Gecko [ nrupathungauniversityblr.ac.in ]

Name	Size	Permission
.deps	[ DIR ]	drwxrwxr-x
.libs	[ DIR ]	drwxrwxr-x
.dirstamp	0 B	-rw-rw-r--
ImageMagick-7.Q16HDRI.pc	867 B	-rw-rw-r--
ImageMagick.pc	867 B	-rw-rw-r--
ImageMagick.pc.in	575 B	-rw-rw-r--
MagickCore-7.Q16HDRI.pc	916 B	-rw-rw-r--
MagickCore-config	1.5 KB	-rwxrwxr-x
MagickCore-config.1	1.85 KB	-rw-rw-r--
MagickCore-config.in	1.57 KB	-rw-rw-r--
MagickCore.h	4.94 KB	-rw-rw-r--
MagickCore.pc	916 B	-rw-rw-r--
MagickCore.pc.in	688 B	-rw-rw-r--
Makefile.am	14.76 KB	-rw-rw-r--
accelerate-kernels-private.h	102.16 KB	-rw-rw-r--
accelerate-private.h	2.63 KB	-rw-rw-r--
accelerate.c	169.72 KB	-rw-rw-r--
animate-private.h	1.23 KB	-rw-rw-r--
animate.c	103.29 KB	-rw-rw-r--
animate.h	979 B	-rw-rw-r--
annotate-private.h	1022 B	-rw-rw-r--
annotate.c	71.69 KB	-rw-rw-r--
annotate.h	1.26 KB	-rw-rw-r--
artifact.c	18.74 KB	-rw-rw-r--
artifact.h	1.35 KB	-rw-rw-r--
attribute.c	69.33 KB	-rw-rw-r--
attribute.h	1.78 KB	-rw-rw-r--
blob-private.h	4.07 KB	-rw-rw-r--
blob.c	207.68 KB	-rw-rw-r--
blob.h	3.29 KB	-rw-rw-r--
cache-private.h	6.63 KB	-rw-rw-r--
cache-view.c	44.83 KB	-rw-rw-r--
cache-view.h	3.63 KB	-rw-rw-r--
cache.c	211.11 KB	-rw-rw-r--
cache.h	2.5 KB	-rw-rw-r--
channel.c	41.69 KB	-rw-rw-r--
channel.h	1.28 KB	-rw-rw-r--
cipher.c	40.58 KB	-rw-rw-r--
cipher.h	1.11 KB	-rw-rw-r--
client.c	7.37 KB	-rw-rw-r--
client.h	1.03 KB	-rw-rw-r--
coder-private.h	1005 B	-rw-rw-r--
coder.c	20.03 KB	-rw-rw-r--
coder.h	1.28 KB	-rw-rw-r--
color-private.h	2.28 KB	-rw-rw-r--
color.c	105.5 KB	-rw-rw-r--
color.h	2.22 KB	-rw-rw-r--
colormap-private.h	1.8 KB	-rw-rw-r--
colormap.c	13.3 KB	-rw-rw-r--
colormap.h	1.05 KB	-rw-rw-r--
colorspace-private.h	4.23 KB	-rw-rw-r--
colorspace.c	99.03 KB	-rw-rw-r--
colorspace.h	2.35 KB	-rw-rw-r--
compare.c	72.32 KB	-rw-rw-r--
compare.h	1.86 KB	-rw-rw-r--
composite-private.h	5.5 KB	-rw-rw-r--
composite.c	81.18 KB	-rw-rw-r--
composite.h	2.85 KB	-rw-rw-r--
compress.c	39.93 KB	-rw-rw-r--
compress.h	2.15 KB	-rw-rw-r--
configure-private.h	1019 B	-rw-rw-r--
configure.c	44.68 KB	-rw-rw-r--
configure.h	1.65 KB	-rw-rw-r--
constitute-private.h	890 B	-rw-rw-r--
constitute.c	50.54 KB	-rw-rw-r--
constitute.h	1.45 KB	-rw-rw-r--
decorate.c	31.1 KB	-rw-rw-r--
decorate.h	1.34 KB	-rw-rw-r--
delegate-private.h	2.16 KB	-rw-rw-r--
delegate.c	83.77 KB	-rw-rw-r--
delegate.h	1.98 KB	-rw-rw-r--
deprecate.c	13.45 KB	-rw-rw-r--
deprecate.h	1.21 KB	-rw-rw-r--
display-private.h	1.24 KB	-rw-rw-r--
display.c	515.56 KB	-rw-rw-r--
display.h	1.05 KB	-rw-rw-r--
distort.c	134.29 KB	-rw-rw-r--
distort.h	2.65 KB	-rw-rw-r--
distribute-cache-private.h	2.24 KB	-rw-rw-r--
distribute-cache.c	49.1 KB	-rw-rw-r--
distribute-cache.h	997 B	-rw-rw-r--
draw-private.h	2.1 KB	-rw-rw-r--
draw.c	245.29 KB	-rw-rw-r--
draw.h	5.55 KB	-rw-rw-r--
effect.c	125.86 KB	-rw-rw-r--
effect.h	2.85 KB	-rw-rw-r--
enhance.c	137.51 KB	-rw-rw-r--
enhance.h	2.32 KB	-rw-rw-r--
exception-private.h	3.18 KB	-rw-rw-r--
exception.c	44.49 KB	-rw-rw-r--
exception.h	4.35 KB	-rw-rw-r--
feature.c	83.79 KB	-rw-rw-r--
feature.h	1.7 KB	-rw-rw-r--
fourier.c	49.36 KB	-rw-rw-r--
fourier.h	1.38 KB	-rw-rw-r--
fx-private.h	1.21 KB	-rw-rw-r--
fx.c	87.87 KB	-rw-rw-r--
fx.h	956 B	-rw-rw-r--
gem-private.h	6.28 KB	-rw-rw-r--
gem.c	53.31 KB	-rw-rw-r--
gem.h	1.15 KB	-rw-rw-r--
geometry.c	55.44 KB	-rw-rw-r--
geometry.h	3.98 KB	-rw-rw-r--
histogram.c	39.72 KB	-rw-rw-r--
histogram.h	1.35 KB	-rw-rw-r--
identify.c	57.07 KB	-rw-rw-r--
identify.h	971 B	-rw-rw-r--
image-private.h	2.89 KB	-rw-rw-r--
image-view.c	42.98 KB	-rw-rw-r--
image-view.h	2.72 KB	-rw-rw-r--
image.c	142.86 KB	-rw-rw-r--
image.h	13.87 KB	-rw-rw-r--
layer.c	75.49 KB	-rw-rw-r--
layer.h	2 KB	-rw-rw-r--
libMagickCore-7.Q16HDRI.la	1.32 KB	-rw-rw-r--
libMagickCore.map	46 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-acc...	374 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-acc...	6.25 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ani...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ani...	245.7 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ann...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ann...	225.34 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-art...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-art...	57.34 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-att...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-att...	198.58 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-blo...	356 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-blo...	559.89 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cac...	374 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cac...	130.77 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cac...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cac...	575.03 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cha...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cha...	132.27 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cip...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cip...	99.63 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cli...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cli...	11.99 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cod...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-cod...	48.66 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-col...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-col...	187.05 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-col...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-col...	64.29 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-col...	374 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-col...	416.23 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-com...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-com...	244.2 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-com...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-com...	205.62 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-com...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-com...	116.91 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-con...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-con...	92.49 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-con...	374 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-con...	134.21 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dec...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dec...	140.39 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-del...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-del...	181.88 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dep...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dep...	40.1 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dis...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dis...	1001.06 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dis...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dis...	257.94 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dis...	392 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dis...	138.98 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dra...	356 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-dra...	629.21 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-eff...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-eff...	359.09 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-enh...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-enh...	435.72 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-exc...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-exc...	79.98 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-fea...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-fea...	231.75 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-fou...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-fou...	147.25 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-fx....	350 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-fx....	285.02 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-gem...	353 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-gem...	222.46 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-geo...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-geo...	111.41 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-his...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-his...	103.51 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ide...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ide...	183.14 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ima...	374 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ima...	103.35 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ima...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ima...	311.29 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-lay...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-lay...	140.62 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-lin...	377 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-lin...	41.23 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-lis...	356 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-lis...	137.44 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-loc...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-loc...	93.1 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-log...	353 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-log...	109.05 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mag...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mag...	54.52 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mag...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mag...	123.44 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mat...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mat...	90.06 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mem...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mem...	64.4 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mim...	356 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mim...	69.73 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mod...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mod...	46.27 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mon...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mon...	37.7 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mon...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mon...	102.55 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mor...	374 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-mor...	249.84 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ope...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ope...	14.32 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-opt...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-opt...	238.09 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pai...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pai...	158.05 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pix...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pix...	1.12 MB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pol...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pol...	84.46 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pre...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pre...	50.55 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pro...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pro...	178.05 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pro...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-pro...	375.58 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	308.11 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	386 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	886.72 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	386 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	690.47 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-qua...	93.22 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ran...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ran...	71.95 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-reg...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-reg...	58.8 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-res...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-res...	101.68 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-res...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-res...	484.14 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-res...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-res...	130.89 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-seg...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-seg...	137.09 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sem...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sem...	27.5 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-she...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-she...	209.97 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sig...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sig...	77.59 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-spl...	374 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-spl...	71.54 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sta...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sta...	42.69 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sta...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-sta...	361.96 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-str...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-str...	389.89 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-str...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-str...	145.78 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-thr...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-thr...	9.66 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-thr...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-thr...	223.15 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-tim...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-tim...	38.76 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-tok...	359 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-tok...	220.66 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-tra...	371 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-tra...	228.2 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-typ...	356 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-typ...	88.52 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-uti...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-uti...	121.42 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ver...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-ver...	27.84 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-vis...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-vis...	161.29 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-vis...	386 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-vis...	490.88 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-wid...	362 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-wid...	450.54 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-xml...	368 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-xml...	166.75 KB	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-xwi...	365 B	-rw-rw-r--
libMagickCore_7_Q16HDRI_la-xwi...	641.91 KB	-rw-rw-r--
linked-list.c	33.55 KB	-rw-rw-r--
linked-list.h	1.92 KB	-rw-rw-r--
list.c	52.79 KB	-rw-rw-r--
list.h	2.3 KB	-rw-rw-r--
locale-private.h	1.35 KB	-rw-rw-r--
locale.c	58.89 KB	-rw-rw-r--
locale_.h	2.2 KB	-rw-rw-r--
log-private.h	1 KB	-rw-rw-r--
log.c	56.53 KB	-rw-rw-r--
log.h	2.73 KB	-rw-rw-r--
magic-private.h	999 B	-rw-rw-r--
magic.c	27.52 KB	-rw-rw-r--
magic.h	1.32 KB	-rw-rw-r--
magick-baseconfig.h	44.5 KB	-rw-rw-r--
magick-config.h	8.75 KB	-rw-rw-r--
magick-private.h	1.04 KB	-rw-rw-r--
magick-type.h	5.78 KB	-rw-rw-r--
magick.c	66.91 KB	-rw-rw-r--
magick.h	4.18 KB	-rw-rw-r--
matrix-private.h	1.1 KB	-rw-rw-r--
matrix.c	38.14 KB	-rw-rw-r--
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montage.c	32.5 KB	-rw-rw-r--
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morphology-private.h	1.17 KB	-rw-rw-r--
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Code Editor : morphology.c

