-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathfinite_radon_transform.py
985 lines (842 loc) · 58.6 KB
/
finite_radon_transform.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
<!DOCTYPE html>
<html>
<head prefix="og: http://ogp.me/ns# fb: http://ogp.me/ns/fb# githubog: http://ogp.me/ns/fb/githubog#">
<meta charset='utf-8'>
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<title>scikits-image/skimage/transform/finite_radon_transform.py at master · scikits-image/scikits-image · GitHub</title>
<link rel="search" type="application/opensearchdescription+xml" href="/opensearch.xml" title="GitHub" />
<link rel="fluid-icon" href="https://github.com/fluidicon.png" title="GitHub" />
<link rel="shortcut icon" href="/favicon.ico" type="image/x-icon" />
<meta content="authenticity_token" name="csrf-param" />
<meta content="mqCjKcLvJEF4Ut8zduKCzRZWNTb0UBlSlD04/Aggz6M=" name="csrf-token" />
<link href="https://a248.e.akamai.net/assets.github.com/stylesheets/bundles/github-e2a66f70d831aada662d99108fbb8d26c1efb6eb.css" media="screen" rel="stylesheet" type="text/css" />
<link href="https://a248.e.akamai.net/assets.github.com/stylesheets/bundles/github2-e3d528062f9480d9819936572554df3183b4e6b2.css" media="screen" rel="stylesheet" type="text/css" />
<script src="https://a248.e.akamai.net/assets.github.com/javascripts/bundles/frameworks-a450c7f907bdc1ee6b362ab1ecca811c761fd259.js" type="text/javascript"></script>
<script defer="defer" src="https://a248.e.akamai.net/assets.github.com/javascripts/bundles/github-2311f5da3b6f3e6dcb4546848c45e76739f397b4.js" type="text/javascript"></script>
<link rel='permalink' href='/scikits-image/scikits-image/blob/2eb0a2552fa40fcaa14511143863f164ab0d7adb/skimage/transform/finite_radon_transform.py'>
<meta property="og:title" content="scikits-image"/>
<meta property="og:type" content="githubog:gitrepository"/>
<meta property="og:url" content="https://github.com/scikits-image/scikits-image"/>
<meta property="og:image" content="https://a248.e.akamai.net/assets.github.com/images/gravatars/gravatar-140.png?1329275856"/>
<meta property="og:site_name" content="GitHub"/>
<meta property="og:description" content="Image Processing SciKit (Toolbox for SciPy). Contribute to scikits-image development by creating an account on GitHub."/>
<meta name="description" content="Image Processing SciKit (Toolbox for SciPy). Contribute to scikits-image development by creating an account on GitHub." />
<link href="https://github.com/scikits-image/scikits-image/commits/master.atom" rel="alternate" title="Recent Commits to scikits-image:master" type="application/atom+xml" />
</head>
<body class="logged_out page-blob linux vis-public env-production " data-blob-contribs-enabled="yes">
<div id="wrapper">
<div id="header" class="true clearfix">
<div class="container clearfix">
<a class="site-logo" href="https://github.com/">
<!--[if IE]>
<img alt="GitHub" class="github-logo" src="https://a248.e.akamai.net/assets.github.com/images/modules/header/logov7.png?1323882717" />
<img alt="GitHub" class="github-logo-hover" src="https://a248.e.akamai.net/assets.github.com/images/modules/header/logov7-hover.png?1324325358" />
<![endif]-->
<img alt="GitHub" class="github-logo-4x" height="30" src="https://a248.e.akamai.net/assets.github.com/images/modules/header/[email protected]?1337118066" />
<img alt="GitHub" class="github-logo-4x-hover" height="30" src="https://a248.e.akamai.net/assets.github.com/images/modules/header/[email protected]?1337118066" />
</a>
<!--
make sure to use fully qualified URLs here since this nav
is used on error pages on other domains
-->
<ul class="top-nav logged_out">
<li class="pricing"><a href="https://github.com/plans">Signup and Pricing</a></li>
<li class="explore"><a href="https://github.com/explore">Explore GitHub</a></li>
<li class="features"><a href="https://github.com/features">Features</a></li>
<li class="blog"><a href="https://github.com/blog">Blog</a></li>
<li class="login"><a href="https://github.com/login?return_to=%2Fscikits-image%2Fscikits-image%2Fblob%2Fmaster%2Fskimage%2Ftransform%2Ffinite_radon_transform.py">Login</a></li>
</ul>
</div>
</div>
<div class="site hfeed" itemscope itemtype="http://schema.org/WebPage">
<div class="container hentry">
<div class="pagehead repohead instapaper_ignore readability-menu">
<div class="title-actions-bar">
<ul class="pagehead-actions">
<li>
<span class="watch-button"><a href="/login?return_to=%2Fscikits-image%2Fscikits-image" class="minibutton btn-watch js-toggler-target entice tooltipped leftwards" title="You must be logged in to use this feature" rel="nofollow"><span class="icon"></span> Watch</a><a class="social-count js-social-count" href="/scikits-image/scikits-image/watchers">92</a></span>
</li>
<li>
<a href="/login?return_to=%2Fscikits-image%2Fscikits-image" class="minibutton btn-fork js-toggler-target fork-button entice tooltipped leftwards" title="You must be logged in to use this feature" rel="nofollow"><span class="icon"></span>Fork</a><a href="/scikits-image/scikits-image/network" class="social-count">45</a>
</li>
</ul>
<h1 itemscope itemtype="http://data-vocabulary.org/Breadcrumb" class="entry-title public">
<span class="repo-label"><span>public</span></span>
<span class="mega-icon mega-icon-public-repo"></span>
<span class="author vcard">
<a href="/scikits-image" class="url fn" itemprop="url" rel="author"> <span itemprop="title">scikits-image</span>
</a></span> /
<strong><a href="/scikits-image/scikits-image" class="js-current-repository">scikits-image</a></strong>
</h1>
</div>
<ul class="tabs">
<li><a href="/scikits-image/scikits-image" class="selected" highlight="repo_sourcerepo_downloadsrepo_commitsrepo_tagsrepo_branches">Code</a></li>
<li><a href="/scikits-image/scikits-image/network" highlight="repo_network">Network</a>
<li><a href="/scikits-image/scikits-image/pulls" highlight="repo_pulls">Pull Requests <span class='counter'>11</span></a></li>
<li><a href="/scikits-image/scikits-image/issues" highlight="repo_issues">Issues <span class='counter'>18</span></a></li>
<li><a href="/scikits-image/scikits-image/wiki" highlight="repo_wiki">Wiki</a></li>
<li><a href="/scikits-image/scikits-image/graphs" highlight="repo_graphsrepo_contributors">Graphs</a></li>
</ul>
<div class="frame frame-center tree-finder" style="display:none"
data-tree-list-url="/scikits-image/scikits-image/tree-list/2eb0a2552fa40fcaa14511143863f164ab0d7adb"
data-blob-url-prefix="/scikits-image/scikits-image/blob/2eb0a2552fa40fcaa14511143863f164ab0d7adb"
>
<div class="breadcrumb">
<span class="bold"><a href="/scikits-image/scikits-image">scikits-image</a></span> /
<input class="tree-finder-input js-navigation-enable" type="text" name="query" autocomplete="off" spellcheck="false">
</div>
<div class="octotip">
<p>
<a href="/scikits-image/scikits-image/dismiss-tree-finder-help" class="dismiss js-dismiss-tree-list-help" title="Hide this notice forever" rel="nofollow">Dismiss</a>
<span class="bold">Octotip:</span> You've activated the <em>file finder</em>
by pressing <span class="kbd">t</span> Start typing to filter the
file list. Use <span class="kbd badmono">↑</span> and
<span class="kbd badmono">↓</span> to navigate,
<span class="kbd">enter</span> to view files.
