const MagickRealType c7 = -0.187208577776590710853865174371617338991e-11L;
const MagickRealType c8 = 0.253524321426864752676094495396308636823e-13L;
const MagickRealType c9 = -0.177084805010701112639035485248501049364e-15L;
- const MagickRealType p =
+ const MagickRealType p =
c0+xx*(c1+xx*(c2+xx*(c3+xx*(c4+xx*(c5+xx*(c6+xx*(c7+xx*(c8+xx*c9))))))));
return((xx-1.0)*(xx-4.0)*(xx-9.0)*(xx-16.0)*p);
#else
% Kaiser Lanczos
%
% Special purpose Filters
-% SincFast Lanczos2D
+% SincFast Lanczos2D Robidoux
%
% The users "-filter" selection is used to lookup the default 'expert'
% settings for that filter from a internal table. However any provided
% and rational (high Q) approximations, and will be used by default in
% most cases.
%
-% The Lanczos2D filter is often just a normal 2-lobed Lanczos
-% filter. If selected as a cylindrical (radial) filter, the support
-% of the 2-lobed Jinc windowed Jinc is modified (through the blur
-% property) in order to make the results sharper.
+% 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)
%
% 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 */
};
/*
Table mapping the filter/window from the above table to an actual
{ Quadratic, 1.5, 1.5, 0.0, 0.0 }, /* Quadratic gaussian */
{ CubicBC, 2.0, 2.0, 1.0, 0.0 }, /* Cubic B-Spline (B=1,C=0) */
{ CubicBC, 2.0, 1.0, 0.0, 0.5 }, /* Catmull-Rom (B=0,C=1/2) */
- { CubicBC, 2.0, 1.0, 1./3., 1./3. }, /* Mitchell (B=C=1/3) */
- { SincFast, 3.0, 1.0, 0.0, 0.0 }, /* Lanczos, 3-lobed sinc-sinc */
- { Jinc, 3.0, 1.21967, 0.0, 0.0 }, /* Raw 3-lobed Jinc */
+ { CubicBC, 2.0, 1.0, 1./3., 1./3. }, /* Mitchell (B=C=1/3) */
+ { SincFast, 3.0, 1.0, 0.0, 0.0 }, /* Lanczos, 3-lobed Sinc-Sinc */
+ { Jinc, 3.0, 1.21967, 0.0, 0.0 }, /* Raw 3-lobed Jinc */
{ Sinc, 4.0, 1.0, 0.0, 0.0 }, /* Raw 4-lobed Sinc */
{ Kaiser, 1.0, 1.0, 0.0, 0.0 }, /* Kaiser (square root window) */
{ Welsh, 1.0, 1.0, 0.0, 0.0 }, /* Welsh (parabolic window) */
{ Bohman, 1.0, 1.0, 0.0, 0.0 }, /* Bohman, 2*Cosine window */
{ 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, adjusted below */
+ { 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 */
};
/*
The known zero crossings of the Jinc() or more accurately the
}
if (option == LanczosFilter)
{ /* Lanczos is not a real filter but a self windowing Sinc/Jinc. */
- filter_type=cylindrical != MagickFalse ? JincFilter : Lanczos2DFilter;
+ filter_type=cylindrical != MagickFalse ? JincFilter : LanczosFilter;
window_type=cylindrical != MagickFalse ? JincFilter : SincFastFilter;
}
/* Filter override with a specific window function. */
resize_filter->blur *= MagickSQ2;
resize_filter->support = (MagickRealType) MagickSQ2; /* which times blur => 2.0 */
break;
- case Lanczos2DFilter:
- /* Special 2-lobed cylindrical Jinc-Jinc filter with a special
- * "blur" adjustment (actually, a "negative blur," since the
- * support is scaled to make it slightly smaller, with the
- * consequence that the results are slightly sharper).
- *
- * Used as default filter for EWA Resampling and Distorts.
- *
- * Executive summary:
- *
- * This is the closest a two-lobe Jinc-Jinc used radially
- * (with Clamped EWA) comes to preserving straight
- * vertical---and straight horizontal---features.
- *
- * Details:
+ 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
*
- * Basically, this is the standard
- *
- * 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) rescaled 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 is the
- * identity (a.k.a. "no-op").
- *
- * Specifically, it is Lanczos2D(s*x) with support r2/s, where
- * s is chosen so that
+ * 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 ).
*
- * 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---with no-op---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.
+ * 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:
switch (filter_type)
{
case Lanczos2DFilter:
- /* Demote to a 2-lobe Sinc-Sinc for orthogonal use. */
+ case RobidouxFilter:
+ /* Demote to a 2-lobe Lanczos (Sinc-Sinc) for orthogonal use. */
resize_filter->filter=SincFast;
break;
default:
projects / imagemagick / commitdiff