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%    M   M    OOO    RRRR   PPPP   H   H   OOO   L       OOO    GGGG  Y   Y   %
%    MM MM   O   O   R   R  P   P  H   H  O   O  L      O   O  G       Y Y    %
%    M M M   O   O   RRRR   PPPP   HHHHH  O   O  L      O   O  G GGG    Y     %
%    M   M   O   O   R R    P      H   H  O   O  L      O   O  G   G    Y     %
%    M   M    OOO    R  R   P      H   H   OOO   LLLLL   OOO    GGG     Y     %
%                                                                             %
%                                                                             %
%                        MagickCore Morphology Methods                        %
%                                                                             %
%                              Software Design                                %
%                              Anthony Thyssen                                %
%                               January 2010                                  %
%                                                                             %
%                                                                             %
%  Copyright 1999-2020 ImageMagick Studio LLC, a non-profit organization      %
%  dedicated to making software imaging solutions freely available.           %
%                                                                             %
%  You may not use this file except in compliance with the License.  You may  %
%  obtain a copy of the License at                                            %
%                                                                             %
%    https://imagemagick.org/script/license.php                               %
%                                                                             %
%  Unless required by applicable law or agreed to in writing, software        %
%  distributed under the License is distributed on an "AS IS" BASIS,          %
%  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   %
%  See the License for the specific language governing permissions and        %
%  limitations under the License.                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Morphology is the application of various kernels, of any size or shape, to an
% image in various ways (typically binary, but not always).
%
% Convolution (weighted sum or average) is just one specific type of
% morphology. Just one that is very common for image bluring and sharpening
% effects.  Not only 2D Gaussian blurring, but also 2-pass 1D Blurring.
%
% This module provides not only a general morphology function, and the ability
% to apply more advanced or iterative morphologies, but also functions for the
% generation of many different types of kernel arrays from user supplied
% arguments. Prehaps even the generation of a kernel from a small image.
*/

/*
  Include declarations.
*/
#include "MagickCore/studio.h"
#include "MagickCore/artifact.h"
#include "MagickCore/cache-view.h"
#include "MagickCore/channel.h"
#include "MagickCore/color-private.h"
#include "MagickCore/enhance.h"
#include "MagickCore/exception.h"
#include "MagickCore/exception-private.h"
#include "MagickCore/gem.h"
#include "MagickCore/gem-private.h"
#include "MagickCore/image.h"
#include "MagickCore/image-private.h"
#include "MagickCore/linked-list.h"
#include "MagickCore/list.h"
#include "MagickCore/magick.h"
#include "MagickCore/memory_.h"
#include "MagickCore/memory-private.h"
#include "MagickCore/monitor-private.h"
#include "MagickCore/morphology.h"
#include "MagickCore/morphology-private.h"
#include "MagickCore/option.h"
#include "MagickCore/pixel-accessor.h"
#include "MagickCore/pixel-private.h"
#include "MagickCore/prepress.h"
#include "MagickCore/quantize.h"
#include "MagickCore/resource_.h"
#include "MagickCore/registry.h"
#include "MagickCore/semaphore.h"
#include "MagickCore/splay-tree.h"
#include "MagickCore/statistic.h"
#include "MagickCore/string_.h"
#include "MagickCore/string-private.h"
#include "MagickCore/thread-private.h"
#include "MagickCore/token.h"
#include "MagickCore/utility.h"
#include "MagickCore/utility-private.h"

/*
  Other global definitions used by module.
*/
#define Minimize(assign,value) assign=MagickMin(assign,value)
#define Maximize(assign,value) assign=MagickMax(assign,value)

/* Integer Factorial Function - for a Binomial kernel */
#if 1
static inline size_t fact(size_t n)
{
  size_t f,l;
  for(f=1, l=2; l <= n; f=f*l, l++);
  return(f);
}
#elif 1 /* glibc floating point alternatives */
#define fact(n) ((size_t)tgamma((double)n+1))
#else
#define fact(n) ((size_t)lgamma((double)n+1))
#endif

/* Currently these are only internal to this module */
static void
  CalcKernelMetaData(KernelInfo *),
  ExpandMirrorKernelInfo(KernelInfo *),
  ExpandRotateKernelInfo(KernelInfo *, const double),
  RotateKernelInfo(KernelInfo *, double);

/* Quick function to find last kernel in a kernel list */
static inline KernelInfo *LastKernelInfo(KernelInfo *kernel)
{
  while (kernel->next != (KernelInfo *) NULL)
    kernel=kernel->next;
  return(kernel);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     A c q u i r e K e r n e l I n f o                                       %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  AcquireKernelInfo() takes the given string (generally supplied by the
%  user) and converts it into a Morphology/Convolution Kernel.  This allows
%  users to specify a kernel from a number of pre-defined kernels, or to fully
%  specify their own kernel for a specific Convolution or Morphology
%  Operation.
%
%  The kernel so generated can be any rectangular array of floating point
%  values (doubles) with the 'control point' or 'pixel being affected'
%  anywhere within that array of values.
%
%  Previously IM was restricted to a square of odd size using the exact
%  center as origin, this is no longer the case, and any rectangular kernel
%  with any value being declared the origin. This in turn allows the use of
%  highly asymmetrical kernels.
%
%  The floating point values in the kernel can also include a special value
%  known as 'nan' or 'not a number' to indicate that this value is not part
%  of the kernel array. This allows you to shaped the kernel within its
%  rectangular area. That is 'nan' values provide a 'mask' for the kernel
%  shape.  However at least one non-nan value must be provided for correct
%  working of a kernel.
%
%  The returned kernel should be freed using the DestroyKernelInfo() when you
%  are finished with it.  Do not free this memory yourself.
%
%  Input kernel defintion strings can consist of any of three types.
%
%    "name:args[[@><]"
%         Select from one of the built in kernels, using the name and
%         geometry arguments supplied.  See AcquireKernelBuiltIn()
%
%    "WxH[+X+Y][@><]:num, num, num ..."
%         a kernel of size W by H, with W*H floating point numbers following.
%         the 'center' can be optionally be defined at +X+Y (such that +0+0
%         is top left corner). If not defined the pixel in the center, for
%         odd sizes, or to the immediate top or left of center for even sizes
%         is automatically selected.
%
%    "num, num, num, num, ..."
%         list of floating point numbers defining an 'old style' odd sized
%         square kernel.  At least 9 values should be provided for a 3x3
%         square kernel, 25 for a 5x5 square kernel, 49 for 7x7, etc.
%         Values can be space or comma separated.  This is not recommended.
%
%  You can define a 'list of kernels' which can be used by some morphology
%  operators A list is defined as a semi-colon separated list kernels.
%
%     " kernel ; kernel ; kernel ; "
%
%  Any extra ';' characters, at start, end or between kernel defintions are
%  simply ignored.
%
%  The special flags will expand a single kernel, into a list of rotated
%  kernels. A '@' flag will expand a 3x3 kernel into a list of 45-degree
%  cyclic rotations, while a '>' will generate a list of 90-degree rotations.
%  The '<' also exands using 90-degree rotates, but giving a 180-degree
%  reflected kernel before the +/- 90-degree rotations, which can be important
%  for Thinning operations.
%
%  Note that 'name' kernels will start with an alphabetic character while the
%  new kernel specification has a ':' character in its specification string.
%  If neither is the case, it is assumed an old style of a simple list of
%  numbers generating a odd-sized square kernel has been given.
%
%  The format of the AcquireKernal method is:
%
%      KernelInfo *AcquireKernelInfo(const char *kernel_string)
%
%  A description of each parameter follows:
%
%    o kernel_string: the Morphology/Convolution kernel wanted.
%
*/