</p>
</div>
<table class="tree-browser" cellpadding="0" cellspacing="0">
<tr class="js-header"><th> </th><th>name</th></tr>
<tr class="js-no-results no-results" style="display: none">
<th colspan="2">No matching files</th>
</tr>
<tbody class="js-results-list js-navigation-container">
</tbody>
</table>
</div>
<div id="jump-to-line" style="display:none">
<h2>Jump to Line</h2>
<form accept-charset="UTF-8">
<input class="textfield" type="text">
<div class="full-button">
<button type="submit" class="classy">
<span>Go</span>
</button>
</div>
</form>
</div>
<div class="subnav-bar">
<ul class="actions subnav">
<li><a href="/scikits-image/scikits-image/tags" class="" highlight="repo_tags">Tags <span class="counter">11</span></a></li>
<li><a href="/scikits-image/scikits-image/downloads" class="blank downloads-blank" highlight="repo_downloads">Downloads <span class="counter">0</span></a></li>
</ul>
<ul class="scope">
<li class="switcher">
<div class="context-menu-container js-menu-container js-context-menu">
<a href="#"
class="minibutton bigger switcher js-menu-target js-commitish-button btn-branch repo-tree"
data-hotkey="w"
data-master-branch="master"
data-ref="master">
<span><span class="icon"></span><i>branch:</i> master</span>
</a>
<div class="context-pane commitish-context js-menu-content">
<a href="javascript:;" class="close js-menu-close"><span class="mini-icon mini-icon-remove-close"></span></a>
<div class="context-title">Switch Branches/Tags</div>
<div class="context-body pane-selector commitish-selector js-navigation-container">
<div class="filterbar">
<input type="text" id="context-commitish-filter-field" class="js-navigation-enable" placeholder="Filter branches/tags" data-filterable />
<ul class="tabs">
<li><a href="#" data-filter="branches" class="selected">Branches</a></li>
<li><a href="#" data-filter="tags">Tags</a></li>
</ul>
</div>
<div class="js-filter-tab js-filter-branches" data-filterable-for="context-commitish-filter-field">
<div class="no-results js-not-filterable">Nothing to show</div>
<div class="commitish-item branch-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/0.3.1/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="0.3.1" rel="nofollow">0.3.1</a>
</h4>
</div>
<div class="commitish-item branch-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/debian/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="debian" rel="nofollow">debian</a>
</h4>
</div>
<div class="commitish-item branch-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/master/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="master" rel="nofollow">master</a>
</h4>
</div>
</div>
<div class="js-filter-tab js-filter-tags" style="display:none" data-filterable-for="context-commitish-filter-field">
<div class="no-results js-not-filterable">Nothing to show</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.5/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.5" rel="nofollow">v0.5</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.4.2/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.4.2" rel="nofollow">v0.4.2</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.4.1/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.4.1" rel="nofollow">v0.4.1</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.4/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.4" rel="nofollow">v0.4</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.3.1/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.3.1" rel="nofollow">v0.3.1</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.3/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.3" rel="nofollow">v0.3</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.2.1/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.2.1" rel="nofollow">v0.2.1</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.2/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.2" rel="nofollow">v0.2</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/v0.1/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="v0.1" rel="nofollow">v0.1</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/debian/0.5.0+git100-gfeb3e92-2/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="debian/0.5.0+git100-gfeb3e92-2" rel="nofollow">debian/0.5.0+git100-gfeb3e92-2</a>
</h4>
</div>
<div class="commitish-item tag-commitish selector-item js-navigation-item js-navigation-target">
<h4>
<a href="/scikits-image/scikits-image/blob/debian/0.5.0+git100-gfeb3e92-1/skimage/transform/finite_radon_transform.py" class="js-navigation-open" data-name="debian/0.5.0+git100-gfeb3e92-1" rel="nofollow">debian/0.5.0+git100-gfeb3e92-1</a>
</h4>
</div>
</div>
</div>
</div><!-- /.commitish-context-context -->
</div>
</li>
</ul>
<ul class="subnav with-scope">
<li><a href="/scikits-image/scikits-image" class="selected" highlight="repo_source">Files</a></li>
<li><a href="/scikits-image/scikits-image/commits/master" highlight="repo_commits">Commits</a></li>
<li><a href="/scikits-image/scikits-image/branches" class="" highlight="repo_branches" rel="nofollow">Branches <span class="counter">3</span></a></li>
</ul>
</div>
</div><!-- /.repohead -->
<!-- block_view_fragment_key: views10/v8/blob:v21:6307fcb056476fa716b0612186b14f36 -->
<div id="slider">
<div class="breadcrumb" data-path="skimage/transform/finite_radon_transform.py/">
