||||
<i>u = (expected # of unsampled pixels) / (expected # of sampled pixels)</i>
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||||
</blockquote>
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||||
|
||||
is calculated. Pixels are sampled in such a manner that <i>u</i> is
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approximately satisified.
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||||
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||||
<p>At this stage, the region of overlap with the new frame is not considered.
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With a limited area of overlap, the number of actual samples contributing to
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the final error value will typically be reduced proportionally. (Angelo Pesce
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||||
has pointed out that better approaches may be possible, wherein explicit
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||||
calculation of overlapping areas reduces the number of coordinate
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transformations performed.)
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||||
<h2>Sampling Algorithm</h2>
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||||
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||||
<p>Pixels are considered in order of index, where the accumulated image pixel
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at position <i>(i, j)</i> is numbered with an index <i>(i * width + j)</i>.
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||||
In order of index, we skip and sample pixels in such a manner that the
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||||
expected size of a run of consecutive skipped pixels preceding a sampled pixel
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||||
is <i>u</i>. We select the size of each run of consecutive skipped pixels as
|
||||
follows:
|
||||
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||||
<p>If <i>2 * u</i> is an integer, then we draw uniformly from integer values in
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||||
the interval <i>[0,2u]</i>. If it is not an integer, then we draw from integer values in
|
||||
the interval <i>[0,2u + 1]</i> in such a manner that integer values in
|
||||
<i>[0,2u]</i> are equally likely to be chosen.
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||||
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||||
<p>(Also, see the section below on interaction with level-of-detail.)
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||||
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||||
<h2>Cache behavior</h2>
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||||
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||||
<p>Since indices are monotonically increasing in memory address, this approach
|
||||
to sampling may make effective use of memory cache where other approaches (e.g.
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||||
repeated random draws from the entire index space) would not.
|
||||
|
||||
<h2>Randomization</h2>
|
||||
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||||
<p>ALE versions 0.4.7 and earlier do not reseed the pseudorandom number generator,
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||||
and so a new random subset is selected every time the error is evaluated.
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||||
Hence, as more or fewer of the pixels critical to alignment are sampled, the
|
||||
reported alignment can worsen or improve even in the absence of any change in
|
||||
transformation.
|
||||
|
||||
<p>With this approach, since many transformations are inspected during the
|
||||
alignment of any given frame, it is likely, especially with greater precision
|
||||
of alignment, that some measured differences between transformations are due to
|
||||
a difference in sample sets rather than a difference in alignment accuracy.
|
||||
|
||||
<p>By reseeding the pseudorandom number generator, ALE versions 0.4.8 and later
|
||||
instead use a consistent set of pixels from the accumulated image when
|
||||
comparing two transformations. Tests sampling 3% of pixels from a set of
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||||
320x240 frames indicate that this approach improves alignment.
|
||||
|
||||
<h2>Sampling characteristics</h2>
|
||||
|
||||
<p>For an image with 100,000 pixels and specified
|
||||
<i>s</i> in the interval <i>[0.005,0.995]</i>, ALE's sampling method results in
|
||||
a ratio <i>s</i> within 0.000003 of the specified <i>s</i>. This number
|
||||
improves with image size. (The results are outlined in a <a
|
||||
href="ratios/">table</a>.) However, note that s only represents an expected
|
||||
value, and the actual number of sampled pixels may vary by more than the
|
||||
numbers given here.
|
||||
|
||||
<h2>Interaction with level-of-detail</h2>
|
||||
|
||||
<p>When reduced level-of-detail is used, the number of reduced-detail pixels
|
||||
sampled is taken to be a percentage of the total number of pixels in the
|
||||
full-detail image, rather than as a percentage of the total number of pixels in
|
||||
the reduced-detail image. (When this fraction of pixels in the full-detail
|
||||
image is more than the number of reduced-detail pixels available, all
|
||||
reduced-detail pixels are used.) This may improve the likelihood of successful
|
||||
alignment, but may also add overhead to the alignment process.
|
||||
|
||||
<br><br>
|
||||
|
||||
<hr>
|
||||
<i>Copyright 2002, 2003, 2004 <a href="mailto:dhilvert@auricle.dyndns.org">David Hilvert</a></i>
|
||||
<p>Verbatim copying and distribution of this entire article is permitted in any
|
||||
medium, provided this notice is preserved.
