It was originally developed by Greg Ward for storing HDR-output of his Radiance-photonmapper at a time where storage space was a crucial factor.
Logluv TIFF's design solves two specific problems: storing high-dynamic image data and doing so within a reasonable amount of space.
Instead of using RGB, LogLuv uses the logarithm of the luminance and the CIELUV (u’, v’) chromaticity coordinates in order to provide a perceptually uniform color space.
LogLuv allocates 8 bits for each of the u’ and v’ coordinates, which allows encoding the full visible gamut with imperceptible step sizes.
In an attempt to prevent the expansion of data-size, Logluv comes in a 24-bit flavour, which in a rather complicated way quantizes lightness to 10 bit and merges U/V into a 14-bit look-up based value.