<b itemscope="" itemtype="http://data-vocabulary.org/Breadcrumb"><a href="/scikits-image/scikits-image/tree/2eb0a2552fa40fcaa14511143863f164ab0d7adb" class="js-rewrite-sha" itemprop="url"><span itemprop="title">scikits-image</span></a></b> / <span itemscope="" itemtype="http://data-vocabulary.org/Breadcrumb"><a href="/scikits-image/scikits-image/tree/2eb0a2552fa40fcaa14511143863f164ab0d7adb/skimage" class="js-rewrite-sha" itemscope="url"><span itemprop="title">skimage</span></a></span> / <span itemscope="" itemtype="http://data-vocabulary.org/Breadcrumb"><a href="/scikits-image/scikits-image/tree/2eb0a2552fa40fcaa14511143863f164ab0d7adb/skimage/transform" class="js-rewrite-sha" itemscope="url"><span itemprop="title">transform</span></a></span> / <strong class="final-path">finite_radon_transform.py</strong> <span class="js-clippy mini-icon mini-icon-clippy " data-clipboard-text="skimage/transform/finite_radon_transform.py" data-copied-hint="copied!" data-copy-hint="copy to clipboard"></span>
</div>
<div class="commit file-history-tease" data-path="skimage/transform/finite_radon_transform.py/">
<img class="main-avatar" height="24" src="https://secure.gravatar.com/avatar/8ffe68e4b19092aab184e4aa09ca4bff?s=140&d=https://a248.e.akamai.net/assets.github.com%2Fimages%2Fgravatars%2Fgravatar-140.png" width="24" />
<span class="author"><a href="/amueller">amueller</a></span>
<time class="js-relative-date" datetime="2012-02-21T09:01:22-08:00" title="2012-02-21 09:01:22">February 21, 2012</time>
<div class="commit-title">
<a href="/scikits-image/scikits-image/commit/2b6208cf3e6a44f56066a6b1ef09c1bf8c269b0a" class="message">DOC some sphinx and rst fixes</a>
</div>
<div class="participation">
<p class="quickstat"><a href="#blob_contributors_box" rel="facebox"><strong>2</strong> contributors</a></p>
<a class="avatar tooltipped downwards" title="amueller" href="/scikits-image/scikits-image/commits/master/skimage/transform/finite_radon_transform.py?author=amueller"><img height="20" src="https://secure.gravatar.com/avatar/8ffe68e4b19092aab184e4aa09ca4bff?s=140&d=https://a248.e.akamai.net/assets.github.com%2Fimages%2Fgravatars%2Fgravatar-140.png" width="20" /></a>
<a class="avatar tooltipped downwards" title="NelleV" href="/scikits-image/scikits-image/commits/master/skimage/transform/finite_radon_transform.py?author=NelleV"><img height="20" src="https://secure.gravatar.com/avatar/18f719a71cd957dc6f79655448cacad1?s=140&d=https://a248.e.akamai.net/assets.github.com%2Fimages%2Fgravatars%2Fgravatar-140.png" width="20" /></a>
</div>
<div id="blob_contributors_box" style="display:none">
<h2>Users on GitHub who have contributed to this file</h2>
<ul class="facebox-user-list">
<li>
<img height="24" src="https://secure.gravatar.com/avatar/8ffe68e4b19092aab184e4aa09ca4bff?s=140&d=https://a248.e.akamai.net/assets.github.com%2Fimages%2Fgravatars%2Fgravatar-140.png" width="24" />
<a href="/amueller">amueller</a>
</li>
<li>
<img height="24" src="https://secure.gravatar.com/avatar/18f719a71cd957dc6f79655448cacad1?s=140&d=https://a248.e.akamai.net/assets.github.com%2Fimages%2Fgravatars%2Fgravatar-140.png" width="24" />
<a href="/NelleV">NelleV</a>
</li>
</ul>
</div>
</div>
<div class="frames">
<div class="frame frame-center" data-path="skimage/transform/finite_radon_transform.py/" data-permalink-url="/scikits-image/scikits-image/blob/2eb0a2552fa40fcaa14511143863f164ab0d7adb/skimage/transform/finite_radon_transform.py" data-title="scikits-image/skimage/transform/finite_radon_transform.py at master · scikits-image/scikits-image · GitHub" data-type="blob">
<div id="files" class="bubble">
<div class="file">
<div class="meta">
<div class="info">
<span class="icon"><b class="mini-icon mini-icon-text-file"></b></span>
<span class="mode" title="File Mode">100644</span>
<span>143 lines (108 sloc)</span>
<span>3.447 kb</span>
</div>
<ul class="button-group actions">
<li>
<a class="grouped-button file-edit-link minibutton bigger lighter js-rewrite-sha" href="/scikits-image/scikits-image/edit/2eb0a2552fa40fcaa14511143863f164ab0d7adb/skimage/transform/finite_radon_transform.py" data-method="post" rel="nofollow" data-hotkey="e">Edit this file</a>
</li>
<li>
<a href="/scikits-image/scikits-image/raw/master/skimage/transform/finite_radon_transform.py" class="minibutton btn-raw grouped-button bigger lighter" id="raw-url"><span class="icon"></span>Raw</a>
</li>
<li>
<a href="/scikits-image/scikits-image/blame/master/skimage/transform/finite_radon_transform.py" class="minibutton btn-blame grouped-button bigger lighter"><span class="icon"></span>Blame</a>
</li>
<li>
<a href="/scikits-image/scikits-image/commits/master/skimage/transform/finite_radon_transform.py" class="minibutton btn-history grouped-button bigger lighter" rel="nofollow"><span class="icon"></span>History</a>
</li>
</ul>
</div>
<div class="data type-python">
<table cellpadding="0" cellspacing="0" class="lines">
<tr>
<td>
<pre class="line_numbers"><span id="L1" rel="#L1">1</span>
<span id="L2" rel="#L2">2</span>
<span id="L3" rel="#L3">3</span>
<span id="L4" rel="#L4">4</span>
<span id="L5" rel="#L5">5</span>
<span id="L6" rel="#L6">6</span>
<span id="L7" rel="#L7">7</span>
<span id="L8" rel="#L8">8</span>
<span id="L9" rel="#L9">9</span>
<span id="L10" rel="#L10">10</span>
<span id="L11" rel="#L11">11</span>
<span id="L12" rel="#L12">12</span>
<span id="L13" rel="#L13">13</span>
<span id="L14" rel="#L14">14</span>
<span id="L15" rel="#L15">15</span>
<span id="L16" rel="#L16">16</span>
<span id="L17" rel="#L17">17</span>
<span id="L18" rel="#L18">18</span>
<span id="L19" rel="#L19">19</span>
<span id="L20" rel="#L20">20</span>
<span id="L21" rel="#L21">21</span>
<span id="L22" rel="#L22">22</span>
<span id="L23" rel="#L23">23</span>
<span id="L24" rel="#L24">24</span>
<span id="L25" rel="#L25">25</span>
<span id="L26" rel="#L26">26</span>
<span id="L27" rel="#L27">27</span>
<span id="L28" rel="#L28">28</span>
<span id="L29" rel="#L29">29</span>
<span id="L30" rel="#L30">30</span>
<span id="L31" rel="#L31">31</span>
<span id="L32" rel="#L32">32</span>