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,255 @@
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<html>
|
||||
<head>
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||||
<title>Expected sample ratio for --mc <x> argument</title>
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||||
<style type="text/css">
|
||||
TABLE.ba { max-width: 678; text-align: center; padding-bottom: 15; padding-top: 5}
|
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TD {padding-left: 0; padding-right: 0; border-width: 0}
|
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TD.text_table {padding-left: 2; padding-right: 2; border-width: 1}
|
||||
H2 {clear: left}
|
||||
P {max-width: 640; clear: left}
|
||||
LI {max-width: 640; clear: left}
|
||||
P.footer {max-width: none; width: auto; padding-left: 0}
|
||||
P.header {max-width: none; width: auto; padding-left: 0}
|
||||
HR.main {max-width: 640; clear: left; padding-left: 0; margin-left: 0}
|
||||
HR.footer {clear: both}
|
||||
</style>
|
||||
|
||||
</HEAD>
|
||||
|
||||
<BODY TEXT="#000000" BGCOLOR="#FFFFFF" LINK="#0000EF" VLINK="#55188A" ALINK="#FF0000">
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<table align=right valign=top width=160>
|
||||
<td valign=top height=600 width=160>
|
||||
<a href="http://auricle.dyndns.org/ALE/">
|
||||
<big>ALE</big>
|
||||
<br>
|
||||
Image Processing Software
|
||||
<br>
|
||||
<br>
|
||||
<small>Deblurring, Anti-aliasing, and Superresolution.</small></a>
|
||||
<br><br>
|
||||
<big>
|
||||
Local Operation
|
||||
</big>
|
||||
<hr>
|
||||
localhost<br>
|
||||
7119814098<br>
|
||||
</table>
|
||||
|
||||
|
||||
|
||||
|
||||
<pre>
|
||||
Expected sample ratio for specified --mc <x> argument in a 100,000 pixel
|
||||
image. This table illustrates the effects of a bug in ALE version 0.4.3.
|
||||
|
||||
Column A: Specified expected sample ratio x*10^-2
|
||||
Column B: Expected sample ratio in release 0.4.4
|
||||
Column C: Expected sample ratio in release 0.4.3
|
||||
|
||||
A B C (buggy)
|
||||
|
||||
0.005000 0.004997 0.004997
|
||||
0.010000 0.009997 0.009997
|
||||
0.015000 0.014997 0.014997
|
||||
0.020000 0.019997 0.019997
|
||||
0.025000 0.024997 0.024997
|
||||
0.030000 0.029997 0.029995
|
||||
0.035000 0.034997 0.034995
|
||||
0.040000 0.039997 0.039997
|
||||
0.045000 0.044997 0.044991
|
||||
0.050000 0.049997 0.049997
|
||||
0.055000 0.054997 0.054987
|
||||
0.060000 0.059997 0.059984
|
||||
0.065000 0.064997 0.064984
|
||||
0.070000 0.069997 0.069975
|
||||
0.075000 0.074997 0.074973
|
||||
0.080000 0.079997 0.079997
|
||||
0.085000 0.084997 0.084957
|
||||
0.090000 0.089997 0.089964
|
||||
0.095000 0.094997 0.094986
|
||||
0.100000 0.099997 0.099997
|
||||
0.105000 0.104997 0.104983
|
||||
0.110000 0.109997 0.109945
|
||||
0.115000 0.114997 0.114901
|
||||
0.120000 0.119997 0.119895
|
||||
0.125000 0.124997 0.124997
|
||||
0.130000 0.129997 0.129858
|
||||
0.135000 0.134997 0.134898
|
||||
0.140000 0.139997 0.139847
|
||||
0.145000 0.144997 0.144862
|
||||
0.150000 0.149997 0.149795
|
||||
0.155000 0.154997 0.154909
|
||||
0.160000 0.159997 0.159719
|
||||
0.165000 0.164997 0.164867
|
||||
0.170000 0.169997 0.169756
|
||||
0.175000 0.174997 0.174638
|
||||
0.180000 0.179997 0.179839
|
||||
0.185000 0.184997 0.184730
|
||||
0.190000 0.189997 0.189526
|
||||
