-
Notifications
You must be signed in to change notification settings - Fork 0
/
glo.bib
2018 lines (1824 loc) · 97.4 KB
/
glo.bib
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
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
@PhdThesis{Thiel_hdr,
Address = {Aix-Marseille 2},
Month = {dec},
Note = {\tt http\string://www.\linebreak[0]lif-sud.univ-mrs.fr/\string thiel/hdr},
School = {Universit{\'{e}} de la M{\'{e}}diterran{\'{e}}e},
author = {Thiel, E.},
title = {G{\'{e}}om{\'{e}}trie des distances de chanfrein},
year = {2001},
}
@Article{Lachaud00a,
Publisher = {Academic Press},
author = {Lachaud, J. O. and Montanvert, A.},
title = {Continuous analogs of digital boundaries: A topological approach to iso-surfaces},
journal = {Graphical Models and Image Processing},
volume = {62},
pages = {129-164},
year = {2000},
}
@PhdThesis{havran,
School = {Czech Technical University, Faculty of Electrical Engineering, Department of Computer Science and Engineering},
Url = {http://www.cgg.cvut.cz/~havran/DISSVH/phdthesis.html},
author = {Havran, V.},
title = {Heuristic Ray Shooting Algorithms},
year = {2001},
}
@TechReport{antoine_RR,
Language = {en},
Publisher = {LIRIS UMR 5205 CNRS/INSA de Lyon/Universit{\'{e}} Claude Bernard Lyon 1/Universit{\'{e}} Lumi{\`{e}}re Lyon 2/Ecole Centrale de Lyon},
Url = {http://liris.cnrs.fr/publis/?id=2962},
author = {Vacavant, Antoine and Coeurjolly, David and Tougne, Laure},
title = {A framework for dynamic implicit curve approximation by an irregular discrete approach},
number = {RR-LIRIS-2007-020},
year = {2007},
}
@PhdThesis{dexet_these,
School = {Universit{\'{e}} de Poitiers},
author = {Dexet, M.},
title = {Architecture d{'}un modeleur g{\'{e}}om{\'{e}}trique {\`{a}} base topologique d{'}objets discrets et m{\'{e}}thodes de reconstruction en dimensions 2 et 3},
year = {2006},
}
@Article{bb20013,
Month = {mar},
Url = {http://dx.doi.org/10.1023/A:1008273227913},
author = {Latecki, L. J. and Conrad, C. and Gross, A.},
title = {Preserving Topology by a Digitization Process},
journal = {Journal of Mathematical Imaging and Vision},
volume = {8},
number = {2},
pages = {131-159},
year = {1998},
}
@InProceedings{Cook:1971,
Address = {New York},
BookTitle = {Proceedings of the 3rd Annual ACM Symposium on Theory of Computing},
author = {Cook, S. A.},
title = {The complexity of theorem-proving procedures},
pages = {151-158},
year = {1971},
}
@Book{cormen,
Isbn = {2 10 003128 7},
Publisher = {Dunod},
author = {Cormen, T. and Leiserson, C. and Rivest, R.},
title = {Introduction {\`{a}} l{'}algorithmique},
year = {1990},
}
@Article{journals/rc/RueherS97,
Url = {http://dx.doi.org/10.1023/A:1009939327927},
author = {Rueher, M. and Solnon, C.},
title = {Concurrent Cooperating Solvers over Reals},
journal = {Reliable Computing},
volume = {3},
number = {3},
pages = {325-333},
year = {1997},
}
@InProceedings{bruynooghe1994cir,
BookTitle = {Proceedings of the 1994 International Symposium on Logic Programming},
Publisher = {MIT Press},
author = {Benhamou, F. and Mc Allester, D. and Van Hentenryck, P.},
title = {CLP(intervals) Revisited},
pages = {124-138},
year = {1994},
}
@Article{snyder-92,
Month = {jul},
Note = {Proceedings SIGGRAPH{'}92.},
author = {Snyder, J. M.},
title = {Interval Analysis For Computer Graphics},
journal = {Computer Graphics},
volume = {26},
number = {2},
year = {1992},
}
@Book{mo:RatschekRokne:84,
Address = {Chichester},
Publisher = {Ellis Horwood Ltd.},
author = {Ratschek, H. and Rokne, J.},
title = {Computer Methods for the Range of Functions},
year = {1984},
}
@Book{citeulike:748022,
Abstract = {This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in scientific computing. },
Isbn = {0898711614},
Keywords = {arithmetic interval},
Publisher = {Soc for Industrial \& Applied Math},
Url = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike04-20\&path=ASIN/0898711614},
author = {Moore, R. E. and Bierbaum, F.},
title = {Methods and Applications of Interval Analysis},
year = {1979},
}
@Book{Moor66a,
Abstract = {Chapter ten of this book discusses the machine generation of Taylor coefficients. Basic recursion relations are presented.},