<span id="L33" rel="#L33">33</span>
<span id="L34" rel="#L34">34</span>
<span id="L35" rel="#L35">35</span>
<span id="L36" rel="#L36">36</span>
<span id="L37" rel="#L37">37</span>
<span id="L38" rel="#L38">38</span>
<span id="L39" rel="#L39">39</span>
<span id="L40" rel="#L40">40</span>
<span id="L41" rel="#L41">41</span>
<span id="L42" rel="#L42">42</span>
<span id="L43" rel="#L43">43</span>
<span id="L44" rel="#L44">44</span>
<span id="L45" rel="#L45">45</span>
<span id="L46" rel="#L46">46</span>
<span id="L47" rel="#L47">47</span>
<span id="L48" rel="#L48">48</span>
<span id="L49" rel="#L49">49</span>
<span id="L50" rel="#L50">50</span>
<span id="L51" rel="#L51">51</span>
<span id="L52" rel="#L52">52</span>
<span id="L53" rel="#L53">53</span>
<span id="L54" rel="#L54">54</span>
<span id="L55" rel="#L55">55</span>
<span id="L56" rel="#L56">56</span>
<span id="L57" rel="#L57">57</span>
<span id="L58" rel="#L58">58</span>
<span id="L59" rel="#L59">59</span>
<span id="L60" rel="#L60">60</span>
<span id="L61" rel="#L61">61</span>
<span id="L62" rel="#L62">62</span>
<span id="L63" rel="#L63">63</span>
<span id="L64" rel="#L64">64</span>
<span id="L65" rel="#L65">65</span>
<span id="L66" rel="#L66">66</span>
<span id="L67" rel="#L67">67</span>
<span id="L68" rel="#L68">68</span>
<span id="L69" rel="#L69">69</span>
<span id="L70" rel="#L70">70</span>
<span id="L71" rel="#L71">71</span>
<span id="L72" rel="#L72">72</span>
<span id="L73" rel="#L73">73</span>
<span id="L74" rel="#L74">74</span>
<span id="L75" rel="#L75">75</span>
<span id="L76" rel="#L76">76</span>
<span id="L77" rel="#L77">77</span>
<span id="L78" rel="#L78">78</span>
<span id="L79" rel="#L79">79</span>
<span id="L80" rel="#L80">80</span>
<span id="L81" rel="#L81">81</span>
<span id="L82" rel="#L82">82</span>
<span id="L83" rel="#L83">83</span>
<span id="L84" rel="#L84">84</span>
<span id="L85" rel="#L85">85</span>
<span id="L86" rel="#L86">86</span>
<span id="L87" rel="#L87">87</span>
<span id="L88" rel="#L88">88</span>
<span id="L89" rel="#L89">89</span>
<span id="L90" rel="#L90">90</span>
<span id="L91" rel="#L91">91</span>
<span id="L92" rel="#L92">92</span>
<span id="L93" rel="#L93">93</span>
<span id="L94" rel="#L94">94</span>
<span id="L95" rel="#L95">95</span>
<span id="L96" rel="#L96">96</span>
<span id="L97" rel="#L97">97</span>
<span id="L98" rel="#L98">98</span>
<span id="L99" rel="#L99">99</span>
<span id="L100" rel="#L100">100</span>
<span id="L101" rel="#L101">101</span>
<span id="L102" rel="#L102">102</span>
<span id="L103" rel="#L103">103</span>
<span id="L104" rel="#L104">104</span>
<span id="L105" rel="#L105">105</span>
<span id="L106" rel="#L106">106</span>
<span id="L107" rel="#L107">107</span>
<span id="L108" rel="#L108">108</span>
<span id="L109" rel="#L109">109</span>
<span id="L110" rel="#L110">110</span>
<span id="L111" rel="#L111">111</span>
<span id="L112" rel="#L112">112</span>
<span id="L113" rel="#L113">113</span>
<span id="L114" rel="#L114">114</span>
<span id="L115" rel="#L115">115</span>
<span id="L116" rel="#L116">116</span>
<span id="L117" rel="#L117">117</span>
<span id="L118" rel="#L118">118</span>
<span id="L119" rel="#L119">119</span>
<span id="L120" rel="#L120">120</span>
<span id="L121" rel="#L121">121</span>
<span id="L122" rel="#L122">122</span>
<span id="L123" rel="#L123">123</span>
<span id="L124" rel="#L124">124</span>
<span id="L125" rel="#L125">125</span>
<span id="L126" rel="#L126">126</span>
<span id="L127" rel="#L127">127</span>
<span id="L128" rel="#L128">128</span>
<span id="L129" rel="#L129">129</span>
<span id="L130" rel="#L130">130</span>
<span id="L131" rel="#L131">131</span>
<span id="L132" rel="#L132">132</span>
<span id="L133" rel="#L133">133</span>
<span id="L134" rel="#L134">134</span>
<span id="L135" rel="#L135">135</span>
<span id="L136" rel="#L136">136</span>
<span id="L137" rel="#L137">137</span>
<span id="L138" rel="#L138">138</span>
<span id="L139" rel="#L139">139</span>
<span id="L140" rel="#L140">140</span>
<span id="L141" rel="#L141">141</span>
<span id="L142" rel="#L142">142</span>
</pre>
</td>
<td width="100%">
<div class="highlight"><pre><div class='line' id='LC1'><span class="sd">"""</span></div><div class='line' id='LC2'><span class="sd">:author: Gary Ruben, 2009</span></div><div class='line' id='LC3'><span class="sd">:license: modified BSD</span></div><div class='line' id='LC4'><span class="sd">"""</span></div><div class='line' id='LC5'><br/></div><div class='line' id='LC6'><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s">"frt2"</span><span class="p">,</span> <span class="s">"ifrt2"</span><span class="p">]</span></div><div class='line' id='LC7'><span class="n">__docformat__</span> <span class="o">=</span> <span class="s">"restructuredtext en"</span></div><div class='line' id='LC8'><br/></div><div class='line' id='LC9'><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span></div><div class='line' id='LC10'><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">roll</span><span class="p">,</span> <span class="n">newaxis</span></div><div class='line' id='LC11'><br/></div><div class='line' id='LC12'><span class="k">def</span> <span class="nf">frt2</span><span class="p">(</span><span class="n">a</span><span class="p">):</span></div><div class='line' id='LC13'> <span class="sd">"""Compute the 2-dimensional finite radon transform (FRT) for an n x n</span></div><div class='line' id='LC14'><span class="sd"> integer array.</span></div><div class='line' id='LC15'><br/></div><div class='line' id='LC16'><span class="sd"> Parameters</span></div><div class='line' id='LC17'><span class="sd"> ----------</span></div><div class='line' id='LC18'><span class="sd"> a : array_like</span></div><div class='line' id='LC19'><span class="sd"> A 2-D square n x n integer array.