0.195000 0.194997 0.194606
|
||||
0.200000 0.199997 0.199997
|
||||
0.205000 0.204997 0.204556
|
||||
0.210000 0.209997 0.209354
|
||||
0.215000 0.214997 0.214412
|
||||
0.220000 0.219997 0.219750
|
||||
0.225000 0.224997 0.224681
|
||||
0.230000 0.229997 0.229272
|
||||
0.235000 0.234997 0.234082
|
||||
0.240000 0.239997 0.239128
|
||||
0.245000 0.244997 0.244426
|
||||
0.250000 0.249998 0.249997
|
||||
0.255000 0.254998 0.254371
|
||||
0.260000 0.259998 0.258926
|
||||
0.265000 0.264998 0.263675
|
||||
0.270000 0.269998 0.268631
|
||||
0.275000 0.274998 0.273807
|
||||
0.280000 0.279998 0.279218
|
||||
0.285000 0.284998 0.284881
|
||||
0.290000 0.289998 0.289338
|
||||
0.295000 0.294998 0.293710
|
||||
0.300000 0.299998 0.298243
|
||||
0.305000 0.304998 0.302947
|
||||
0.310000 0.309998 0.307830
|
||||
0.315000 0.314998 0.312904
|
||||
0.320000 0.319998 0.318180
|
||||
0.325000 0.324998 0.323669
|
||||
0.330000 0.329998 0.329386
|
||||
0.335000 0.334998 0.334671
|
||||
0.340000 0.339998 0.338773
|
||||
0.345000 0.344998 0.343003
|
||||
0.350000 0.349998 0.347366
|
||||
0.355000 0.354998 0.351870
|
||||
0.360000 0.359998 0.356520
|
||||
0.365000 0.364998 0.361324
|
||||
0.370000 0.369998 0.366290
|
||||
0.375000 0.374998 0.371427
|
||||
0.380000 0.379998 0.376742
|
||||
0.385000 0.384998 0.382247
|
||||
0.390000 0.389998 0.387950
|
||||
0.395000 0.394998 0.393863
|
||||
0.400000 0.399998 0.399998
|
||||
0.405000 0.404998 0.403795
|
||||
0.410000 0.409998 0.407690
|
||||
0.415000 0.414998 0.411686
|
||||
0.420000 0.419998 0.415788
|
||||
0.425000 0.424998 0.419998
|
||||
0.430000 0.429998 0.424322
|
||||
0.435000 0.434998 0.428765
|
||||
0.440000 0.439998 0.433332
|
||||
0.445000 0.444998 0.438026
|
||||
0.450000 0.449998 0.442855
|
||||
0.455000 0.454998 0.447824
|
||||
0.460000 0.459998 0.452939
|
||||
0.465000 0.464998 0.458207
|
||||
0.470000 0.469998 0.463635
|
||||
0.475000 0.474998 0.469229
|
||||
0.480000 0.479998 0.474998
|
||||
0.485000 0.484998 0.480951
|
||||
0.490000 0.489998 0.487095
|
||||
0.495000 0.494998 0.493441
|
||||
0.500000 0.499998 0.499998
|
||||
0.505000 0.504998 0.503365
|
||||
0.510000 0.509998 0.506801
|
||||
0.515000 0.514998 0.510308
|
||||
0.520000 0.519998 0.513887
|
||||
0.525000 0.524998 0.517542
|
||||
0.530000 0.529999 0.521275
|
||||
0.535000 0.534999 0.525088
|
||||
0.540000 0.539999 0.528984
|
||||
0.545000 0.544999 0.532966
|
||||
0.550000 0.549999 0.537036
|
||||
0.555000 0.554999 0.541197
|
||||
0.560000 0.559999 0.545453
|
||||
0.565000 0.564999 0.549807
|
||||
0.570000 0.569999 0.554262
|
||||
0.575000 0.574999 0.558822
|
||||
0.580000 0.579999 0.563491
|
||||
0.585000 0.584999 0.568272
|
||||
0.590000 0.589999 0.573169
|
||||
0.595000 0.594999 0.578188
|
||||
0.600000 0.599999 0.583332
|
||||
0.605000 0.604999 0.588606
|
||||
0.610000 0.609999 0.594016
|
||||
0.615000 0.614999 0.599566
|
||||
0.620000 0.619999 0.605262
|
||||
0.625000 0.624999 0.611110
|
||||
0.630000 0.629999 0.617116
|
||||
0.635000 0.634999 0.623287
|
||||
0.640000 0.639999 0.629628
|
||||
0.645000 0.644999 0.636149
|
||||
0.650000 0.649999 0.642856
|
||||
0.655000 0.654999 0.649757
|
||||
0.660000 0.659999 0.656862
|
||||
0.665000 0.664999 0.664178
|
||||
0.670000 0.669999 0.668341
|
||||
0.675000 0.674999 0.670885
|
||||
0.680000 0.679999 0.673468
|
||||