/* This was separated so that it could be used as a separate
** array input handling function, such as for -color-matrix
*/
static KernelInfo *ParseKernelArray(const char *kernel_string)
{
  KernelInfo
    *kernel;

char
    token[MagickPathExtent];

const char
    *p,
    *end;

double
    nan = sqrt((double)-1.0);  /* Special Value : Not A Number */

MagickStatusType
    flags;

GeometryInfo
    args;

kernel=(KernelInfo *) AcquireQuantumMemory(1,sizeof(*kernel));
  if (kernel == (KernelInfo *) NULL)
    return(kernel);
  (void) memset(kernel,0,sizeof(*kernel));
  kernel->minimum = kernel->maximum = kernel->angle = 0.0;
  kernel->negative_range = kernel->positive_range = 0.0;
  kernel->type = UserDefinedKernel;
  kernel->next = (KernelInfo *) NULL;
  kernel->signature=MagickCoreSignature;
  if (kernel_string == (const char *) NULL)
    return(kernel);

/* find end of this specific kernel definition string */
  end = strchr(kernel_string, ';');
  if ( end == (char *) NULL )
    end = strchr(kernel_string, '\0');

/* clear flags - for Expanding kernel lists thorugh rotations */
   flags = NoValue;

/* Has a ':' in argument - New user kernel specification
     FUTURE: this split on ':' could be done by StringToken()
   */
  p = strchr(kernel_string, ':');
  if ( p != (char *) NULL && p < end)
    {
      /* ParseGeometry() needs the geometry separated! -- Arrgghh */
      memcpy(token, kernel_string, (size_t) (p-kernel_string));
      token[p-kernel_string] = '\0';
      SetGeometryInfo(&args);
      flags = ParseGeometry(token, &args);

/* Size handling and checks of geometry settings */
      if ( (flags & WidthValue) == 0 ) /* if no width then */
        args.rho = args.sigma;         /* then  width = height */
      if ( args.rho < 1.0 )            /* if width too small */
         args.rho = 1.0;               /* then  width = 1 */
      if ( args.sigma < 1.0 )          /* if height too small */
        args.sigma = args.rho;         /* then  height = width */
      kernel->width = (size_t)args.rho;
      kernel->height = (size_t)args.sigma;

/* Offset Handling and Checks */
      if ( args.xi  < 0.0 || args.psi < 0.0 )
        return(DestroyKernelInfo(kernel));
      kernel->x = ((flags & XValue)!=0) ? (ssize_t)args.xi
                                        : (ssize_t) (kernel->width-1)/2;
      kernel->y = ((flags & YValue)!=0) ? (ssize_t)args.psi
                                        : (ssize_t) (kernel->height-1)/2;
      if ( kernel->x >= (ssize_t) kernel->width ||
           kernel->y >= (ssize_t) kernel->height )
        return(DestroyKernelInfo(kernel));

p++; /* advance beyond the ':' */
    }
  else
    { /* ELSE - Old old specification, forming odd-square kernel */
      /* count up number of values given */
      p=(const char *) kernel_string;
      while ((isspace((int) ((unsigned char) *p)) != 0) || (*p == '\''))
        p++;  /* ignore "'" chars for convolve filter usage - Cristy */
      for (i=0; p < end; i++)
      {
        (void) GetNextToken(p,&p,MagickPathExtent,token);
        if (*token == ',')
          (void) GetNextToken(p,&p,MagickPathExtent,token);
      }
      /* set the size of the kernel - old sized square */
      kernel->width = kernel->height= (size_t) sqrt((double) i+1.0);
      kernel->x = kernel->y = (ssize_t) (kernel->width-1)/2;
      p=(const char *) kernel_string;
      while ((isspace((int) ((unsigned char) *p)) != 0) || (*p == '\''))
        p++;  /* ignore "'" chars for convolve filter usage - Cristy */
    }

/* Read in the kernel values from rest of input string argument */
  kernel->values=(MagickRealType *) MagickAssumeAligned(AcquireAlignedMemory(
    kernel->width,kernel->height*sizeof(*kernel->values)));
  if (kernel->values == (MagickRealType *) NULL)
    return(DestroyKernelInfo(kernel));
  kernel->minimum=MagickMaximumValue;
  kernel->maximum=(-MagickMaximumValue);
  kernel->negative_range = kernel->positive_range = 0.0;
  for (i=0; (i < (ssize_t) (kernel->width*kernel->height)) && (p < end); i++)
  {
    (void) GetNextToken(p,&p,MagickPathExtent,token);
    if (*token == ',')
      (void) GetNextToken(p,&p,MagickPathExtent,token);
    if (    LocaleCompare("nan",token) == 0
        || LocaleCompare("-",token) == 0 ) {
      kernel->values[i] = nan; /* this value is not part of neighbourhood */
    }
    else {
      kernel->values[i] = StringToDouble(token,(char **) NULL);
      ( kernel->values[i] < 0)
          ?  ( kernel->negative_range += kernel->values[i] )
          :  ( kernel->positive_range += kernel->values[i] );
      Minimize(kernel->minimum, kernel->values[i]);
      Maximize(kernel->maximum, kernel->values[i]);
    }
  }

/* sanity check -- no more values in kernel definition */
  (void) GetNextToken(p,&p,MagickPathExtent,token);
  if ( *token != '\0' && *token != ';' && *token != '\'' )
    return(DestroyKernelInfo(kernel));

#if 0
  /* this was the old method of handling a incomplete kernel */
  if ( i < (ssize_t) (kernel->width*kernel->height) ) {
    Minimize(kernel->minimum, kernel->values[i]);
    Maximize(kernel->maximum, kernel->values[i]);
    for ( ; i < (ssize_t) (kernel->width*kernel->height); i++)
      kernel->values[i]=0.0;
  }
#else
  /* Number of values for kernel was not enough - Report Error */
  if ( i < (ssize_t) (kernel->width*kernel->height) )
    return(DestroyKernelInfo(kernel));
#endif

/* check that we recieved at least one real (non-nan) value! */
  if (kernel->minimum == MagickMaximumValue)
    return(DestroyKernelInfo(kernel));

if ( (flags & AreaValue) != 0 )         /* '@' symbol in kernel size */
    ExpandRotateKernelInfo(kernel, 45.0); /* cyclic rotate 3x3 kernels */
  else if ( (flags & GreaterValue) != 0 ) /* '>' symbol in kernel args */
    ExpandRotateKernelInfo(kernel, 90.0); /* 90 degree rotate of kernel */
  else if ( (flags & LessValue) != 0 )    /* '<' symbol in kernel args */
    ExpandMirrorKernelInfo(kernel);       /* 90 degree mirror rotate */

return(kernel);
}

static KernelInfo *ParseKernelName(const char *kernel_string,
  ExceptionInfo *exception)
{
  char
    token[MagickPathExtent];

const char
    *p,
    *end;

GeometryInfo
    args;

KernelInfo
    *kernel;

MagickStatusType
    flags;

ssize_t
    type;

/* Parse special 'named' kernel */
  (void) GetNextToken(kernel_string,&p,MagickPathExtent,token);
  type=ParseCommandOption(MagickKernelOptions,MagickFalse,token);
  if ( type < 0 || type == UserDefinedKernel )
    return((KernelInfo *) NULL);  /* not a valid named kernel */

while (((isspace((int) ((unsigned char) *p)) != 0) ||
          (*p == ',') || (*p == ':' )) && (*p != '\0') && (*p != ';'))
    p++;

end = strchr(p, ';'); /* end of this kernel defintion */
  if ( end == (char *) NULL )
    end = strchr(p, '\0');

/* ParseGeometry() needs the geometry separated! -- Arrgghh */
  memcpy(token, p, (size_t) (end-p));
  token[end-p] = '\0';
  SetGeometryInfo(&args);
  flags = ParseGeometry(token, &args);

#if 0
  /* For Debugging Geometry Input */
  (void) FormatLocaleFile(stderr, "Geometry = 0x%04X : %lg x %lg %+lg %+lg\n",
    flags, args.rho, args.sigma, args.xi, args.psi );
#endif

