ALE
Image Processing Software
Deblurring, Anti-aliasing, and Superresolution.
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# ALE Certainty

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.

## Motivation

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.

## Related Work

Steve Mann's original approach to certainty is described in his comparametric paper. 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).

## Two-sided Certainty

Two-sided certainty operator κ is used by ALE's incremental renderer, and applies a parameterized heuristic function:

> κd(i, j) = max(0.001, [1 - 4 * (0.5 - d(i, j))2]k)

Where all operations are applied componentwise, and k is the certainty exponent parameter.

## Symmetrically One-sided Certainty

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 c(i, j) against a modeled pixel value m(i, j). The following expression assumes the range of m to be [0, 1], and expresses condition using the C trinary if-else operator:

> Κ(c, m, i, j) = [c(i, j) * (m(i, j) - 0.5) > 0] ? 1 : κd(i, j)

Where all operations are applied componentwise, and κ is the operator for two-sided certainty.

## Asymmetrically one-sided certainty

Asymmetrically one-sided certainty applies the one-sided condition asymmetrically.

> Κ'(c, m, i, j) = [c(i, j) > 0 && (m(i, j) - 0.5) > 0] ? 1 : κd(i, j)

## Estimate-based Certainty

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.

Copyright 2002, 2003, 2004 David Hilvert

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