% most cases.
%
% The Lanczos2D filter is just 2-lobed Lanczos using Sinc/Jinc as
-% appropriate. The Robidoux is the same thing but is modified (through
-% the blur setting) in order to make the results sharper in the 'no-op' case.
-% (see notes below)
+% appropriate. The Robidoux used to be a slightly sharpened version
+% of this, but is now the equivelent Cubic 'Keys' filter very similar to
+% "Mitchell". Remember these are designed specifically for use as
+% cylindrical (radial) EWA Distortion filters, to be less blurry in the
+% 'no-op' situation.
%
% Special 'expert' options can be used to override any and all filter
% settings. This is not advised unless you have expert knowledge of
{ SincFastFilter, TriangleFilter }, /* Bartlett -- triangle-sinc */
{ SincFastFilter, BoxFilter }, /* Raw fast sinc ("Pade"-type) */
{ Lanczos2DFilter, JincFilter }, /* SPECIAL: 2-lobed jinc-jinc */
- { RobidouxFilter, JincFilter }, /* SPECIAL: Lanzcos2D blurred */
+ { RobidouxFilter, BoxFilter }, /* SPECIAL: cubic jinc-jinc equiv. */
};
/*
Table mapping the filter/window from the above table to an actual
{ Triangle, 1.0, 1.0, 0.0, 0.0 }, /* Bartlett (triangle window) */
{ SincFast, 4.0, 1.0, 0.0, 0.0 }, /* Raw fast sinc ("Pade"-type) */
{ Jinc, 2.0, 1.0, 0.0, 0.0 }, /* Lanczos2D, Jinc-Jinc */
- { Jinc, 2.0, 1.0, 0.0, 0.0 }, /* Robidoux, blured Jinc-Jinc */
+ /* Robidoux, A Cubic 'Keys' equiv of a Lanczos2D with a blur=0.958033808 */
+ { CubicBC, 2.0, 1.0, 0.37821575509399862, 0.31089212245300069 }
};
/*
The known zero crossings of the Jinc() or more accurately the
switch (filter_type)
{
case Lanczos2DFilter:
- case RobidouxFilter:
/* Demote to a 2-lobe Sinc-Sinc for orthogonal use. */
window_type=SincFastFilter;
break;
resize_filter->blur *= MagickSQ2;
resize_filter->support = (MagickRealType) MagickSQ2; /* which times blur => 2.0 */
break;
- case RobidouxFilter:
- /* Special 2-lobed cylindrical Jinc-Jinc filter created by Nicolas
- * Robidoux, Professor of Mathematics, Laurentian University.
- *
- * It is a "blur" (negative blur actually) adjusted 2-lobed
- * Jinc-windowed-Jinc Cylindrical (radial) filter, designed to
- * preserve straight vertical and horizontal features.
- *
- * Given the "Lanczos2D" filter defined by Andreas Gustafsson in his
- * "Interactive Image Warping" (page 24)
- * http://www.gson.org/thesis/warping-thesis.pdf
- *
- * Lanczos2D(x) = Jinc(x)*Jinc(x*r1/r2) with support r2
- *
- * (where r1 is the first root of the Jinc function, and r2 is the
- * second), rescale the filter by a value 's'.
- *
- * Robidoux(x) = Lanczos2D(s*x) with support r2/s
- *
- * the value 's' is chossen so that images which are constant in the
- * vertical direction, and images which are constant in the horizontal
- * direction, are almost unchanged (the change being generically as
- * small as possible) when the geometrical transformation applied to
- * the image is the identity (a.k.a. "no-op" or no scaling ).
- *
- * As such this formula needs to hold true
- *
- * Lanczos2D(s)=-2*Lanczos2D(s*sqrt(2))-Lanczos2D(s*2).
- *
- * This value of s ensures that the value of a one-pixel-wide vertical
- * line (equal to 1, say, on a black=0 background) is exactly
- * preserved when no-op is applied to the image. It also ensures
- * that, in the no-op case, the nearest two columns on either side are
- * minimally changed (the farther columns are unchanged no matter
- * what). Specifically, the nearest columns on the left and the right
- * have values raised from zero to c, and the second closest columns
- * on the left and right are lowered from 0 to minus c. That is, the
- * very closest columns are made slightly positive, and the second
- * closest are made slightly negative, in equal amounts. The size c
- * of this blur/halo is .002042317. Consequently, image values
- * between 0 and M which are constant on columns (or rows) are
- * preserved by no-op to within 2Mc (less than one half of one percent
- * of the dynamic range).
- *
- * Note that "high frequency modes" which are not aligned with image
- * rows or columns are damped considerably. For example, the amplitude
- * of the very highest energy mode, the so-called "checkerboard" mode,
- * is reduced by almost 62% (still less than with "standard" Lanczos2D
- * or with a comparable Gaussian kernel).
- *
- * This "optimal" scaling was discovered by Nicolas Robidoux of
- * Laurentian University.
- *
- * Below, resize_filter->blur is 1/s.
- */
- resize_filter->blur *= (MagickRealType) 0.958033808;
default:
break;
}
switch (filter_type)
{
case Lanczos2DFilter:
- case RobidouxFilter:
/* Demote to a 2-lobe Lanczos (Sinc-Sinc) for orthogonal use. */
resize_filter->filter=SincFast;
break;
return(scale_image);
}
\f
+#if 0
+ THIS IS NOT USED -- to be removed
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
assert(resize_filter->signature == MagickSignature);
resize_filter->support=support;
}
+#endif
\f
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
projects / imagemagick / commitdiff