/* special handling of missing values in input string */
  switch( type ) {
    /* Shape Kernel Defaults */
    case UnityKernel:
      if ( (flags & WidthValue) == 0 )
        args.rho = 1.0;    /* Default scale = 1.0, zero is valid */
      break;
    case SquareKernel:
    case DiamondKernel:
    case OctagonKernel:
    case DiskKernel:
    case PlusKernel:
    case CrossKernel:
      if ( (flags & HeightValue) == 0 )
        args.sigma = 1.0;    /* Default scale = 1.0, zero is valid */
      break;
    case RingKernel:
      if ( (flags & XValue) == 0 )
        args.xi = 1.0;       /* Default scale = 1.0, zero is valid */
      break;
    case RectangleKernel:    /* Rectangle - set size defaults */
      if ( (flags & WidthValue) == 0 ) /* if no width then */
        args.rho = args.sigma;         /* then  width = height */
      if ( args.rho < 1.0 )            /* if width too small */
          args.rho = 3;                /* then  width = 3 */
      if ( args.sigma < 1.0 )          /* if height too small */
        args.sigma = args.rho;         /* then  height = width */
      if ( (flags & XValue) == 0 )     /* center offset if not defined */
        args.xi = (double)(((ssize_t)args.rho-1)/2);
      if ( (flags & YValue) == 0 )
        args.psi = (double)(((ssize_t)args.sigma-1)/2);
      break;
    /* Distance Kernel Defaults */
    case ChebyshevKernel:
    case ManhattanKernel:
    case OctagonalKernel:
    case EuclideanKernel:
      if ( (flags & HeightValue) == 0 )           /* no distance scale */
        args.sigma = 100.0;                       /* default distance scaling */
      else if ( (flags & AspectValue ) != 0 )     /* '!' flag */
        args.sigma = QuantumRange/(args.sigma+1); /* maximum pixel distance */
      else if ( (flags & PercentValue ) != 0 )    /* '%' flag */
        args.sigma *= QuantumRange/100.0;         /* percentage of color range */
      break;
    default:
      break;
  }

kernel = AcquireKernelBuiltIn((KernelInfoType)type, &args, exception);
  if ( kernel == (KernelInfo *) NULL )
    return(kernel);

/* global expand to rotated kernel list - only for single kernels */
  if ( kernel->next == (KernelInfo *) NULL ) {
    if ( (flags & AreaValue) != 0 )         /* '@' symbol in kernel args */
      ExpandRotateKernelInfo(kernel, 45.0);
    else if ( (flags & GreaterValue) != 0 ) /* '>' symbol in kernel args */
      ExpandRotateKernelInfo(kernel, 90.0);
    else if ( (flags & LessValue) != 0 )    /* '<' symbol in kernel args */
      ExpandMirrorKernelInfo(kernel);
  }

return(kernel);
}

MagickExport KernelInfo *AcquireKernelInfo(const char *kernel_string,
  ExceptionInfo *exception)
{
  KernelInfo
    *kernel,
    *new_kernel;

char
    *kernel_cache,
    token[MagickPathExtent];

const char
    *p;

if (kernel_string == (const char *) NULL)
    return(ParseKernelArray(kernel_string));
  p=kernel_string;
  kernel_cache=(char *) NULL;
  if (*kernel_string == '@')
    {
      kernel_cache=FileToString(kernel_string+1,~0UL,exception);
      if (kernel_cache == (char *) NULL)
        return((KernelInfo *) NULL);
      p=(const char *) kernel_cache;
    }
  kernel=NULL;
  while (GetNextToken(p,(const char **) NULL,MagickPathExtent,token), *token != '\0')
  {
    /* ignore extra or multiple ';' kernel separators */
    if (*token != ';')
      {
        /* tokens starting with alpha is a Named kernel */
        if (isalpha((int) ((unsigned char) *token)) != 0)
          new_kernel=ParseKernelName(p,exception);
        else /* otherwise a user defined kernel array */
          new_kernel=ParseKernelArray(p);

/* Error handling -- this is not proper error handling! */
        if (new_kernel == (KernelInfo *) NULL)
          {
            if (kernel != (KernelInfo *) NULL)
              kernel=DestroyKernelInfo(kernel);
            return((KernelInfo *) NULL);
          }

/* initialise or append the kernel list */
        if (kernel == (KernelInfo *) NULL)
          kernel=new_kernel;
        else
          LastKernelInfo(kernel)->next=new_kernel;
      }