0.685000 0.684999 0.676091
|
||||
0.690000 0.689999 0.678755
|
||||
0.695000 0.694999 0.681461
|
||||
0.700000 0.699999 0.684210
|
||||
0.705000 0.704999 0.687002
|
||||
0.710000 0.709999 0.689839
|
||||
0.715000 0.714999 0.692721
|
||||
0.720000 0.719999 0.695651
|
||||
0.725000 0.724999 0.698629
|
||||
0.730000 0.729999 0.701657
|
||||
0.735000 0.734999 0.704735
|
||||
0.740000 0.739999 0.707864
|
||||
0.745000 0.744999 0.711047
|
||||
0.750000 0.749999 0.714285
|
||||
0.755000 0.754999 0.717578
|
||||
0.760000 0.759999 0.720929
|
||||
0.765000 0.764999 0.724339
|
||||
0.770000 0.769999 0.727810
|
||||
0.775000 0.774999 0.731343
|
||||
0.780000 0.780000 0.734939
|
||||
0.785000 0.785000 0.738601
|
||||
0.790000 0.790000 0.742331
|
||||
0.795000 0.795000 0.746129
|
||||
0.800000 0.800000 0.749999
|
||||
0.805000 0.805000 0.753943
|
||||
0.810000 0.810000 0.757961
|
||||
0.815000 0.815000 0.762057
|
||||
0.820000 0.820000 0.766233
|
||||
0.825000 0.825000 0.770491
|
||||
0.830000 0.830000 0.774834
|
||||
0.835000 0.835000 0.779264
|
||||
0.840000 0.840000 0.783783
|
||||
0.845000 0.845000 0.788395
|
||||
0.850000 0.850000 0.793103
|
||||
0.855000 0.855000 0.797909
|
||||
0.860000 0.860000 0.802817
|
||||
0.865000 0.865000 0.807829
|
||||
0.870000 0.870000 0.812949
|
||||
0.875000 0.875000 0.818181
|
||||
0.880000 0.880000 0.823529
|
||||
0.885000 0.885000 0.828996
|
||||
0.890000 0.890000 0.834586
|
||||
0.895000 0.895000 0.840304
|
||||
0.900000 0.900000 0.846154
|
||||
0.905000 0.905000 0.852140
|
||||
0.910000 0.910000 0.858268
|
||||
0.915000 0.915000 0.864542
|
||||
0.920000 0.920000 0.870968
|
||||
0.925000 0.925000 0.877551
|
||||
0.930000 0.930000 0.884297
|
||||
0.935000 0.935000 0.891213
|
||||
0.940000 0.940000 0.898305
|
||||
0.945000 0.945000 0.905579
|
||||
0.950000 0.950000 0.913043
|
||||
0.955000 0.955000 0.920705
|
||||
0.960000 0.960000 0.928571
|
||||
0.965000 0.965000 0.936652
|
||||
0.970000 0.970000 0.944954
|
||||
0.975000 0.975000 0.953488
|
||||
0.980000 0.980000 0.962264
|
||||
0.985000 0.985000 0.971292
|
||||
0.990000 0.990000 0.980583
|
||||
0.995000 0.995000 0.990148
|
||||
@@ -0,0 +1,180 @@
|
||||
<html>
|
||||
<title>Alignment</title>
|
||||
<style type="text/css">
|
||||
TABLE.ba { max-width: 678; text-align: center; padding-bottom: 15; padding-top: 5}
|
||||
TABLE.inline { padding-right: 300; clear: left}
|
||||
TD.text_table {padding-left: 2; padding-right: 2; border-width: 1}
|
||||
H2 {clear: left}
|
||||
P {max-width: none; padding-right: 300; clear: left}
|
||||
BLOCKQUOTE {padding-right: 400 }
|
||||
LI {max-width: 640; clear: left}
|
||||
P.footer {max-width: none; width: auto; padding-left: 0}
|
||||
P.header {max-width: none; width: auto; padding-left: 0}
|
||||
HR.main {max-width: 640; clear: left; padding-left: 0; margin-left: 0}
|
||||
HR.footer {clear: both}
|
||||
</style>
|
||||
|
||||
<body>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<table align=right valign=top width=160>
|
||||
<td valign=top height=600 width=160>
|
||||
<a href="http://auricle.dyndns.org/ALE/">
|
||||
<big>ALE</big>
|
||||
<br>
|
||||
Image Processing Software
|
||||
<br>
|
||||
<br>
|
||||
<small>Deblurring, Anti-aliasing, and Superresolution.</small></a>
|
||||
<br><br>
|
||||
<big>
|
||||
Local Operation
|
||||
</big>
|
||||
<hr>
|
||||
localhost<br>
|
||||