Address = {Englewood Cliffs, N.J.},
Keywords = {boundary value problems; wrapping effect; coordinate transformation; Taylor coefficients.},
Publisher = {Prentice-Hall},
author = {Moore, R. E.},
title = {Interval Analysis},
year = {1966},
}
@Book{Moore79a,
Address = {Philadelphia},
Publisher = {SIAM},
Series = {Studies in Applied Mathematics},
author = {Moore, R. E.},
title = {Methods and Applications of Interval Arithmetic},
year = {1979},
}
@PhdThesis{pion,
School = {Universit{\'{e}} Nice Sophia-Antipolis},
author = {Pion, S.},
title = {De la g{\'{e}}om{\'{e}}trie algorithmique au calcul g{\'{e}}om{\'{e}}trique},
year = {1999},
}
@Article{bb33412,
Month = {nov},
author = {Or, D. Cohen and Kaufman, A.},
title = {Fundamentals of Surface Voxelization},
journal = {Graphical Models and Image Processing},
volume = {57},
number = {6},
pages = {453-461},
year = {1995},
}
@Article{journals/pami/HilaireT06,
Url = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2006.127},
author = {Hilaire, X. and Tombre, K.},
title = {Robust and Accurate Vectorization of Line Drawings},
journal = {IEEE Trans. Pattern Anal. Mach. Intell},
volume = {28},
number = {6},
pages = {890-904},
year = {2006},
}
@InProceedings{Vee02,
Address = {Bordeaux, France},
BookTitle = {DGCI},
Editor = {Braquelaire, A. and Lachaud, J. O. and Vialard, A.},
Publisher = {Springer-Verlag},
Title = {LNCS},
author = {Veelaert, P.},
title = {Concurrency of Line Segments in Uncertain Geometry},
volume = {2301},
pages = {289-300},
year = {2002},
}
@Article{Vee99,
author = {Veelaert, P.},
title = {Geometric Constructions in the Digital Plane},
journal = {Journal of Mathematical Imaging and Vision},
volume = {11},
pages = {99-118},
year = {1999},
}
@Book{Herman98b,
Publisher = {Birkh{\"{a}}user, Boston},
author = {Herman, G. T.},
title = {Geometry of digital spaces},
year = {1998},
}
@Book{samet90,
Publisher = {Addison-Wesley Reading MA},
author = {Samet, H.},
title = {The Design and Analysis of Spatial Data Structures},
year = {1990},
}
@Article{citeulike_1259280,
Abstract = {A variation of the Hough Transform that is aimed at detecting digital lines has been recently suggested. Other Hough algorithms are intended to detect straight lines in the analog pre-image. These approaches are analyzed and compared in terms of the relation between the achievable resolution and the required number of accumulators, using a definition of resolution that is based on the Geometric Probability measure of straight lines. It is shown that the {`}analog{'} approach is greatly superior in high resolution applications, where a {`}digital{'} Hough Transform would generally require an infeasibly large number of accumulators.},
Keywords = {aht},
Month = {may},
Url = {http://www.sciencedirect.com/science/article/B6V15-4F5V7W4-5/2/0865c5a772b30bc3ebd5bd0759b57ab5},
author = {Kiryati, N. and Lindenbaum, M. and Bruckstein, A. M.},
title = {Digital or analog Hough transform?},
journal = {Pattern Recognition Letters},
volume = {12},
number = {5},
pages = {291-297},
year = {1991},
}
@InProceedings{citeulike_1259277,
Abstract = {Not Available},
BookTitle = {Proc. SPIE Vol. 1260, p. 148-159, Sensing and Reconstruction of Three-Dimensional Objects and Scenes, Bernd Girod; Ed.},
Editor = {Girod, B.},
Keywords = {aht},
Month = {jan},
Title = {Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference},
Url = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990SPIE.1260..148C},
author = {Cyganski, D. and Noel, W. F. and Orr, J. A.},
title = {Analytic Hough transform},
volume = {1260},
pages = {148-159},
year = {1990},
}
@InProceedings{citeulike_1259274,
Abstract = {In this paper an implementation of the analytic Hough transform (AHT) for exact digital line detection is developed that employs a new, efficient data structure. This new structure eliminates the need to represent each digital line parameter region that is developed during the analysis of the image by empolying a region divider representation. A relative storage scheme is employed thast permits reconstruction of region occupancy information during the search for digital line support. Furthermore, it is shown that all values in the AHT data structure may be stored as rational numbers with fixed and finite numerator and denominator ranges defined by the image resolution. As a result, all floating point computations are replaced by faster, fixed word-size, integer operations.},
