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<title>ALE Certainty</title>
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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>ALE Certainty</h1>
<p>When used with a sequence of differently-exposed images, the certainty
techniques implemented in ALE may produce output having higher fidelity overall
than that of any single exposure.
<h2>Motivation</h2>
<p>When multiple, differently-exposed images of the same scene are available,
variations of intensity visible in one image might not be visible in another.
In particular, if the difference between maximal light and dark values in the
scene exceeds the range of the image capture apparatus, then no single exposure
can faithfully record the scene. Using multiple exposures allows discernment
of at least as many details as any single exposure in the set can provide, and
may allow discernment of more details, and better estimates of intensities.
<h2>Related Work</h2>
<p>Steve Mann's original approach to certainty is described in his <a
href="http://wearcam.org/comparam.htm">comparametric paper</a>. ALE extends
his approach to Irani-Peleg rendering by defining certainty for (intensity,
correction) pairs (in versions 0.7.x) and by basing certainty on estimated
intensities (in version 0.8.0).
<h2>Two-sided Certainty</h2>
<p>Two-sided certainty operator <b>&kappa;</b> is used by ALE's incremental
renderer, and applies a parameterized heuristic function:
<blockquote>
<b>&kappa;d(i, j) = max(0.001, [1 - 4 * (0.5 - d(i, j))<sup>2</sup>]<sup>k</sup>)</b>
</blockquote>
Where all operations are applied componentwise, and <b>k</b> is the certainty
exponent parameter.
<h2>Symmetrically One-sided Certainty</h2>
<p>Symmetrically one-sided certainty is used by ALE's Irani-Peleg renderer in
versions 0.7.x, and is calculated using the direction of bias of a correction
<b>c(i, j)</b> against a modeled pixel value <b>m(i, j)</b>. The following
expression assumes the range of <b>m</b> to be <b>[0, 1]</b>, and expresses
condition using the C trinary if-else operator:
<blockquote>
<b>&Kappa;(c, m, i, j) = [c(i, j) * (m(i, j) - 0.5) > 0] ? 1 : &kappa;d(i, j)</b>
</blockquote>
<P>Where all operations are applied componentwise, and <b>&kappa;</b> is the
operator for two-sided certainty.</p>
<h2>Asymmetrically one-sided certainty</h2>
Asymmetrically one-sided certainty applies the one-sided condition asymmetrically.
<blockquote>
<b>&Kappa;'(c, m, i, j) = [c(i, j) > 0 && (m(i, j) - 0.5) > 0] ? 1 : &kappa;d(i, j)</b>
</blockquote>
<h2>Estimate-based Certainty</h2>
<p>Estimate-based certainty uses an estimate of intensity, rather than measured
intensity, to determine certainty, and can be used in a one-sided or two-sided
way. ALE version 0.8.0 uses estimate-based asymmetrically one-sided certainty
to weight Irani-Peleg correction values.</p>
<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.
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