</span></div><div class='line' id='LC20'><br/></div><div class='line' id='LC21'><span class="sd"> Returns</span></div><div class='line' id='LC22'><span class="sd"> -------</span></div><div class='line' id='LC23'><span class="sd"> FRT : 2-D ndarray</span></div><div class='line' id='LC24'><span class="sd"> Finite Radon Transform array of (n+1) x n integer coefficients.</span></div><div class='line' id='LC25'><br/></div><div class='line' id='LC26'><span class="sd"> See Also</span></div><div class='line' id='LC27'><span class="sd"> --------</span></div><div class='line' id='LC28'><span class="sd"> ifrt2 : The two-dimensional inverse FRT.</span></div><div class='line' id='LC29'><br/></div><div class='line' id='LC30'><span class="sd"> Notes</span></div><div class='line' id='LC31'><span class="sd"> -----</span></div><div class='line' id='LC32'><span class="sd"> The FRT has a unique inverse iff n is prime. [FRT]</span></div><div class='line' id='LC33'><span class="sd"> The idea for this algorithm is due to Vlad Negnevitski.</span></div><div class='line' id='LC34'><br/></div><div class='line' id='LC35'><span class="sd"> Examples</span></div><div class='line' id='LC36'><span class="sd"> --------</span></div><div class='line' id='LC37'><br/></div><div class='line' id='LC38'><span class="sd"> Generate a test image:</span></div><div class='line' id='LC39'><span class="sd"> Use a prime number for the array dimensions</span></div><div class='line' id='LC40'><br/></div><div class='line' id='LC41'><span class="sd"> >>> SIZE = 59</span></div><div class='line' id='LC42'><span class="sd"> >>> img = np.tri(SIZE, dtype=np.int32)</span></div><div class='line' id='LC43'><br/></div><div class='line' id='LC44'><span class="sd"> Apply the Finite Radon Transform:</span></div><div class='line' id='LC45'><br/></div><div class='line' id='LC46'><span class="sd"> >>> f = frt2(img)</span></div><div class='line' id='LC47'><br/></div><div class='line' id='LC48'><span class="sd"> Plot the results:</span></div><div class='line' id='LC49'><br/></div><div class='line' id='LC50'><span class="sd"> >>> import matplotlib.pyplot as plt</span></div><div class='line' id='LC51'><span class="sd"> >>> plt.imshow(f, interpolation='nearest', cmap=plt.cm.gray)</span></div><div class='line' id='LC52'><span class="sd"> >>> plt.xlabel('Angle')</span></div><div class='line' id='LC53'><span class="sd"> >>> plt.ylabel('Translation')</span></div><div class='line' id='LC54'><span class="sd"> >>> plt.show()</span></div><div class='line' id='LC55'><br/></div><div class='line' id='LC56'><span class="sd"> References</span></div><div class='line' id='LC57'><span class="sd"> ----------</span></div><div class='line' id='LC58'><span class="sd"> .. [FRT] A. Kingston and I. Svalbe, "Projective transforms on periodic</span></div><div class='line' id='LC59'><span class="sd"> discrete image arrays," in P. Hawkes (Ed), Advances in Imaging</span></div><div class='line' id='LC60'><span class="sd"> and Electron Physics, 139 (2006)</span></div><div class='line' id='LC61'><br/></div><div class='line' id='LC62'><span class="sd"> """</span></div><div class='line' id='LC63'> <span class="k">if</span> <span class="n">a</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">2</span> <span class="ow">or</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span></div><div class='line' id='LC64'> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"Input must be a square, 2-D array"</span><span class="p">)</span></div><div class='line' id='LC65'><br/></div><div class='line' id='LC66'> <span class="n">ai</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span></div><div class='line' id='LC67'> <span class="n">n</span> <span class="o">=</span> <span class="n">ai</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span></div><div class='line' id='LC68'> <span class="n">f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">uint32</span><span class="p">)</span></div><div class='line' id='LC69'> <span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">ai</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span></div><div class='line' id='LC70'> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span></div><div class='line' id='LC71'> <span class="c"># Roll the pth row of ai left by p places</span></div><div class='line' id='LC72'> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span></div><div class='line' id='LC73'> <span class="n">ai</span><span class="p">[</span><span class="n">row</span><span class="p">]</span> <span class="o">=</span> <span class="n">roll</span><span class="p">(</span><span class="n">ai</span><span class="p">[</span><span class="n">row</span><span class="p">],</span> <span class="o">-</span><span class="n">row</span><span class="p">)</span></div><div class='line' id='LC74'> <span class="n">f</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">ai</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span></div><div class='line' id='LC75'> <span class="n">f</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">=</span> <span class="n">ai</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span></div><div class='line' id='LC76'> <span class="k">return</span> <span class="n">f</span></div><div class='line' id='LC77'><br/></div><div class='line' id='LC78'><br/></div><div class='line' id='LC79'><span class="k">def</span> <span class="nf">ifrt2</span><span class="p">(</span><span class="n">a</span><span class="p">):</span></div><div class='line' id='LC80'> <span class="sd">"""Compute the 2-dimensional inverse finite radon transform (iFRT) for</span></div><div class='line' id='LC81'><span class="sd"> an (n+1) x n integer array.