BookTitle = {Proc. SPIE Vol. 1607, p. 298-309, Intelligent Robots and Computer Vision X: Algorithms and Techniques, David P. Casasent; Ed.},
Editor = {Casasent, D. P.},
Keywords = {aht},
Month = {feb},
Title = {Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference},
Url = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1992SPIE.1607..298L},
author = {Liu, Y. and Cyganski, D. and Vaz, R. F.},
title = {Efficient implementation of the analytic Hough transform for exact linear feature extraction},
volume = {1607},
pages = {298-309},
year = {1992},
}
@Book{citeulike_1210872,
Doi = {10.1007/11907350_1},
Keywords = {perso preimage},
Url = {http://dx.doi.org/10.1007/11907350_1},
author = {Chassery, Jean-Marc and Coeurjolly, David and Sivignon, Isabelle},
title = {Duality and Geometry Straightness, Characterization and Envelope},
year = {2006},
}
@InProceedings{citeulike_1210870,
Doi = {10.1007/11907350_35},
Keywords = {perso reversible},
Url = {http://dx.doi.org/10.1007/11907350_35},
author = {Coeurjolly, David and Dupont, Florent and Jospin, Laurent and Sivignon, Isabelle},
title = {Optimization Schemes for the Reversible Discrete Volume Polyhedrization Using Marching Cubes Simplification},
pages = {413-424},
year = {2006},
}
@Book{citeulike_1210869,
Doi = {10.1007/11907350_57},
Keywords = {digital np perso plane},
Url = {http://dx.doi.org/10.1007/11907350_57},
author = {Sivignon, Isabelle and Coeurjolly, David},
title = {Minimal Decomposition of a Digital Surface into Digital Plane Segments Is NP-Hard},
year = {2006},
}
@Book{bernoulli,
Keywords = {digital line},
author = {Bernoulli, J.},
title = {Recueil pour les astronomes},
year = {1771},
}
@Article{citeulike_1191383,
Address = {Piscataway, NJ, USA},
Doi = {10.1109/2945.582354},
Issn = {1077-2626},
Keywords = {circle sphere},
Month = {jan},
Publisher = {IEEE Educational Activities Department},
Url = {http://dx.doi.org/10.1109/2945.582354},
author = {Andres, Eric and Jacob, Marie-Andr\ée},
title = {The Discrete Analytical Hyperspheres},
journal = {IEEE Transactions on Visualization and Computer Graphics},
volume = {3},
number = {1},
pages = {75-86},
year = {1997},
}
@Article{citeulike_1191382,
Abstract = {This paper presents a new approach to discrete circles, rings, and an immediate extension to spheres. The circle, called arithmetical circle is defined by diophantine equations. The integer radius circles with the same centre pave the plane. It is easy to determine if a point is on, inside, or outside a circle. This was not easy to do with previous definitions of circles, like Bresenham{'}s. We show that the arithmetical circle extends Bresenham{'}s circle. We give an efficient incremental generation algorithm. The arithmetical circle has many extensions. We present briefly half-integer centered circles with a generation algorithm, 4-connected circles, and a general ring definition. We finish with the arithmetical sphere, an immediate 3D extension of arithmetical circle. We give elements to build a algorithm for generating the sphere.},
Doi = {10.1016/0097-8493(94)90164-3},
Keywords = {circle},
Url = {http://www.sciencedirect.com/science/article/B6TYG-48TKKK6-B/2/aeeefd3348fdac950085ea0ddf8c57a6},
author = {Andres, Eric},
title = {Discrete circles, rings and spheres},
journal = {Computers \& Graphics},
volume = {18},
number = {5},
pages = {695-706},
year = {1994},
}
@Book{citeulike_1191380,