5393119533<br>
|
||||
</table>
|
||||
|
||||
|
||||
|
||||
|
||||
<p><b>[ <a href="../">Up</a> | <a href="error/">Error Function</a> ]</b></p>
|
||||
<h1>Alignment</h1>
|
||||
|
||||
<p>ALE aligns each supplemental frame, in sequence, with an <i>alignment
|
||||
reference image</i> constructed from previous frames. This page outlines
|
||||
supported transformation classes, the algorithm used for alignment, and the
|
||||
properties of the alignment algorithm. Following this is a discussion of
|
||||
practical use of alignment options, including alignment classes and alignment
|
||||
in the case of spatial extension.
|
||||
|
||||
<h2>Transformations</h2>
|
||||
|
||||
<p>ALE offers the following classes of transformations: </p>
|
||||
|
||||
<table border>
|
||||
<tr><td>Translations</td><td>introduced in version 0.0.0</td>
|
||||
<tr><td>Euclidean transformations (excluding reflections)</td><td>introduced in version 0.1.0</td>
|
||||
<tr><td>Projective transformations</td><td>introduced in version 0.2.0</td>
|
||||
<tr><td>Barrel distortion correction</td><td>introduced in version 0.7.0</td>
|
||||
</table>
|
||||
|
||||
<h2>Algorithm</h2>
|
||||
|
||||
<p>Alignment proceeds by a deterministic search, beginning with an initial
|
||||
transformation and modifying this transformation through a series of
|
||||
perturbations.
|
||||
|
||||
<p>The initial transformation may be loaded from a file (when
|
||||
<code>--trans-load</code> is used) or selected by default, or may be the
|
||||
result of a global search (when <code>--gs</code> is used [0.7.1 only]). The
|
||||
default initial transformation is either the transformation of the original
|
||||
frame (when the <code>--identity</code> option is specified) or the most
|
||||
recently aligned frame's final alignment (when the <code>--follow</code> option
|
||||
is specified). When the initial transformation is loaded from a file, and if
|
||||
the <code>--follow</code> option is specified, any changes to the alignment of
|
||||
the previous frame are applied to the current frame at the outset.
|
||||
|
||||
<p>Once the initial transformation is determined, an initial perturbation
|
||||
amount determines the step size by which each of the transformation parameters
|
||||
are changed. In translational or Euclidean alignment, the perturbation amount
|
||||
is applied to translation -- in units of pixels on the two image axes -- and
|
||||
rotation -- in units of degrees about the image center. An additional
|
||||
configurable upper bound, <code>--rot-upper</code>, constrains rotational
|
||||
perturbation separately, preventing, e.g., a 360 degree perturbation of
|
||||
rotation. In the case of projective alignment, the perturbation amount is
|
||||
applied to the position of the corners of the projected quadrilateral in units
|
||||
of pixels, where the projection is from the boundary of the supplemental frame
|
||||
into the coordinate system of the alignment reference image. In the case of barrel
|
||||
distortion correction, the perturbation amount is scaled by a multiplier
|
||||
(<code>--bda-mult</code>) before being applied to each barrel distortion
|
||||
coefficient (if any have been defined). The rate of change of barrel distortion
|
||||
coefficients per frame can be limited with the option <code>--bda-rate</code>.