</span></div><div class='line' id='LC82'><br/></div><div class='line' id='LC83'><span class="sd"> Parameters</span></div><div class='line' id='LC84'><span class="sd"> ----------</span></div><div class='line' id='LC85'><span class="sd"> a : array_like</span></div><div class='line' id='LC86'><span class="sd"> A 2-D (n+1) row x n column integer array.</span></div><div class='line' id='LC87'><br/></div><div class='line' id='LC88'><span class="sd"> Returns</span></div><div class='line' id='LC89'><span class="sd"> -------</span></div><div class='line' id='LC90'><span class="sd"> iFRT : 2-D n x n ndarray</span></div><div class='line' id='LC91'><span class="sd"> Inverse Finite Radon Transform array of n x n integer coefficients.</span></div><div class='line' id='LC92'><br/></div><div class='line' id='LC93'><span class="sd"> See Also</span></div><div class='line' id='LC94'><span class="sd"> --------</span></div><div class='line' id='LC95'><span class="sd"> frt2 : The two-dimensional FRT</span></div><div class='line' id='LC96'><br/></div><div class='line' id='LC97'><span class="sd"> Notes</span></div><div class='line' id='LC98'><span class="sd"> -----</span></div><div class='line' id='LC99'><span class="sd"> The FRT has a unique inverse iff n is prime.</span></div><div class='line' id='LC100'><span class="sd"> See [1]_ for an overview.</span></div><div class='line' id='LC101'><span class="sd"> The idea for this algorithm is due to Vlad Negnevitski.</span></div><div class='line' id='LC102'><br/></div><div class='line' id='LC103'><span class="sd"> Examples</span></div><div class='line' id='LC104'><span class="sd"> --------</span></div><div class='line' id='LC105'><br/></div><div class='line' id='LC106'><span class="sd"> >>> SIZE = 59</span></div><div class='line' id='LC107'><span class="sd"> >>> img = np.tri(SIZE, dtype=np.int32)</span></div><div class='line' id='LC108'><br/></div><div class='line' id='LC109'><span class="sd"> Apply the Finite Radon Transform:</span></div><div class='line' id='LC110'><br/></div><div class='line' id='LC111'><span class="sd"> >>> f = frt2(img)</span></div><div class='line' id='LC112'><br/></div><div class='line' id='LC113'><span class="sd"> Apply the Inverse Finite Radon Transform to recover the input</span></div><div class='line' id='LC114'><br/></div><div class='line' id='LC115'><span class="sd"> >>> fi = ifrt2(f)</span></div><div class='line' id='LC116'><br/></div><div class='line' id='LC117'><span class="sd"> Check that it's identical to the original</span></div><div class='line' id='LC118'><br/></div><div class='line' id='LC119'><span class="sd"> >>> assert len(np.nonzero(img-fi)[0]) == 0</span></div><div class='line' id='LC120'><br/></div><div class='line' id='LC121'><span class="sd"> References</span></div><div class='line' id='LC122'><span class="sd"> ----------</span></div><div class='line' id='LC123'><span class="sd"> .. [1] A. Kingston and I. Svalbe, "Projective transforms on periodic</span></div><div class='line' id='LC124'><span class="sd"> discrete image arrays," in P. Hawkes (Ed), Advances in Imaging</span></div><div class='line' id='LC125'><span class="sd"> and Electron Physics, 139 (2006)</span></div><div class='line' id='LC126'><br/></div><div class='line' id='LC127'><span class="sd"> """</span></div><div class='line' id='LC128'> <span class="k">if</span> <span class="n">a</span><span class="o">.</span><span class="n">ndim</span> <span class="o">!=</span> <span class="mi">2</span> <span class="ow">or</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="mi">1</span><span class="p">:</span></div><div class='line' id='LC129'> <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s">"Input must be an (n+1) row x n column, 2-D array"</span><span class="p">)</span></div><div class='line' id='LC130'><br/></div><div class='line' id='LC131'> <span class="n">ai</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">copy</span><span class="p">()[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span></div><div class='line' id='LC132'> <span class="n">n</span> <span class="o">=</span> <span class="n">ai</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span></div><div class='line' id='LC133'> <span class="n">f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">uint32</span><span class="p">)</span></div><div class='line' id='LC134'> <span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">ai</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span></div><div class='line' id='LC135'> <span class="k">for</span> <span class="n">m</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span></div><div class='line' id='LC136'> <span class="c"># Rolls the pth row of ai right by p places.</span></div><div class='line' id='LC137'> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">ai</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span></div><div class='line' id='LC138'> <span class="n">ai</span><span class="p">[</span><span class="n">row</span><span class="p">]</span> <span class="o">=</span> <span class="n">roll</span><span class="p">(</span><span class="n">ai</span><span class="p">[</span><span class="n">row</span><span class="p">],</span> <span class="n">row</span><span class="p">)</span></div><div class='line' id='LC139'> <span class="n">f</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">ai</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span></div><div class='line' id='LC140'> <span class="n">f</span> <span class="o">+=</span> <span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">newaxis</span><span class="p">]</span><span class="o">.</span><span class="n">T</span></div><div class='line' id='LC141'> <span class="n">f</span> <span class="o">=</span> <span class="p">(</span><span class="n">f</span> <span class="o">-</span> <span class="n">ai</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">/</span><span class="n">n</span></div><div class='line' id='LC142'> <span class="k">return</span> <span class="n">f</span></div></pre></div>