Abstract = {Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. <B>Digital Geometry</B> is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures.<br><br>*A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision<BR>*Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data<BR>*Includes exercises, examples, and references to related or more advanced work Computer graphics is about taking mathematical representations of objects and transforming them into visual displays. Digital geometry concerns the reverse process; it is about deriving geometric information from digital pictures. There have been over one thousand papers published in the forty-year history of digital geometry, but until now, never a book that defines and covers the field. Digital Geometry: Geometric Methods for Digital Picture Analysis details the concepts, algorithms, and practices of the field. It is a discipline studied by a huge number of researchers in fields such as digital image processing, medical imaging, robotics, and of course computer graphics. However, digital geometry is relatively new and still emerging as a unique field and the lack of books has made it difficult for researchers in many areas (including applied mathematics) to benefit from this work.},
Isbn = {1-55860-861-3},
Keywords = {no-tag},
Month = {aug},
Publisher = {Morgan Kaufmann},
Url = {http://www.amazon.fr/exec/obidos/ASIN/1558608613/citeulike04-21},
author = {Klette, R. and Rosenfeld, A.},
title = {Digital Geometry: Geometric Methods for Digital Image Analysis (The Morgan Kaufmann Series in Computer Graphics)},
year = {2004},
}
@Article{Pitteway:1967:ADE,
Keywords = {circle},
author = {Pitteway, M. L. V.},
title = {Algorithm for drawing ellipses or hyperbolae with a digital plotter},
journal = {Computer Journal},
volume = {10},
year = {1967},
}
@InProceedings{BRE_1963,
BookTitle = {Proc. ACM Natl. Conf.},
Keywords = {trace},
author = {Bresenham, J.},
title = {An incremental algorithm for digital plotting},
year = {1963},
}
@Article{BOR_1986,
Keywords = {algorithms chanfrein computer digital distance image images kernel part pattern point processing programming recognition transformations},
Month = {jun},
author = {Borgefors, G.},
title = {Distance Transformations in Digital Images},
journal = {Computer Vision, Graphics, and Image Processing},
volume = {34},
number = {3},
pages = {344-371},
year = {1986},
}
@Article{LeymarieL92,
Keywords = {no-tag},
author = {Leymarie, F. F. and Levine, M. D.},
title = {Simulating the Grassfire Transform Using an Active Contour Model},
journal = {IEEE Transactions on Pattern Analysis Machine Intelligence},
volume = {14},
number = {1},
pages = {56-75},
year = {1992},
}
@Article{citeulike_1179321,
Doi = {10.1016/S0167-8655(01)00061-7},
Keywords = {fuzzy line straight},
Month = {nov},
Url = {http://www.sciencedirect.com/science/article/B6V15-43N2KNR-6/2/99af976bf9955ec3fbd3dac930c91ef5},
author = {Bigand, A. and Bouwmans, T. and Dubus, J. P.},
title = {Extraction of line segments from fuzzy images},
journal = {Pattern Recognition Letters},
volume = {22},
number = {13},
pages = {1405-1418},
year = {2001},
}
@Article{citeulike_1179315,
Abstract = {In clustering line segments into a straight line, threshold-based methods such as hierarchical clustering are often used. The line segments comprising a straight line often get misaligned due to noise. Threshold-based methods have difficulty clustering such line segments. A new cluster extraction method is proposed to cope with this problem. This method extracts fuzzy clusters one by one using matrix computation. We evaluated our clustering method using hand-written drawings and obtained promising results.},
Doi = {10.1016/0167-8655(96)00029-3},
Keywords = {fuzzy line straight},
Month = {may},
Url = {http://www.sciencedirect.com/science/article/B6V15-3VTJJ13-Y/2/1dc20dc8441e514918b7cbf16c0298da},
author = {Tsuda, Koji and Minoh, Michihiko and Ikeda, Katsuo},
title = {Extracting straight lines by sequential fuzzy clustering},
journal = {Pattern Recognition Letters},
volume = {17},
number = {6},
pages = {643-649},
year = {1996},
}
@Article{citeulike_1177670,