|
||||
|
||||
<p>If possible, transformation parameters are changed to decrease the <a
|
||||
href="error/">error</a> between the supplemental frame and the alignment reference
|
||||
image. The perturbation amount is halved whenever it is determined that no
|
||||
parameter change of the current perturbation size improves the alignment of the
|
||||
images. A lower bound on the perturbation amount determines when the alignment
|
||||
is complete.
|
||||
|
||||
<!--
|
||||
|
||||
XXX: Even if this was true at one point, it appears to no longer be true.
|
||||
|
||||
<p>The order in which parameters are considered for change is specified in the
|
||||
source code, and has the following property: No modified parameter is
|
||||
considered for further change until all other parameters have been considered.
|
||||
A consequence of this property is that parameters are always considered in a
|
||||
fixed (round robin) order.
|
||||
-->
|
||||
|
||||
<p>When multiple levels of detail are used, the error may be calculated on
|
||||
images with a reduced level of detail. By default, this version of ALE uses a
|
||||
level of detail twice as fine as the perturbation amount for perturbation
|
||||
amounts larger than two, and full detail otherwise. This behavior can be changed
|
||||
by adjusting the <code>--lod-max</code> option.
|
||||
|
||||
<!--
|
||||
|
||||
Is this useful to anyone?
|
||||
|
||||
<h2>Use of Alignment Classes</h2>
|
||||
|
||||
<p>ALE is likely to be most useful when corresponding regions of different
|
||||
frames can be aligned by one of the available alignment classes.
|
||||
|
||||
<p>As described by Steve Mann in his work on <a
|
||||
href="http://wearcam.org/orbits/">Video Orbits</a>, the projective
|
||||
transformation offers particular versatility for camera imaging of (ideal
|
||||
Lambertian) flat scenes.
|
||||
|
||||
<p>In camera imaging of scenes with depth, correction for orientation is almost
|
||||
the same as for flat scenes, since, if focus and lens distortion is ignored, a
|
||||
scene with depth is indistinguishable from a flat scene from the perspective of
|
||||
a camera whose position is fixed.
|
||||
|
||||
<p>For sequences of camera images with small changes in position or
|
||||
orientation, the projective transformations for alignment may closely
|
||||
approximate Euclidean transformations; in this case, using Euclidean
|
||||
transformations may achieve similar results and may require less time for
|
||||
alignment, since there are fewer parameters to tweak (three parameters
|
||||
instead of eight).
|
||||
|
||||
<p>In the case of flatbed scanners that preserve the relative height and width
|
||||
of scans, any change in the position or orientation of flat objects can be
|
||||
corrected using the Euclidean alignment class.</p>
|
||||
|
||||
<p>If a flatbed scanner does not preserve relative height and width, but does
|
||||
preserve straight lines, then any change in the position or orientation of flat
|
||||
objects can be corrected with the projective alignment class.
|
||||
|
||||
<p>However, even if a transformation is within the alignment class used, the
|
||||
alignment algorithm may still be unable to approximate it.
|
||||
|
||||
<h2>Alignment in the case of Extended Renderings</h2>
|
||||
|
||||
<p>By using the --extend flag, ALE can be used to create image mosaics spanning
|
||||
a spatial region larger than that represented by any single image in the frame
|
||||
sequence. In these cases, if adjacent frames in the sequence tend to be more
|
||||
closely aligned with each other than they are with the original frame, it may
|
||||
be helpful to also use the --follow flag as a hint to the alignment algorithm.
|
||||
</p>
|
||||
|
||||
-->
|
||||
|
||||
|
||||
<br><br>
|
||||
<small>
|
||||
</small>
|
||||
|
||||
<hr>
|
||||
<i>Copyright 2002, 2003, 2004 <a href="mailto:dhilvert@auricle.dyndns.org">David Hilvert</a></i>
|
||||
<p>Verbatim copying and distribution of this entire article is permitted in any
|
||||
medium, provided this notice is preserved.
|
||||
</body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user