/* look for the next kernel in list */
    p=strchr(p,';');
    if (p == (char *) NULL)
      break;
    p++;
  }
  if (kernel_cache != (char *) NULL)
    kernel_cache=DestroyString(kernel_cache);
  return(kernel);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     A c q u i r e K e r n e l B u i l t I n                                 %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  AcquireKernelBuiltIn() returned one of the 'named' built-in types of
%  kernels used for special purposes such as gaussian blurring, skeleton
%  pruning, and edge distance determination.
%
%  They take a KernelType, and a set of geometry style arguments, which were
%  typically decoded from a user supplied string, or from a more complex
%  Morphology Method that was requested.
%
%  The format of the AcquireKernalBuiltIn method is:
%
%      KernelInfo *AcquireKernelBuiltIn(const KernelInfoType type,
%           const GeometryInfo args)
%
%  A description of each parameter follows:
%
%    o type: the pre-defined type of kernel wanted
%
%    o args: arguments defining or modifying the kernel
%
%  Convolution Kernels
%
%    Unity
%       The a No-Op or Scaling single element kernel.
%
%    Gaussian:{radius},{sigma}
%       Generate a two-dimensional gaussian kernel, as used by -gaussian.
%       The sigma for the curve is required.  The resulting kernel is
%       normalized,
%
%       If 'sigma' is zero, you get a single pixel on a field of zeros.
%
%       NOTE: that the 'radius' is optional, but if provided can limit (clip)
%       the final size of the resulting kernel to a square 2*radius+1 in size.
%       The radius should be at least 2 times that of the sigma value, or
%       sever clipping and aliasing may result.  If not given or set to 0 the
%       radius will be determined so as to produce the best minimal error
%       result, which is usally much larger than is normally needed.
%
%    LoG:{radius},{sigma}
%        "Laplacian of a Gaussian" or "Mexician Hat" Kernel.
%        The supposed ideal edge detection, zero-summing kernel.
%
%        An alturnative to this kernel is to use a "DoG" with a sigma ratio of
%        approx 1.6 (according to wikipedia).
%
%    DoG:{radius},{sigma1},{sigma2}
%        "Difference of Gaussians" Kernel.
%        As "Gaussian" but with a gaussian produced by 'sigma2' subtracted
%        from the gaussian produced by 'sigma1'. Typically sigma2 > sigma1.
%        The result is a zero-summing kernel.
%
%    Blur:{radius},{sigma}[,{angle}]
%       Generates a 1 dimensional or linear gaussian blur, at the angle given
%       (current restricted to orthogonal angles).  If a 'radius' is given the
%       kernel is clipped to a width of 2*radius+1.  Kernel can be rotated
%       by a 90 degree angle.
%
%       If 'sigma' is zero, you get a single pixel on a field of zeros.
%
%       Note that two convolutions with two "Blur" kernels perpendicular to
%       each other, is equivalent to a far larger "Gaussian" kernel with the
%       same sigma value, However it is much faster to apply. This is how the
%       "-blur" operator actually works.
%
%    Comet:{width},{sigma},{angle}
%       Blur in one direction only, much like how a bright object leaves
%       a comet like trail.  The Kernel is actually half a gaussian curve,
%       Adding two such blurs in opposite directions produces a Blur Kernel.
%       Angle can be rotated in multiples of 90 degrees.
%
%       Note that the first argument is the width of the kernel and not the
%       radius of the kernel.
%
%    Binomial:[{radius}]
%       Generate a discrete kernel using a 2 dimentional Pascel's Triangle
%       of values. Used for special forma of image filters.
%
%    # Still to be implemented...
%    #
%    # Filter2D
%    # Filter1D
%    #    Set kernel values using a resize filter, and given scale (sigma)
%    #    Cylindrical or Linear.   Is this possible with an image?
%    #
%
%  Named Constant Convolution Kernels
%
%  All these are unscaled, zero-summing kernels by default. As such for
%  non-HDRI version of ImageMagick some form of normalization, user scaling,
%  and biasing the results is recommended, to prevent the resulting image
%  being 'clipped'.
%
%  The 3x3 kernels (most of these) can be circularly rotated in multiples of
%  45 degrees to generate the 8 angled varients of each of the kernels.
%
%    Laplacian:{type}
%      Discrete Lapacian Kernels, (without normalization)
%        Type 0 :  3x3 with center:8 surounded by -1  (8 neighbourhood)
%        Type 1 :  3x3 with center:4 edge:-1 corner:0 (4 neighbourhood)
%        Type 2 :  3x3 with center:4 edge:1 corner:-2
%        Type 3 :  3x3 with center:4 edge:-2 corner:1
%        Type 5 :  5x5 laplacian
%        Type 7 :  7x7 laplacian
%        Type 15 : 5x5 LoG (sigma approx 1.4)
%        Type 19 : 9x9 LoG (sigma approx 1.4)
%
%    Sobel:{angle}
%      Sobel 'Edge' convolution kernel (3x3)
%          | -1, 0, 1 |
%          | -2, 0,-2 |
%          | -1, 0, 1 |
%
%    Roberts:{angle}
%      Roberts convolution kernel (3x3)
%          |  0, 0, 0 |
%          | -1, 1, 0 |
%          |  0, 0, 0 |
%
%    Prewitt:{angle}
%      Prewitt Edge convolution kernel (3x3)
%          | -1, 0, 1 |
%          | -1, 0, 1 |
%          | -1, 0, 1 |
%
%    Compass:{angle}
%      Prewitt's "Compass" convolution kernel (3x3)
%          | -1, 1, 1 |
%          | -1,-2, 1 |
%          | -1, 1, 1 |
%
%    Kirsch:{angle}
%      Kirsch's "Compass" convolution kernel (3x3)
%          | -3,-3, 5 |
%          | -3, 0, 5 |
%          | -3,-3, 5 |
%
%    FreiChen:{angle}
%      Frei-Chen Edge Detector is based on a kernel that is similar to
%      the Sobel Kernel, but is designed to be isotropic. That is it takes
%      into account the distance of the diagonal in the kernel.
%
%          |   1,     0,   -1     |
%          | sqrt(2), 0, -sqrt(2) |
%          |   1,     0,   -1     |
%
%    FreiChen:{type},{angle}
%
%      Frei-Chen Pre-weighted kernels...
%
%        Type 0:  default un-nomalized version shown above.
%
%        Type 1: Orthogonal Kernel (same as type 11 below)
%          |   1,     0,   -1     |
%          | sqrt(2), 0, -sqrt(2) | / 2*sqrt(2)
%          |   1,     0,   -1     |
%
%        Type 2: Diagonal form of Kernel...
%          |   1,     sqrt(2),    0     |
%          | sqrt(2),   0,     -sqrt(2) | / 2*sqrt(2)
%          |   0,    -sqrt(2)    -1     |
%
%      However this kernel is als at the heart of the FreiChen Edge Detection
%      Process which uses a set of 9 specially weighted kernel.  These 9
%      kernels not be normalized, but directly applied to the image. The
%      results is then added together, to produce the intensity of an edge in
%      a specific direction.  The square root of the pixel value can then be
%      taken as the cosine of the edge, and at least 2 such runs at 90 degrees
%      from each other, both the direction and the strength of the edge can be
%      determined.
%
%        Type 10: All 9 of the following pre-weighted kernels...
%
%        Type 11: |   1,     0,   -1     |
%                 | sqrt(2), 0, -sqrt(2) | / 2*sqrt(2)
%                 |   1,     0,   -1     |
%
%        Type 12: | 1, sqrt(2), 1 |
%                 | 0,   0,     0 | / 2*sqrt(2)
%                 | 1, sqrt(2), 1 |
%
%        Type 13: | sqrt(2), -1,    0     |
%                 |  -1,      0,    1     | / 2*sqrt(2)
%                 |   0,      1, -sqrt(2) |
%
%        Type 14: |    0,     1, -sqrt(2) |
%                 |   -1,     0,     1    | / 2*sqrt(2)
%                 | sqrt(2), -1,     0    |
%
%        Type 15: | 0, -1, 0 |
%                 | 1,  0, 1 | / 2
%                 | 0, -1, 0 |
%
%        Type 16: |  1, 0, -1 |
%                 |  0, 0,  0 | / 2
%                 | -1, 0,  1 |
%
%        Type 17: |  1, -2,  1 |
%                 | -2,  4, -2 | / 6
%                 | -1, -2,  1 |
%
%        Type 18: | -2, 1, -2 |
%                 |  1, 4,  1 | / 6
%                 | -2, 1, -2 |
%
%        Type 19: | 1, 1, 1 |
%                 | 1, 1, 1 | / 3
%                 | 1, 1, 1 |
%
%      The first 4 are for edge detection, the next 4 are for line detection
%      and the last is to add a average component to the results.
%
%      Using a special type of '-1' will return all 9 pre-weighted kernels
%      as a multi-kernel list, so that you can use them directly (without
%      normalization) with the special "-set option:morphology:compose Plus"
%      setting to apply the full FreiChen Edge Detection Technique.
%
%      If 'type' is large it will be taken to be an actual rotation angle for
%      the default FreiChen (type 0) kernel.  As such  FreiChen:45  will look
%      like a  Sobel:45  but with 'sqrt(2)' instead of '2' values.
%
%      WARNING: The above was layed out as per
%          http://www.math.tau.ac.il/~turkel/notes/edge_detectors.pdf
%      But rotated 90 degrees so direction is from left rather than the top.
%      I have yet to find any secondary confirmation of the above. The only
%      other source found was actual source code at
%          http://ltswww.epfl.ch/~courstiv/exos_labos/sol3.pdf
%      Neigher paper defineds the kernels in a way that looks locical or
%      correct when taken as a whole.
%
%  Boolean Kernels
%
%    Diamond:[{radius}[,{scale}]]
%       Generate a diamond shaped kernel with given radius to the points.
%       Kernel size will again be radius*2+1 square and defaults to radius 1,
%       generating a 3x3 kernel that is slightly larger than a square.
%
%    Square:[{radius}[,{scale}]]
%       Generate a square shaped kernel of size radius*2+1, and defaulting
%       to a 3x3 (radius 1).
%
%    Octagon:[{radius}[,{scale}]]
%       Generate octagonal shaped kernel of given radius and constant scale.
%       Default radius is 3 producing a 7x7 kernel. A radius of 1 will result
%       in "Diamond" kernel.
%
%    Disk:[{radius}[,{scale}]]
%       Generate a binary disk, thresholded at the radius given, the radius
%       may be a float-point value. Final Kernel size is floor(radius)*2+1
%       square. A radius of 5.3 is the default.
%
%       NOTE: That a low radii Disk kernels produce the same results as
%       many of the previously defined kernels, but differ greatly at larger
%       radii.  Here is a table of equivalences...
%          "Disk:1"    => "Diamond", "Octagon:1", or "Cross:1"
%          "Disk:1.5"  => "Square"
%          "Disk:2"    => "Diamond:2"
%          "Disk:2.5"  => "Octagon"
%          "Disk:2.9"  => "Square:2"
%          "Disk:3.5"  => "Octagon:3"
%          "Disk:4.5"  => "Octagon:4"
%          "Disk:5.4"  => "Octagon:5"
%          "Disk:6.4"  => "Octagon:6"
%       All other Disk shapes are unique to this kernel, but because a "Disk"
%       is more circular when using a larger radius, using a larger radius is
%       preferred over iterating the morphological operation.
%
%    Rectangle:{geometry}
%       Simply generate a rectangle of 1's with the size given. You can also
%       specify the location of the 'control point', otherwise the closest
%       pixel to the center of the rectangle is selected.
%
%       Properly centered and odd sized rectangles work the best.
%
%  Symbol Dilation Kernels
%
%    These kernel is not a good general morphological kernel, but is used
%    more for highlighting and marking any single pixels in an image using,
%    a "Dilate" method as appropriate.
%
%    For the same reasons iterating these kernels does not produce the
%    same result as using a larger radius for the symbol.
%
%    Plus:[{radius}[,{scale}]]
%    Cross:[{radius}[,{scale}]]
%       Generate a kernel in the shape of a 'plus' or a 'cross' with
%       a each arm the length of the given radius (default 2).
%
%       NOTE: "plus:1" is equivalent to a "Diamond" kernel.
%
%    Ring:{radius1},{radius2}[,{scale}]
%       A ring of the values given that falls between the two radii.
%       Defaults to a ring of approximataly 3 radius in a 7x7 kernel.
%       This is the 'edge' pixels of the default "Disk" kernel,
%       More specifically, "Ring" -> "Ring:2.5,3.5,1.0"
%
%  Hit and Miss Kernels
%
%    Peak:radius1,radius2
%       Find any peak larger than the pixels the fall between the two radii.
%       The default ring of pixels is as per "Ring".
%    Edges
%       Find flat orthogonal edges of a binary shape
%    Corners
%       Find 90 degree corners of a binary shape
%    Diagonals:type
%       A special kernel to thin the 'outside' of diagonals
%    LineEnds:type
%       Find end points of lines (for pruning a skeletion)
%       Two types of lines ends (default to both) can be searched for
%         Type 0: All line ends
%         Type 1: single kernel for 4-conneected line ends
%         Type 2: single kernel for simple line ends
%    LineJunctions
%       Find three line junctions (within a skeletion)
%         Type 0: all line junctions
%         Type 1: Y Junction kernel
%         Type 2: Diagonal T Junction kernel
%         Type 3: Orthogonal T Junction kernel
%         Type 4: Diagonal X Junction kernel
%         Type 5: Orthogonal + Junction kernel
%    Ridges:type
%       Find single pixel ridges or thin lines
%         Type 1: Fine single pixel thick lines and ridges
%         Type 2: Find two pixel thick lines and ridges
%    ConvexHull
%       Octagonal Thickening Kernel, to generate convex hulls of 45 degrees
%    Skeleton:type
%       Traditional skeleton generating kernels.
%         Type 1: Tradional Skeleton kernel (4 connected skeleton)
%         Type 2: HIPR2 Skeleton kernel (8 connected skeleton)
%         Type 3: Thinning skeleton based on a ressearch paper by
%                 Dan S. Bloomberg (Default Type)
%    ThinSE:type
%       A huge variety of Thinning Kernels designed to preserve conectivity.
%       many other kernel sets use these kernels as source definitions.
%       Type numbers are 41-49, 81-89, 481, and 482 which are based on
%       the super and sub notations used in the source research paper.
%
%  Distance Measuring Kernels
%
%    Different types of distance measuring methods, which are used with the
%    a 'Distance' morphology method for generating a gradient based on
%    distance from an edge of a binary shape, though there is a technique
%    for handling a anti-aliased shape.
%
%    See the 'Distance' Morphological Method, for information of how it is
%    applied.
%
%    Chebyshev:[{radius}][x{scale}[%!]]
%       Chebyshev Distance (also known as Tchebychev or Chessboard distance)
%       is a value of one to any neighbour, orthogonal or diagonal. One why
%       of thinking of it is the number of squares a 'King' or 'Queen' in
%       chess needs to traverse reach any other position on a chess board.
%       It results in a 'square' like distance function, but one where
%       diagonals are given a value that is closer than expected.
%
%    Manhattan:[{radius}][x{scale}[%!]]
%       Manhattan Distance (also known as Rectilinear, City Block, or the Taxi
%       Cab distance metric), it is the distance needed when you can only
%       travel in horizontal or vertical directions only.  It is the
%       distance a 'Rook' in chess would have to travel, and results in a
%       diamond like distances, where diagonals are further than expected.
%
%    Octagonal:[{radius}][x{scale}[%!]]
%       An interleving of Manhatten and Chebyshev metrics producing an
%       increasing octagonally shaped distance.  Distances matches those of
%       the "Octagon" shaped kernel of the same radius.  The minimum radius
%       and default is 2, producing a 5x5 kernel.
%
%    Euclidean:[{radius}][x{scale}[%!]]
%       Euclidean distance is the 'direct' or 'as the crow flys' distance.
%       However by default the kernel size only has a radius of 1, which
%       limits the distance to 'Knight' like moves, with only orthogonal and
%       diagonal measurements being correct.  As such for the default kernel
%       you will get octagonal like distance function.
%
%       However using a larger radius such as "Euclidean:4" you will get a
%       much smoother distance gradient from the edge of the shape. Especially
%       if the image is pre-processed to include any anti-aliasing pixels.
%       Of course a larger kernel is slower to use, and not always needed.
%
%    The first three Distance Measuring Kernels will only generate distances
%    of exact multiples of {scale} in binary images. As such you can use a
%    scale of 1 without loosing any information.  However you also need some
%    scaling when handling non-binary anti-aliased shapes.
%
%    The "Euclidean" Distance Kernel however does generate a non-integer
%    fractional results, and as such scaling is vital even for binary shapes.
%
*/