Abstract = {This paper is concerned with the digital line recognition problem for lines of fixed thickness in the naive and general cases. Previous incremental algorithms from Debled-Rennesson and Reveilles [A linear algorithm for segmentation of digital curves, Int. J. Pattern Recognition Artif. Intell. 9(6) (1995)] and from Buzer [A linear incremental algorithm for naive and standard digital lines and planes recognition, Graphical Models 65(1-3) (2003) 61-76] deal with the 8-connected case or with sophisticated machinery coming from linear programming. We present the first elementary method that works with any set of points (not necessarily 8-connected) and we propose a linear time algorithm under some restrictions. This paper deals with implementation details giving pseudo-code of our method. We insist on linking the recognition problem to the intrinsic properties of convex hulls.},
Doi = {10.1016/j.patcog.2006.10.005},
Keywords = {dss recognition},
Month = {jun},
Url = {http://www.sciencedirect.com/science/article/B6V14-4MD9G0V-1/2/e603aaffa660030ecda1468c98be581e},
author = {Buzer, Lilian},
title = {A simple algorithm for digital line recognition in the general case},
journal = {Pattern Recognition},
volume = {40},
number = {6},
pages = {1675-1684},
year = {2007},
}
@Article{citeulike_1177669,
Abstract = {We present a study of compression efficiency for binary objects or bi-level images for different chain-code schemes. Chain-code techniques are used for compression of bi-level images because they preserve information and allow a considerable data reduction. Furthermore, chain codes are the standard input format for numerous shape-analysis algorithms. In this work we apply chain codes to represent object with holes and we compare their compression efficiency for seven chain codes. We have also compared all these chain codes with the JBIG standard for bi-level images.},
Doi = {10.1016/j.patcog.2006.10.013},
Keywords = {chain code},
Month = {jun},
Url = {http://www.sciencedirect.com/science/article/B6V14-4MFJT64-3/2/61155eadc10fdcb2fd7e7ac78e714a4c},
author = {Sanchez-Cruz, Hermilo and Bribiesca, Ernesto and Rodriguez-Dagnino, Ramon M.},
title = {Efficiency of chain codes to represent binary objects},
journal = {Pattern Recognition},
volume = {40},
number = {6},
pages = {1660-1674},
year = {2007},
}
@Article{DBLP:journals/ijcga/Bar-YehudaB96,
Keywords = {covering square},
author = {Yehuda, Reuven B. and Hanoch, Ben E.},
title = {A linear time algorithm for covering simple polygons with similar rectangles.},
journal = {Int. J. Comput. Geometry Appl.},
volume = {6},
number = {1},
pages = {79-102},
year = {1996},
}
@Article{citeulike_1084397,
Abstract = {In this paper I am interested in transformation of digitized images by affine applications; the discrete nature of a computer screen makes this operation rather difficult. I propose to discretize real affine applications in order to obtain quasi-affine transformations which are similar to the calculus of real applications in fixed point arithmetic. Until now, the computer graphists avoided this digitization, replacing it by other methods (inverse mapping, over-sampling) which require heavy calculation. I present an algorithm for the determination of reciprocal images of a point by a quasi-affine transformation; this algorithm will permit the transformation of digitized images by discrete affine applications. In general, a one-to-one mapping is not obtained, but it is possible to determine where the points are without antecedent or those with more than one antecedent. In addition if the affine application is sufficiently dilating, the associated discrete transformation is inversible. The algorithm I propose uses integer arithmetic with only tests and additions (no multiplication nor division) so that it can be quickly performed.},
Doi = {10.1016/0097-8493(95)00008-Z},
Keywords = {transformation},
Url = {http://dx.doi.org/10.1016/0097-8493(95)00008-Z},
author = {Jacob, Marie-Andree},
title = {Transformation of digital images by discrete affine applications},
journal = {Computers \& Graphics},
volume = {19},
number = {3},
pages = {373-389},
year = {1995},
}
@Article{citeulike1029899,
Abstract = {Digital planarity is defined by digitizing Euclidean planes in the three-dimensional digital space of voxels; voxels are given either in the grid-point or the grid-cube model. The paper summarizes results (also including most of the proofs) about different aspects of digital planarity, such as supporting or separating Euclidean planes, characterizations in arithmetic geometry, periodicity, connectivity, and algorithmic solutions. The paper provides a uniform presentation, which further extends and details a recent book chapter in [R. Klette, A. Rosenfeld, Digital Geometry{--}Geometric Methods for Digital Picture Analysis, Morgan Kaufmann, San Francisco, 2004].},
