In photography the
dynamic range is the ratio between the maximum and the minimum light intensity measurable by the camera film or the camera digital sensors. Basically we live in a
High Dynamic Range world but our cameras can capture only a part of it. In 2004
Paul Debevec presented an algorithm to recover the HDR radiance map of a scene from a set of images taken at different exposures. The pixel values of the HDR radiance map are proportional to the real world radiance values and, once remapped to RBG values through some
tone-mapping technique, they represent the image more accurately.
Algorithm Overview
The pixel values of an image are the result of a non linear function
f(X) where
X is the exposure. This function is a composition of the characteristic curve (the response to the variations in exposure) of the film or, for digital images, of the digital sensors, and of others non linearities introduced by the next processing steps. The problems is that camera sensors record only a low dynamic range of light intensities while the real scenes are made of a much wider range.
Debevec solves this problem reconstructing the radiance map from a set of images representing the same scene but recorded at different exposure levels. The algorithm can be splitted into the following steps:
1. Recovering the camera response curve g(Z).
The response curve is recovered solving an over-constrained linear system of equations
[(g(Z) - lnE - lnDT)], where
g(Z) is the logarithm of the exposure corresponding to the pixel value
Z,
lnE is the logarithm of the irradiance and
lnDT is the logarithm of the exposure time (shutter speed). Once built, the over-constrained linear system is solved in a least square sense.
In green, interest points etained by the ANMS algorithm.
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2. Reconstructing the HDR radiance map.
Through the camera response function it is possible to construct the HDR radiance map. This is equal to the exponential of the weighted average of the radiance maps of the images taken at different exposures.
In green, interest points etained by the ANMS algorithm.
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2. Tonemapping.
The image in High Dynamic Range must be re-mapped to a lower dynamic range to be displayed correctly on a monitor. I used the
Reinhard Global Tonemapper Operator defined as Ld =
L / (L + 1), where L is a scaled luminance value. Here is the final result:
In green, interest points etained by the ANMS algorithm.
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