MagickExport KernelInfo *AcquireKernelBuiltIn(const KernelInfoType type,
  const GeometryInfo *args,ExceptionInfo *exception)
{
  KernelInfo
    *kernel;

double
    nan = sqrt((double)-1.0);  /* Special Value : Not A Number */

/* Generate a new empty kernel if needed */
  kernel=(KernelInfo *) NULL;
  switch(type) {
    case UndefinedKernel:    /* These should not call this function */
    case UserDefinedKernel:
      assert("Should not call this function" != (char *) NULL);
      break;
    case LaplacianKernel:   /* Named Descrete Convolution Kernels */
    case SobelKernel:       /* these are defined using other kernels */
    case RobertsKernel:
    case PrewittKernel:
    case CompassKernel:
    case KirschKernel:
    case FreiChenKernel:
    case EdgesKernel:       /* Hit and Miss kernels */
    case CornersKernel:
    case DiagonalsKernel:
    case LineEndsKernel:
    case LineJunctionsKernel:
    case RidgesKernel:
    case ConvexHullKernel:
    case SkeletonKernel:
    case ThinSEKernel:
      break;               /* A pre-generated kernel is not needed */
#if 0
    /* set to 1 to do a compile-time check that we haven't missed anything */
    case UnityKernel:
    case GaussianKernel:
    case DoGKernel:
    case LoGKernel:
    case BlurKernel:
    case CometKernel:
    case BinomialKernel:
    case DiamondKernel:
    case SquareKernel:
    case RectangleKernel:
    case OctagonKernel:
    case DiskKernel:
    case PlusKernel:
    case CrossKernel:
    case RingKernel:
    case PeaksKernel:
    case ChebyshevKernel:
    case ManhattanKernel:
    case OctangonalKernel:
    case EuclideanKernel:
#else
    default:
#endif
      /* Generate the base Kernel Structure */
      kernel=(KernelInfo *) AcquireMagickMemory(sizeof(*kernel));
      if (kernel == (KernelInfo *) NULL)
        return(kernel);
      (void) memset(kernel,0,sizeof(*kernel));
      kernel->minimum = kernel->maximum = kernel->angle = 0.0;
      kernel->negative_range = kernel->positive_range = 0.0;
      kernel->type = type;
      kernel->next = (KernelInfo *) NULL;
      kernel->signature=MagickCoreSignature;
      break;
  }

switch(type) {
    /*
      Convolution Kernels
    */
    case UnityKernel:
      {
        kernel->height = kernel->width = (size_t) 1;
        kernel->x = kernel->y = (ssize_t) 0;
        kernel->values=(MagickRealType *) MagickAssumeAligned(
          AcquireAlignedMemory(1,sizeof(*kernel->values)));
        if (kernel->values == (MagickRealType *) NULL)
          return(DestroyKernelInfo(kernel));
        kernel->maximum = kernel->values[0] = args->rho;
        break;
      }
      break;
    case GaussianKernel:
    case DoGKernel:
    case LoGKernel:
      { double
          sigma = fabs(args->sigma),
          sigma2 = fabs(args->xi),
          A, B, R;

if ( args->rho >= 1.0 )
          kernel->width = (size_t)args->rho*2+1;
        else if ( (type != DoGKernel) || (sigma >= sigma2) )
          kernel->width = GetOptimalKernelWidth2D(args->rho,sigma);
        else
          kernel->width = GetOptimalKernelWidth2D(args->rho,sigma2);
        kernel->height = kernel->width;
        kernel->x = kernel->y = (ssize_t) (kernel->width-1)/2;
        kernel->values=(MagickRealType *) MagickAssumeAligned(
          AcquireAlignedMemory(kernel->width,kernel->height*
          sizeof(*kernel->values)));
        if (kernel->values == (MagickRealType *) NULL)
          return(DestroyKernelInfo(kernel));

/* WARNING: The following generates a 'sampled gaussian' kernel.
         * What we really want is a 'discrete gaussian' kernel.
         *
         * How to do this is I don't know, but appears to be basied on the
         * Error Function 'erf()' (intergral of a gaussian)
         */

if ( type == GaussianKernel || type == DoGKernel )
          { /* Calculate a Gaussian,  OR positive half of a DoG */
            if ( sigma > MagickEpsilon )
              { A = 1.0/(2.0*sigma*sigma);  /* simplify loop expressions */
                B = (double) (1.0/(Magick2PI*sigma*sigma));
                for ( i=0, v=-kernel->y; v <= (ssize_t)kernel->y; v++)
                  for ( u=-kernel->x; u <= (ssize_t)kernel->x; u++, i++)
                      kernel->values[i] = exp(-((double)(u*u+v*v))*A)*B;
              }
            else /* limiting case - a unity (normalized Dirac) kernel */
              { (void) memset(kernel->values,0, (size_t)
                  kernel->width*kernel->height*sizeof(*kernel->values));
                kernel->values[kernel->x+kernel->y*kernel->width] = 1.0;
              }
          }

if ( type == DoGKernel )
          { /* Subtract a Negative Gaussian for "Difference of Gaussian" */
            if ( sigma2 > MagickEpsilon )
              { sigma = sigma2;                /* simplify loop expressions */
                A = 1.0/(2.0*sigma*sigma);
                B = (double) (1.0/(Magick2PI*sigma*sigma));
                for ( i=0, v=-kernel->y; v <= (ssize_t)kernel->y; v++)
                  for ( u=-kernel->x; u <= (ssize_t)kernel->x; u++, i++)
                    kernel->values[i] -= exp(-((double)(u*u+v*v))*A)*B;
              }
            else /* limiting case - a unity (normalized Dirac) kernel */
              kernel->values[kernel->x+kernel->y*kernel->width] -= 1.0;
          }

if ( type == LoGKernel )
          { /* Calculate a Laplacian of a Gaussian - Or Mexician Hat */
            if ( sigma > MagickEpsilon )
              { A = 1.0/(2.0*sigma*sigma);  /* simplify loop expressions */
                B = (double) (1.0/(MagickPI*sigma*sigma*sigma*sigma));
                for ( i=0, v=-kernel->y; v <= (ssize_t)kernel->y; v++)
                  for ( u=-kernel->x; u <= (ssize_t)kernel->x; u++, i++)
                    { R = ((double)(u*u+v*v))*A;
                      kernel->values[i] = (1-R)*exp(-R)*B;
                    }
              }
            else /* special case - generate a unity kernel */
              { (void) memset(kernel->values,0, (size_t)
                  kernel->width*kernel->height*sizeof(*kernel->values));
                kernel->values[kernel->x+kernel->y*kernel->width] = 1.0;
              }
          }

/* Note the above kernels may have been 'clipped' by a user defined
        ** radius, producing a smaller (darker) kernel.  Also for very small
        ** sigma's (> 0.1) the central value becomes larger than one, and thus
        ** producing a very bright kernel.
        **
        ** Normalization will still be needed.
        */

/* Normalize the 2D Gaussian Kernel
        **
        ** NB: a CorrelateNormalize performs a normal Normalize if
        ** there are no negative values.
        */
        CalcKernelMetaData(kernel);  /* the other kernel meta-data */
        ScaleKernelInfo(kernel, 1.0, CorrelateNormalizeValue);

break;
      }
    case BlurKernel:
      { double
          sigma = fabs(args->sigma),
          alpha, beta;

if ( args->rho >= 1.0 )
          kernel->width = (size_t)args->rho*2+1;
        else
          kernel->width = GetOptimalKernelWidth1D(args->rho,sigma);
        kernel->height = 1;
        kernel->x = (ssize_t) (kernel->width-1)/2;
        kernel->y = 0;
        kernel->negative_range = kernel->positive_range = 0.0;
        kernel->values=(MagickRealType *) MagickAssumeAligned(
          AcquireAlignedMemory(kernel->width,kernel->height*
          sizeof(*kernel->values)));
        if (kernel->values == (MagickRealType *) NULL)
          return(DestroyKernelInfo(kernel));