Doi = {10.1016/j.dam.2006.08.004},
Keywords = {planarity},
Month = {feb},
Url = {http://dx.doi.org/10.1016/j.dam.2006.08.004},
author = {Brimkov, V. and Coeurjolly, D. and Klette, R.},
title = {Digital planarity{--}A review},
journal = {Discrete Applied Mathematics},
volume = {155},
number = {4},
pages = {468-495},
year = {2007},
}
@Article{citeulike_1023183,
Abstract = {"We introduce the notion of the medial scaffold, a hierarchical organization of the medial axis of a 3D shape in the form of a graph constructed from special medial curves connecting special medial points. A key advantage of the scaffold is that it captures the qualitative aspects of shape in a hierarchical and tightly condensed representation. We propose an efficient and exact method for computing the medial scaffold based on a notion of propagation along the scaffold itself, starting from initial sources of the flow and constructing the scaffold during the propagation. We examine this method specifically in the context of an unorganized cloud of points in 3D, e.g., as obtained from laser range finders, which typically involve hundreds of thousands of points, but the ideas are generalizable to data arising from geometrically described surface patches. The computational bottleneck in the propagation-based scheme is in finding the initial sources of the flow. We thus present several ideas to avoid the unnecessary consideration of pairs of points which cannot possibly form a medial point source, such as the {"}visibility{?'}ofapointfromanothergivenathirdpointandtheinteractionofclustersofpoints.Anapplicationofusingthemedialscaffoldfortherepresentationofpointsamplingsofreal-lifeobjectsisalsoillustrated.", author = "F.F.LeymarieandB.B.Kimia", citeulike-article-id = "1023183", journal = "PatternAnalysisandMachineIntelligence},
}
@Article{citeulike_973063,
Abstract = {Given a finite set E and a family F=E1,...,Em of subsets of E such that F covers E, the famous unicost set covering problem (USCP) is to determine the smallest possible subset of F that also covers E. We study in this paper a variant, called the Large Set Covering Problem (LSCP), which differs from the USCP in that E and the subsets Ei are not given in extension because they are very large sets that are possibly infinite. We propose three exact algorithms for solving the LSCP. Two of them determine minimal covers, while the third one produces minimum covers. Heuristic versions of these algorithms are also proposed and analysed. We then give several procedures for the computation of a lower bound on the minimum size of a cover. We finally present algorithms for finding the largest possible subset of F that does not cover E. We also show that a particular case of the LSCP is to determine irreducible infeasible sets in inconsistent constraint satisfaction problems. All concepts presented in the paper are illustrated on the k-colouring problem which is formulated as a constraint satisfaction problem.},
Doi = {10.1016/j.dam.2006.04.043},
Keywords = {minsetcover},
Month = {feb},
Url = {http://dx.doi.org/10.1016/j.dam.2006.04.043},
author = {Galinier, Philippe and Hertz, Alain},
title = {Solution techniques for the Large Set Covering Problem},
journal = {Discrete Applied Mathematics},
volume = {155},
number = {3},
pages = {312-326},
year = {2007},
}
@Article{citeulike_937376,
Abstract = {We present simple output-sensitive algorithms that construct the convex hull of a set of n points in two or three dimensions in worst-case optimal O(n log h) time and O(n) space, where h denotes the number of vertices of the convex hull. 1 Introduction Given a set P of n points in the Euclidean plane E 2 or Euclidean space E 3 , we consider the problem of computing the convex hull of P , conv(P ), which is defined as the smallest convex set containing P . The convex hull problem has...},
