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more lbb resampler comments

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Nicolas Robidoux 2010-03-23 23:41:58 +00:00
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libvips/resample/lbb.cpp
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@ -55,45 +55,44 @@
/*
* LBB is a novel method with the following properties:
*
* --When the limiters are inactive, it gives the same results as
* Catmull-Rom.
*
* --When used on binary images, in which case the limiters clamp
* everything to zero, LBB gives the same results as bicubic Hermite
* with all derivatives at the input pixel locations set to zero.
*
* --It is interpolatory.
*
* --It is a Hermite bicubic method: The bicubic surface is defined,
* one convex hull of four nearby input points at a time, using
* four point values, four x-derivatives, four y-derivatives, and four
* --LBB is a Hermite bicubic method: The bicubic surface is defined,
* one convex hull of four nearby input points at a time, using four
* point values, four x-derivatives, four y-derivatives, and four
* cross-derivatives.
*
* --The stencil for values in a square patch is the usual 4x4.
*
* --LBB is interpolatory.
*
* --It is C^1 with continuous cross derivatives.
*
* --It is locally bounded, in the following sense: Over each square
* --When the limiters are inactive, LBB gives the same results as
* Catmull-Rom.
*
* --When used on binary images, LBB gives the same results as bicubic
* Hermite with all derivatives at the input pixel locations set to
* zero.
*
* --The LBB reconstruction is locally bounded: Over each square
* patch, the surface is contained between the minimum and the
* maximum values among the 16 nearest input pixel values (those in
* the stencil).
*
* --It is globally bounded between the very smallest input pixel
* value and the very largest input pixel value. Consequently, it is
* not necessary to clamp results.
* --Consequently, the LBB reconstruction is globally bounded between
* the very smallest input pixel value and the very largest input
* pixel value. (It is not necessary to clamp results.)
*
* --The LBB method is based on the method of Ken Brodlie, Petros
* Mashwama and Sohail Butt for constraining Hermite interpolants
* between globally defined planes:
* The LBB method is based on the method of Ken Brodlie, Petros
* Mashwama and Sohail Butt for constraining Hermite interpolants
* between globally defined planes:
*
* Visualization of surface data to preserve positivity and other
* simple constraints. Computer & Graphics, Vol. 19, Number 4,
* pages 585-594, 1995. DOI: 10.1016/0097-8493(95)00036-C.
* Visualization of surface data to preserve positivity and other
* simple constraints. Computer & Graphics, Vol. 19, Number 4, pages
* 585-594, 1995. DOI: 10.1016/0097-8493(95)00036-C.
*
* The main novelty of the LBB method (besides its reliance on slope
* limiters in the context of image resampling) lies in the fact
* that the method of Brodlie et al is modified so as to enforce
* local, as opposed to global, boundedness.
* Instead of forcing the reconstructed surface to lie between two
* GLOBALLY defined planes, LBB constrains one patch at a time to lie
* between the local min and max.
*/
#ifdef HAVE_CONFIG_H