</td>
</tr>
</table>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="frame frame-loading large-loading-area" style="display:none;" data-tree-list-url="/scikits-image/scikits-image/tree-list/2eb0a2552fa40fcaa14511143863f164ab0d7adb" data-blob-url-prefix="/scikits-image/scikits-image/blob/2eb0a2552fa40fcaa14511143863f164ab0d7adb">
<img src="https://a248.e.akamai.net/assets.github.com/images/spinners/octocat-spinner-64.gif?1329872007" height="64" width="64">
</div>
</div>
<div class="context-overlay"></div>
</div>
<div id="footer-push"></div><!-- hack for sticky footer -->
</div><!-- end of wrapper - hack for sticky footer -->
<!-- footer -->
<div id="footer" >
<div class="upper_footer">
<div class="container clearfix">
<!--[if IE]><h4 id="blacktocat_ie">GitHub Links</h4><![endif]-->
<![if !IE]><h4 id="blacktocat">GitHub Links</h4><![endif]>
<ul class="footer_nav">
<h4>GitHub</h4>
<li><a href="https://github.com/about">About</a></li>
<li><a href="https://github.com/blog">Blog</a></li>
<li><a href="https://github.com/features">Features</a></li>
<li><a href="https://github.com/contact">Contact & Support</a></li>
<li><a href="https://github.com/training">Training</a></li>
<li><a href="http://enterprise.github.com/">GitHub Enterprise</a></li>
<li><a href="http://status.github.com/">Site Status</a></li>
</ul>
<ul class="footer_nav">
<h4>Tools</h4>
<li><a href="http://get.gaug.es/">Gauges: Analyze web traffic</a></li>
<li><a href="http://speakerdeck.com">Speaker Deck: Presentations</a></li>
<li><a href="https://gist.github.com">Gist: Code snippets</a></li>
<li><a href="http://mac.github.com/">GitHub for Mac</a></li>
<li><a href="http://windows.github.com/">GitHub for Windows</a></li>
<li><a href="http://mobile.github.com/">Issues for iPhone</a></li>
<li><a href="http://jobs.github.com/">Job Board</a></li>
</ul>
<ul class="footer_nav">
<h4>Extras</h4>
<li><a href="http://shop.github.com/">GitHub Shop</a></li>
<li><a href="http://octodex.github.com/">The Octodex</a></li>
</ul>
<ul class="footer_nav">
<h4>Documentation</h4>
<li><a href="http://help.github.com/">GitHub Help</a></li>
<li><a href="http://developer.github.com/">Developer API</a></li>
<li><a href="http://github.github.com/github-flavored-markdown/">GitHub Flavored Markdown</a></li>
<li><a href="http://pages.github.com/">GitHub Pages</a></li>
</ul>
</div><!-- /.site -->
</div><!-- /.upper_footer -->
<div class="lower_footer">
<div class="container clearfix">
<!--[if IE]><div id="legal_ie"><![endif]-->
<![if !IE]><div id="legal"><![endif]>
<ul>
<li><a href="https://github.com/site/terms">Terms of Service</a></li>
<li><a href="https://github.com/site/privacy">Privacy</a></li>
<li><a href="https://github.com/security">Security</a></li>
</ul>
<p>© 2012 <span title="0.23966s from fe12.rs.github.com">GitHub</span> Inc. All rights reserved.</p>
</div><!-- /#legal or /#legal_ie-->
<div class="sponsor">
<a href="http://www.rackspace.com" class="logo">
<img alt="Dedicated Server" height="36" src="https://a248.e.akamai.net/assets.github.com/images/modules/footer/rackspaces_logo.png?1329521040" width="38" />
</a>
Powered by the <a href="http://www.rackspace.com ">Dedicated
Servers</a> and<br/> <a href="http://www.rackspacecloud.com">Cloud
Computing</a> of Rackspace Hosting<span>®</span>
</div>
</div><!-- /.site -->
</div><!-- /.lower_footer -->
</div><!-- /#footer -->
<div id="keyboard_shortcuts_pane" class="instapaper_ignore readability-extra" style="display:none">
<h2>Keyboard Shortcuts <small><a href="#" class="js-see-all-keyboard-shortcuts">(see all)</a></small></h2>
<div class="columns threecols">
<div class="column first">
<h3>Site wide shortcuts</h3>
<dl class="keyboard-mappings">
<dt>s</dt>
<dd>Focus site search</dd>
</dl>
<dl class="keyboard-mappings">
<dt>?</dt>
<dd>Bring up this help dialog</dd>
</dl>
</div><!-- /.column.first -->
<div class="column middle" style='display:none'>
<h3>Commit list</h3>
<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>c <em>or</em> o <em>or</em> enter</dt>
<dd>Open commit</dd>
</dl>
<dl class="keyboard-mappings">
<dt>y</dt>
<dd>Expand URL to its canonical form</dd>
</dl>
</div><!-- /.column.first -->
<div class="column last" style='display:none'>
<h3>Pull request list</h3>
<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o <em>or</em> enter</dt>
<dd>Open issue</dd>
</dl>
<dl class="keyboard-mappings">
<dt><span class="platform-mac">⌘</span><span class="platform-other">ctrl</span> <em>+</em> enter</dt>
<dd>Submit comment</dd>
</dl>
</div><!-- /.columns.last -->
</div><!-- /.columns.equacols -->
<div style='display:none'>
<div class="rule"></div>
<h3>Issues</h3>
<div class="columns threecols">
<div class="column first">
<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>x</dt>
<dd>Toggle selection</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o <em>or</em> enter</dt>
<dd>Open issue</dd>
</dl>
<dl class="keyboard-mappings">
<dt><span class="platform-mac">⌘</span><span class="platform-other">ctrl</span> <em>+</em> enter</dt>
<dd>Submit comment</dd>
</dl>
</div><!-- /.column.first -->
<div class="column last">
<dl class="keyboard-mappings">
<dt>c</dt>
<dd>Create issue</dd>
</dl>
<dl class="keyboard-mappings">
<dt>l</dt>
<dd>Create label</dd>
</dl>
<dl class="keyboard-mappings">