Keywords = {convex hull output sensitive},
Url = {http://citeseer.ist.psu.edu/181154.html},
author = {Chan,},
title = {Optimal Output-Sensitive Convex Hull Algorithms in Two and Three Dimensions},
journal = {GEOMETRY: Discrete \& Computational Geometry},
volume = {16},
year = {1996},
}
@Article{citeulike_910101,
Abstract = {A survey of the development of the marching cubes algorithm [W. Lorensen, H. Cline, Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics 1987; 21(4):163-9], a well-known cell-by-cell method for extraction of isosurfaces from scalar volumetric data sets, is presented. The paper{'}s primary aim is to survey the development of the algorithm and its computational properties, extensions, and limitations (including the attempts to resolve its limitations). A rich body of publications related to this aim are included. Representative applications and spin-off work are also considered and related techniques are briefly discussed.},
Doi = {10.1016/j.cag.2006.07.021},
Keywords = {marching-cubes},
Month = {oct},
Url = {http://dx.doi.org/10.1016/j.cag.2006.07.021},
author = {Newman, T. S. and Yi, H.},
title = {A survey of the marching cubes algorithm},
journal = {Computers \& Graphics},
volume = {30},
number = {5},
pages = {854-879},
year = {2006},
}
@InProceedings{Blum:1967,
BookTitle = {Models for the Perception of Speech and Visual Forms},
Keywords = {ma occlusion shape skeleton vision},
Publisher = {MIT Press},
author = {Blum, H.},
title = {A transformation for extracting descriptors of shape},
pages = {362-380},
year = {1967},
}
@Article{bb17374,
Keywords = {digitization},
author = {Ronse, C. and Tajine, M.},
title = {Discretization in Hausdorff Space},
journal = {Journal of Mathematical Imaging \& Vision},
volume = {12},
number = {3},
pages = {219-242},
year = {2000},
}
@Article{citeulike_869887,
Abstract = {We study a new framework for the discretization of closed sets and operators based on Hausdorff metric: a Hausdorff discretization of an n-dimensional Euclidean figure F of , in the discrete space , is a subset S of whose Hausdorff distance to F is minimal ([rho] can be considered as the resolution of the discrete space ); in particular such a discretization depends on the choice of a metric on . This paper is a continuation of our works (Ronse and Tajine, J. Math. Imaging Vision 12 (3) (2000) 219; Hausdorff discretization for cellular distances, and its relation to cover and supercover discretization (to be revised for JVCIR), 2000, Wagner et al., An Approach to Discretization Based on the Hausdorff Metric. I. ISMM{'}98, Kluwer Academic Publishers, Dordrecht, 1998, pp. 67-74), in which we have studied some properties of Hausdorff discretizations of compact sets.In this paper, we study the properties of Hausdorff discretization for metrics induced by a norm and we refine this study for the class of homogeneous metrics. We prove that for such metrics the popular covering discretizations are Hausdorff discretizations. We also compare the Hausdorff discretization with the Bresenham discretization (Bresenham, IBM Systems J. 4 (1) (1965) 25). Actually, we prove that the Bresenham discretization of a straight line of is not always a good discretization relatively to the Hausdorff metric. This result is an extension of Tajine et al. (Hausdorff Discretization and its Comparison with other Discretization Schemes, DGCI{'}99, Paris, Lecture Notes in Computer Sciences Vol. 1568, Springer, Berlin, 1999, pp. 399-410), in which we prove the same result for a segment of . Finally, we study how some topological properties of the Euclidean plane are translated in discrete space for Hausdorff discretizations. Actually, we prove that a Hausdorff discretization of a connected closed set is 8-connected and its maximal Hausdorff discretization is 4-connected for homogeneous metrics.},
Doi = {10.1016/S0304-3975(01)00082-2},
Keywords = {digitization},
Month = {jun},
Url = {http://dx.doi.org/10.1016/S0304-3975(01)00082-2},
author = {Tajine, Mohamed and Ronse, Christian},
title = {Topological properties of Hausdorff discretization, and comparison to other discretization schemes},
