123 lines
4.0 KiB
HTML
123 lines
4.0 KiB
HTML
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<title>ALE Certainty</title>
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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/">
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<big>ALE</big>
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<br>
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Image Processing Software
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<br>
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<br>
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<small>Deblurring, Anti-aliasing, and Superresolution.</small></a>
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<br><br>
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<big>
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Local Operation
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</big>
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<hr>
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localhost<br>
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5393119533<br>
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</table>
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<p><b>[ <a href="../">Up</a> ]</b></p>
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<h1>ALE Certainty</h1>
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<p>When used with a sequence of differently-exposed images, the certainty
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techniques implemented in ALE may produce output having higher fidelity overall
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than that of any single exposure.
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<h2>Motivation</h2>
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<p>When multiple, differently-exposed images of the same scene are available,
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variations of intensity visible in one image might not be visible in another.
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In particular, if the difference between maximal light and dark values in the
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scene exceeds the range of the image capture apparatus, then no single exposure
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can faithfully record the scene. Using multiple exposures allows discernment
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of at least as many details as any single exposure in the set can provide, and
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may allow discernment of more details, and better estimates of intensities.
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<h2>Related Work</h2>
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<p>Steve Mann's original approach to certainty is described in his <a
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href="http://wearcam.org/comparam.htm">comparametric paper</a>. ALE extends
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his approach to Irani-Peleg rendering by defining certainty for (intensity,
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correction) pairs (in versions 0.7.x) and by basing certainty on estimated
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intensities (in version 0.8.0).
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<h2>Two-sided Certainty</h2>
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<p>Two-sided certainty operator <b>κ</b> is used by ALE's incremental
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renderer, and applies a parameterized heuristic function:
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<blockquote>
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<b>κd(i, j) = max(0.001, [1 - 4 * (0.5 - d(i, j))<sup>2</sup>]<sup>k</sup>)</b>
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</blockquote>
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Where all operations are applied componentwise, and <b>k</b> is the certainty
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exponent parameter.
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<h2>Symmetrically One-sided Certainty</h2>
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<p>Symmetrically one-sided certainty is used by ALE's Irani-Peleg renderer in
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versions 0.7.x, and is calculated using the direction of bias of a correction
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<b>c(i, j)</b> against a modeled pixel value <b>m(i, j)</b>. The following
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expression assumes the range of <b>m</b> to be <b>[0, 1]</b>, and expresses
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condition using the C trinary if-else operator:
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<blockquote>
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<b>Κ(c, m, i, j) = [c(i, j) * (m(i, j) - 0.5) > 0] ? 1 : κd(i, j)</b>
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</blockquote>
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<P>Where all operations are applied componentwise, and <b>κ</b> is the
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operator for two-sided certainty.</p>
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<h2>Asymmetrically one-sided certainty</h2>
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Asymmetrically one-sided certainty applies the one-sided condition asymmetrically.
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<blockquote>
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<b>Κ'(c, m, i, j) = [c(i, j) > 0 && (m(i, j) - 0.5) > 0] ? 1 : κd(i, j)</b>
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</blockquote>
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<h2>Estimate-based Certainty</h2>
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<p>Estimate-based certainty uses an estimate of intensity, rather than measured
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intensity, to determine certainty, and can be used in a one-sided or two-sided
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way. ALE version 0.8.0 uses estimate-based asymmetrically one-sided certainty
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to weight Irani-Peleg correction values.</p>
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<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 medium, provided this notice is preserved.
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