#if 1
#define KernelRank 3
        /* Formula derived from GetBlurKernel() in "effect.c" (plus bug fix).
        ** It generates a gaussian 3 times the width, and compresses it into
        ** the expected range.  This produces a closer normalization of the
        ** resulting kernel, especially for very low sigma values.
        ** As such while wierd it is prefered.
        **
        ** I am told this method originally came from Photoshop.
        **
        ** A properly normalized curve is generated (apart from edge clipping)
        ** even though we later normalize the result (for edge clipping)
        ** to allow the correct generation of a "Difference of Blurs".
        */

/* initialize */
        v = (ssize_t) (kernel->width*KernelRank-1)/2; /* start/end points to fit range */
        (void) memset(kernel->values,0, (size_t)
          kernel->width*kernel->height*sizeof(*kernel->values));
        /* Calculate a Positive 1D Gaussian */
        if ( sigma > MagickEpsilon )
          { sigma *= KernelRank;               /* simplify loop expressions */
            alpha = 1.0/(2.0*sigma*sigma);
            beta= (double) (1.0/(MagickSQ2PI*sigma ));
            for ( u=-v; u <= v; u++) {
              kernel->values[(u+v)/KernelRank] +=
                              exp(-((double)(u*u))*alpha)*beta;
            }
          }
        else /* special case - generate a unity kernel */
          kernel->values[kernel->x+kernel->y*kernel->width] = 1.0;
#else
        /* Direct calculation without curve averaging
           This is equivelent to a KernelRank of 1 */

/* Calculate a Positive Gaussian */
        if ( sigma > MagickEpsilon )
          { alpha = 1.0/(2.0*sigma*sigma);    /* simplify loop expressions */
            beta = 1.0/(MagickSQ2PI*sigma);
            for ( i=0, u=-kernel->x; u <= (ssize_t)kernel->x; u++, i++)
              kernel->values[i] = exp(-((double)(u*u))*alpha)*beta;
          }
        else /* special case - generate a unity kernel */
          { (void) memset(kernel->values,0, (size_t)
              kernel->width*kernel->height*sizeof(*kernel->values));
            kernel->values[kernel->x+kernel->y*kernel->width] = 1.0;
          }
#endif
        /* Note the above kernel may have been 'clipped' by a user defined
        ** radius, producing a smaller (darker) kernel.  Also for very small
        ** sigma's (> 0.1) the central value becomes larger than one, as a
        ** result of not generating a actual 'discrete' kernel, and thus
        ** producing a very bright 'impulse'.
        **
        ** Becuase of these two factors Normalization is required!
        */

/* Normalize the 1D Gaussian Kernel
        **
        ** NB: a CorrelateNormalize performs a normal Normalize if
        ** there are no negative values.
        */
        CalcKernelMetaData(kernel);  /* the other kernel meta-data */
        ScaleKernelInfo(kernel, 1.0, CorrelateNormalizeValue);

/* rotate the 1D kernel by given angle */
        RotateKernelInfo(kernel, args->xi );
        break;
      }
    case CometKernel:
      { double
          sigma = fabs(args->sigma),
          A;

if ( args->rho < 1.0 )
          kernel->width = (GetOptimalKernelWidth1D(args->rho,sigma)-1)/2+1;
        else
          kernel->width = (size_t)args->rho;
        kernel->x = kernel->y = 0;
        kernel->height = 1;
        kernel->negative_range = kernel->positive_range = 0.0;
        kernel->values=(MagickRealType *) MagickAssumeAligned(
          AcquireAlignedMemory(kernel->width,kernel->height*
          sizeof(*kernel->values)));
        if (kernel->values == (MagickRealType *) NULL)
          return(DestroyKernelInfo(kernel));

/* A comet blur is half a 1D gaussian curve, so that the object is
        ** blurred in one direction only.  This may not be quite the right
        ** curve to use so may change in the future. The function must be
        ** normalised after generation, which also resolves any clipping.
        **
        ** As we are normalizing and not subtracting gaussians,
        ** there is no need for a divisor in the gaussian formula
        **
        ** It is less comples
        */
        if ( sigma > MagickEpsilon )
          {
#if 1
#define KernelRank 3
            v = (ssize_t) kernel->width*KernelRank; /* start/end points */
            (void) memset(kernel->values,0, (size_t)
              kernel->width*sizeof(*kernel->values));
            sigma *= KernelRank;            /* simplify the loop expression */
            A = 1.0/(2.0*sigma*sigma);
            /* B = 1.0/(MagickSQ2PI*sigma); */
            for ( u=0; u < v; u++) {
              kernel->values[u/KernelRank] +=
                  exp(-((double)(u*u))*A);
              /*  exp(-((double)(i*i))/2.0*sigma*sigma)/(MagickSQ2PI*sigma); */
            }
            for (i=0; i < (ssize_t) kernel->width; i++)
              kernel->positive_range += kernel->values[i];
#else
            A = 1.0/(2.0*sigma*sigma);     /* simplify the loop expression */
            /* B = 1.0/(MagickSQ2PI*sigma); */
            for ( i=0; i < (ssize_t) kernel->width; i++)
              kernel->positive_range +=
                kernel->values[i] = exp(-((double)(i*i))*A);
                /* exp(-((double)(i*i))/2.0*sigma*sigma)/(MagickSQ2PI*sigma); */
#endif
          }
        else /* special case - generate a unity kernel */
          { (void) memset(kernel->values,0, (size_t)
              kernel->width*kernel->height*sizeof(*kernel->values));
            kernel->values[kernel->x+kernel->y*kernel->width] = 1.0;
            kernel->positive_range = 1.0;
          }

kernel->minimum = 0.0;
        kernel->maximum = kernel->values[0];
        kernel->negative_range = 0.0;

ScaleKernelInfo(kernel, 1.0, NormalizeValue); /* Normalize */
        RotateKernelInfo(kernel, args->xi); /* Rotate by angle */
        break;
      }
    case BinomialKernel:
      {
        size_t
          order_f;

if (args->rho < 1.0)
          kernel->width = kernel->height = 3;  /* default radius = 1 */
        else
          kernel->width = kernel->height = ((size_t)args->rho)*2+1;
        kernel->x = kernel->y = (ssize_t) (kernel->width-1)/2;

order_f = fact(kernel->width-1);

kernel->values=(MagickRealType *) MagickAssumeAligned(
          AcquireAlignedMemory(kernel->width,kernel->height*
          sizeof(*kernel->values)));
        if (kernel->values == (MagickRealType *) NULL)
          return(DestroyKernelInfo(kernel));

/* set all kernel values within diamond area to scale given */
        for ( i=0, v=0; v < (ssize_t)kernel->height; v++)
          { size_t
              alpha = order_f / ( fact((size_t) v) * fact(kernel->height-v-1) );
            for ( u=0; u < (ssize_t)kernel->width; u++, i++)
              kernel->positive_range += kernel->values[i] = (double)
                (alpha * order_f / ( fact((size_t) u) * fact(kernel->height-u-1) ));
          }
        kernel->minimum = 1.0;
        kernel->maximum = kernel->values[kernel->x+kernel->y*kernel->width];
        kernel->negative_range = 0.0;
        break;
      }