<dt>i</dt>
<dd>Back to inbox</dd>
</dl>
<dl class="keyboard-mappings">
<dt>u</dt>
<dd>Back to issues</dd>
</dl>
<dl class="keyboard-mappings">
<dt>/</dt>
<dd>Focus issues search</dd>
</dl>
</div>
</div>
</div>
<div style='display:none'>
<div class="rule"></div>
<h3>Issues Dashboard</h3>
<div class="columns threecols">
<div class="column first">
<dl class="keyboard-mappings">
<dt>j</dt>
<dd>Move selection down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>k</dt>
<dd>Move selection up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o <em>or</em> enter</dt>
<dd>Open issue</dd>
</dl>
</div><!-- /.column.first -->
</div>
</div>
<div style='display:none'>
<div class="rule"></div>
<h3>Network Graph</h3>
<div class="columns equacols">
<div class="column first">
<dl class="keyboard-mappings">
<dt><span class="badmono">←</span> <em>or</em> h</dt>
<dd>Scroll left</dd>
</dl>
<dl class="keyboard-mappings">
<dt><span class="badmono">→</span> <em>or</em> l</dt>
<dd>Scroll right</dd>
</dl>
<dl class="keyboard-mappings">
<dt><span class="badmono">↑</span> <em>or</em> k</dt>
<dd>Scroll up</dd>
</dl>
<dl class="keyboard-mappings">
<dt><span class="badmono">↓</span> <em>or</em> j</dt>
<dd>Scroll down</dd>
</dl>
<dl class="keyboard-mappings">
<dt>t</dt>
<dd>Toggle visibility of head labels</dd>
</dl>
</div><!-- /.column.first -->
<div class="column last">
<dl class="keyboard-mappings">
<dt>shift <span class="badmono">←</span> <em>or</em> shift h</dt>
<dd>Scroll all the way left</dd>
</dl>
<dl class="keyboard-mappings">
<dt>shift <span class="badmono">→</span> <em>or</em> shift l</dt>
<dd>Scroll all the way right</dd>
</dl>
<dl class="keyboard-mappings">
<dt>shift <span class="badmono">↑</span> <em>or</em> shift k</dt>
<dd>Scroll all the way up</dd>
</dl>
<dl class="keyboard-mappings">
<dt>shift <span class="badmono">↓</span> <em>or</em> shift j</dt>
<dd>Scroll all the way down</dd>
</dl>
</div><!-- /.column.last -->
</div>
</div>
<div >
<div class="rule"></div>
<div class="columns threecols">
<div class="column first" >
<h3>Source Code Browsing</h3>
<dl class="keyboard-mappings">
<dt>t</dt>
<dd>Activates the file finder</dd>
</dl>
<dl class="keyboard-mappings">
<dt>l</dt>
<dd>Jump to line</dd>
</dl>
<dl class="keyboard-mappings">
<dt>w</dt>
<dd>Switch branch/tag</dd>
</dl>
<dl class="keyboard-mappings">
<dt>y</dt>
<dd>Expand URL to its canonical form</dd>
</dl>
</div>
</div>
</div>
<div style='display:none'>
<div class="rule"></div>
<div class="columns threecols">
<div class="column first">
<h3>Browsing Commits</h3>
<dl class="keyboard-mappings">
<dt><span class="platform-mac">⌘</span><span class="platform-other">ctrl</span> <em>+</em> enter</dt>
<dd>Submit comment</dd>
</dl>
<dl class="keyboard-mappings">
<dt>escape</dt>
<dd>Close form</dd>
</dl>
<dl class="keyboard-mappings">
<dt>p</dt>
<dd>Parent commit</dd>
</dl>
<dl class="keyboard-mappings">
<dt>o</dt>
<dd>Other parent commit</dd>
</dl>
</div>
</div>
</div>
</div>
<div id="markdown-help" class="instapaper_ignore readability-extra">
<h2>Markdown Cheat Sheet</h2>
<div class="cheatsheet-content">
<div class="mod">
<div class="col">
<h3>Format Text</h3>
<p>Headers</p>
<pre>
# This is an <h1> tag
## This is an <h2> tag
###### This is an <h6> tag</pre>
<p>Text styles</p>
<pre>
*This text will be italic*
_This will also be italic_
**This text will be bold**
__This will also be bold__
*You **can** combine them*
</pre>
</div>
<div class="col">
<h3>Lists</h3>
<p>Unordered</p>
<pre>
* Item 1
* Item 2
* Item 2a
* Item 2b</pre>
<p>Ordered</p>
<pre>
1. Item 1
2. Item 2
3. Item 3
* Item 3a
* Item 3b</pre>
</div>
<div class="col">
<h3>Miscellaneous</h3>
<p>Images</p>
<pre>
Format: 
</pre>
<p>Links</p>
<pre>
http://github.com - automatic!
[GitHub](http://github.com)</pre>
<p>Blockquotes</p>
<pre>
As Kanye West said:
> We're living the future so
> the present is our past.
</pre>
</div>
</div>
<div class="rule"></div>
<h3>Code Examples in Markdown</h3>
<div class="col">
<p>Syntax highlighting with <a href="http://github.github.com/github-flavored-markdown/" title="GitHub Flavored Markdown" target="_blank">GFM</a></p>
<pre>
```javascript
function fancyAlert(arg) {
if(arg) {
$.facebox({div:'#foo'})
}
}
```</pre>
</div>
<div class="col">
<p>Or, indent your code 4 spaces</p>
<pre>
Here is a Python code example
without syntax highlighting:
def foo:
if not bar:
return true</pre>
</div>
<div class="col">
<p>Inline code for comments</p>
<pre>
I think you should use an
`<addr>` element here instead.</pre>
</div>
</div>
</div>
</div>
<div class="ajax-error-message">
<p><span class="mini-icon mini-icon-exclamation"></span> Something went wrong with that request. Please try again. <a href="javascript:;" class="ajax-error-dismiss">Dismiss</a></p>
</div>
<div id="logo-popup">
<h2>Looking for the GitHub logo?</h2>
<ul>
<li>
<h4>GitHub Logo</h4>
<a href="http://github-media-downloads.s3.amazonaws.com/GitHub_Logos.zip"><img alt="Github_logo" src="https://a248.e.akamai.net/assets.github.com/images/modules/about_page/github_logo.png?1315937721" /></a>
<a href="http://github-media-downloads.s3.amazonaws.com/GitHub_Logos.zip" class="minibutton btn-download download"><span class="icon"></span>Download</a>
</li>
<li>
<h4>The Octocat</h4>
<a href="http://github-media-downloads.s3.amazonaws.com/Octocats.zip"><img alt="Octocat" src="https://a248.e.akamai.net/assets.github.com/images/modules/about_page/octocat.png?1315937721" /></a>
<a href="http://github-media-downloads.s3.amazonaws.com/Octocats.zip" class="minibutton btn-download download"><span class="icon"></span>Download</a>
</li>
</ul>
</div>
<span id='server_response_time' data-time='0.24268' data-host='fe12'></span>
</body>
</html>