/*
      Convolution Kernels - Well Known Named Constant Kernels
    */
    case LaplacianKernel:
      { switch ( (int) args->rho ) {
          case 0:
          default: /* laplacian square filter -- default */
            kernel=ParseKernelArray("3: -1,-1,-1  -1,8,-1  -1,-1,-1");
            break;
          case 1:  /* laplacian diamond filter */
            kernel=ParseKernelArray("3: 0,-1,0  -1,4,-1  0,-1,0");
            break;
          case 2:
            kernel=ParseKernelArray("3: -2,1,-2  1,4,1  -2,1,-2");
            break;
          case 3:
            kernel=ParseKernelArray("3: 1,-2,1  -2,4,-2  1,-2,1");
            break;
          case 5:   /* a 5x5 laplacian */
            kernel=ParseKernelArray(
              "5: -4,-1,0,-1,-4  -1,2,3,2,-1  0,3,4,3,0  -1,2,3,2,-1  -4,-1,0,-1,-4");
            break;
          case 7:   /* a 7x7 laplacian */
            kernel=ParseKernelArray(
              "7:-10,-5,-2,-1,-2,-5,-10 -5,0,3,4,3,0,-5 -2,3,6,7,6,3,-2 -1,4,7,8,7,4,-1 -2,3,6,7,6,3,-2 -5,0,3,4,3,0,-5 -10,-5,-2,-1,-2,-5,-10" );
            break;
          case 15:  /* a 5x5 LoG (sigma approx 1.4) */
            kernel=ParseKernelArray(
              "5: 0,0,-1,0,0  0,-1,-2,-1,0  -1,-2,16,-2,-1  0,-1,-2,-1,0  0,0,-1,0,0");
            break;
          case 19:  /* a 9x9 LoG (sigma approx 1.4) */
            /* http://www.cscjournals.org/csc/manuscript/Journals/IJIP/volume3/Issue1/IJIP-15.pdf */
            kernel=ParseKernelArray(
              "9: 0,-1,-1,-2,-2,-2,-1,-1,0  -1,-2,-4,-5,-5,-5,-4,-2,-1  -1,-4,-5,-3,-0,-3,-5,-4,-1  -2,-5,-3,12,24,12,-3,-5,-2  -2,-5,-0,24,40,24,-0,-5,-2  -2,-5,-3,12,24,12,-3,-5,-2  -1,-4,-5,-3,-0,-3,-5,-4,-1  -1,-2,-4,-5,-5,-5,-4,-2,-1  0,-1,-1,-2,-2,-2,-1,-1,0");
            break;
        }
        if (kernel == (KernelInfo *) NULL)
          return(kernel);
        kernel->type = type;
        break;
      }
    case SobelKernel:
      { /* Simple Sobel Kernel */
        kernel=ParseKernelArray("3: 1,0,-1  2,0,-2  1,0,-1");
        if (kernel == (KernelInfo *) NULL)
          return(kernel);
        kernel->type = type;
        RotateKernelInfo(kernel, args->rho);
        break;
      }
    case RobertsKernel:
      {
        kernel=ParseKernelArray("3: 0,0,0  1,-1,0  0,0,0");
        if (kernel == (KernelInfo *) NULL)
          return(kernel);
        kernel->type = type;
        RotateKernelInfo(kernel, args->rho);
        break;
      }
    case PrewittKernel:
      {
        kernel=ParseKernelArray("3: 1,0,-1  1,0,-1  1,0,-1");
        if (kernel == (KernelInfo *) NULL)
          return(kernel);
        kernel->type = type;
        RotateKernelInfo(kernel, args->rho);
        break;
      }
    case CompassKernel:
      {
        kernel=ParseKernelArray("3: 1,1,-1  1,-2,-1  1,1,-1");
        if (kernel == (KernelInfo *) NULL)
          return(kernel);
        kernel->type = type;
        RotateKernelInfo(kernel, args->rho);
        break;
      }
    case KirschKernel:
      {
        kernel=ParseKernelArray("3: 5,-3,-3  5,0,-3  5,-3,-3");
        if (kernel == (KernelInfo *) NULL)
          return(kernel);
        kernel->type = type;
        RotateKernelInfo(kernel, args->rho);
        break;
      }
    case FreiChenKernel:
      /* Direction is set to be left to right positive */
      /* http://www.math.tau.ac.il/~turkel/notes/edge_detectors.pdf -- RIGHT? */
      /* http://ltswww.epfl.ch/~courstiv/exos_labos/sol3.pdf -- WRONG? */
      { switch ( (int) args->rho ) {
          default:
          case 0:
            kernel=ParseKernelArray("3: 1,0,-1  2,0,-2  1,0,-1");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            kernel->values[3] = +(MagickRealType) MagickSQ2;
            kernel->values[5] = -(MagickRealType) MagickSQ2;
            CalcKernelMetaData(kernel);     /* recalculate meta-data */
            break;
          case 2:
            kernel=ParseKernelArray("3: 1,2,0  2,0,-2  0,-2,-1");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            kernel->values[1] = kernel->values[3]= +(MagickRealType) MagickSQ2;
            kernel->values[5] = kernel->values[7]= -(MagickRealType) MagickSQ2;
            CalcKernelMetaData(kernel);     /* recalculate meta-data */
            ScaleKernelInfo(kernel, (double) (1.0/2.0*MagickSQ2), NoValue);
            break;
          case 10:
          {
            kernel=AcquireKernelInfo("FreiChen:11;FreiChen:12;FreiChen:13;FreiChen:14;FreiChen:15;FreiChen:16;FreiChen:17;FreiChen:18;FreiChen:19",exception);
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            break;
          }
          case 1:
          case 11:
            kernel=ParseKernelArray("3: 1,0,-1  2,0,-2  1,0,-1");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            kernel->values[3] = +(MagickRealType) MagickSQ2;
            kernel->values[5] = -(MagickRealType) MagickSQ2;
            CalcKernelMetaData(kernel);     /* recalculate meta-data */
            ScaleKernelInfo(kernel, (double) (1.0/2.0*MagickSQ2), NoValue);
            break;
          case 12:
            kernel=ParseKernelArray("3: 1,2,1  0,0,0  1,2,1");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            kernel->values[1] = +(MagickRealType) MagickSQ2;
            kernel->values[7] = +(MagickRealType) MagickSQ2;
            CalcKernelMetaData(kernel);
            ScaleKernelInfo(kernel, (double) (1.0/2.0*MagickSQ2), NoValue);
            break;
          case 13:
            kernel=ParseKernelArray("3: 2,-1,0  -1,0,1  0,1,-2");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            kernel->values[0] = +(MagickRealType) MagickSQ2;
            kernel->values[8] = -(MagickRealType) MagickSQ2;
            CalcKernelMetaData(kernel);
            ScaleKernelInfo(kernel, (double) (1.0/2.0*MagickSQ2), NoValue);
            break;
          case 14:
            kernel=ParseKernelArray("3: 0,1,-2  -1,0,1  2,-1,0");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            kernel->values[2] = -(MagickRealType) MagickSQ2;
            kernel->values[6] = +(MagickRealType) MagickSQ2;
            CalcKernelMetaData(kernel);
            ScaleKernelInfo(kernel, (double) (1.0/2.0*MagickSQ2), NoValue);
            break;
          case 15:
            kernel=ParseKernelArray("3: 0,-1,0  1,0,1  0,-1,0");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            ScaleKernelInfo(kernel, 1.0/2.0, NoValue);
            break;
          case 16:
            kernel=ParseKernelArray("3: 1,0,-1  0,0,0  -1,0,1");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            ScaleKernelInfo(kernel, 1.0/2.0, NoValue);
            break;
          case 17:
            kernel=ParseKernelArray("3: 1,-2,1  -2,4,-2  -1,-2,1");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            ScaleKernelInfo(kernel, 1.0/6.0, NoValue);
            break;
          case 18:
            kernel=ParseKernelArray("3: -2,1,-2  1,4,1  -2,1,-2");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            ScaleKernelInfo(kernel, 1.0/6.0, NoValue);
            break;
          case 19:
            kernel=ParseKernelArray("3: 1,1,1  1,1,1  1,1,1");
            if (kernel == (KernelInfo *) NULL)
              return(kernel);
            kernel->type = type;
            ScaleKernelInfo(kernel, 1.0/3.0, NoValue);
            break;
        }
        if ( fabs(args->sigma) >= MagickEpsilon )
          /* Rotate by correctly supplied 'angle' */
          RotateKernelInfo(kernel, args->sigma);
        else if ( args->rho > 30.0 || args->rho < -30.0 )
          /* Rotate by out of bounds 'type' */
          RotateKernelInfo(kernel, args->rho);
        break;
      }

/*
      Boolean or Shaped Kernels
    */
    case DiamondKernel:
      {
        if (args->rho < 1.0)
          kernel->width = kernel->height = 3;  /* default radius = 1 */
        else
          kernel->width = kernel->height = ((size_t)args->rho)*2+1;
        kernel->x = kernel->y = (ssize_t) (kernel->width-1)/2;

/* set all kernel values within diamond area to scale given */
        for ( i=0, v=-kernel->y; v <= (ssize_t)kernel->y; v++)
          for ( u=-kernel->x; u <= (ssize_t)kernel->x; u++, i++)
            if ( (labs((long) u)+labs((long) v)) <= (long) kernel->x)
              kernel->positive_range += kernel->values[i] = args->sigma;
            else
              kernel->values[i] = nan;
        kernel->minimum = kernel->maximum = args->sigma;   /* a flat shape */
        break;
      }
    case SquareKernel:
    case RectangleKernel:
      { double
          scale;
        if ( type == SquareKernel )
          {
            if (args->rho < 1.0)
              kernel->width = kernel->height = 3;  /* default radius = 1 */
            else
              kernel->width = kernel->height = (size_t) (2*args->rho+1);
            kernel->x = kernel->y = (ssize_t) (kernel->width-1)/2;
            scale = args->sigma;
          }
        else {
            /* NOTE: user defaults set in "AcquireKernelInfo()" */
            if ( args->rho < 1.0 || args->sigma < 1.0 )
              return(DestroyKernelInfo(kernel));    /* invalid args given */
            kernel->width = (size_t)args->rho;
            kernel->height = (size_t)args->sigma;
            if ( args->xi  < 0.0 || args->xi  > (double)kernel->width ||
                 args->psi < 0.0 || args->psi > (double)kernel->height )
              return(DestroyKernelInfo(kernel));    /* invalid args given */
            kernel->x = (ssize_t) args->xi;
            kernel->y = (ssize_t) args->psi;
            scale = 1.0;
          }
        kernel->values=(MagickRealType *) MagickAssumeAligned(
          AcquireAlignedMemory(kernel->width,kernel->height*
          sizeof(*kernel->values)));
        if (kernel->values == (MagickRealType *) NULL)
          return(DestroyKernelInfo(kernel));

/* set all kernel values to scale given */
        u=(ssize_t) (kernel->width*kernel->height);
        for ( i=0; i < u; i++)
            kernel->values[i] = scale;
        kernel->minimum = kernel->maximum = scale;   /* a flat shape */
        kernel->positive_range = scale*u;
        break;
      }
      case OctagonKernel:
        {
          if (args->rho < 1.0)
            kernel->width = kernel->height = 5;  /* default radius = 2 */
          else
            kernel->width = kernel->height = ((size_t)args->rho)*2+1;
          kernel->x = kernel->y = (ssize_t) (kernel->width-1)/2;