journal = {Theoretical Computer Science},
volume = {283},
number = {1},
pages = {243-268},
year = {2002},
}
@Article{Reiss91,
Bibkey = {Reiss},
Keywords = {moments},
Month = {aug},
author = {Reiss, T. H.},
title = {The Revised Fundamental Theorem of Moment Invarients},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {PAMI-13},
number = {8},
pages = {830-834},
year = {1991},
}
@Article{citeulike_816390,
Abstract = {Affine moment invariants (AMIs) have been derived recently by Flusser and Suk (1992). In this paper, the AMIs are used as the features for recognition of handwritten characters independent of their size, slant and other variations. A comparison with classical moment invariants is also given.},
Doi = {10.1016/0167-8655(94)90092-2},
Keywords = {computation moments},
Month = {apr},
Url = {http://dx.doi.org/10.1016/0167-8655(94)90092-2},
author = {Flusser, Jan and Suk, Tomas},
title = {Affine moment invariants: a new tool for character recognition},
journal = {Pattern Recognition Letters},
volume = {15},
number = {4},
pages = {433-436},
year = {1994},
}
@Article{citeulike_816388,
Abstract = {This paper presents an overview of feature extraction methods for off-line recognition of segmented (isolated) characters. Selection of a feature extraction method is probably the single most important factor in achieving high recognition performance in character recognition systems. Different feature extraction methods are designed for different representations of the characters, such as solid binary characters, character contours, skeletons (thinned characters) or gray-level subimages of each individual character. The feature extraction methods are discussed in terms of invariance properties, reconstructability and expected distortions and variability of the characters. The problem of choosing the appropriate feature extraction method for a given application is also discussed. When a few promising feature extraction methods have been identified, they need to be evaluated experimentally to find the best method for the given application.},
Doi = {10.1016/0031-3203(95)00118-2},
Keywords = {character computation moments},
Month = {apr},
Url = {http://dx.doi.org/10.1016/0031-3203(95)00118-2},
author = {Due, and Jain, Anil K. and Taxt, Torfinn},
title = {Feature extraction methods for character recognition-A survey},
journal = {Pattern Recognition},
volume = {29},
number = {4},
pages = {641-662},
year = {1996},
}
@Article{citeulike_816387,
Abstract = {Zernike moments which are superior to geometric moments because of their special properties of image reconstruction and immunity to noise, suffer from several discretization errors. These errors lead to poor quality of reconstructed image and wide variations in the numerical values of the moments. The predominant factor, as observed in this paper, is due to the discrete integer implementation of the steps involved in moment calculation. It is shown in this paper that by modifying the algorithms to include discrete float implementation, the quality of the reconstructed image improves significantly and the first-order moment becomes zero. Low-order Zernike moments have been found to be stable under linear transformations while the high-order moments have large variations. The large variations in high-order moments, however, do not greatly affect the quality of the reconstructed image, implying that they should be ignored when numerical values of moments are used as features. The 11 functions based on geometric moments have also been found to be stable under linear transformations and thus these can be used as features. Pixel level analysis of the images has been carried out to strengthen the results.},
Doi = {10.1016/j.patcog.2006.05.025},
Keywords = {computation moments},
Month = {nov},
Url = {http://dx.doi.org/10.1016/j.patcog.2006.05.025},
author = {Singh, Chandan},
title = {Improved quality of reconstructed images using floating point arithmetic for moment calculation},
journal = {Pattern Recognition},
volume = {39},
number = {11},
pages = {2047-2064},
year = {2006},
}
@Book{citeulike_815349,
Isbn = {2-253-13013-3},
Keywords = {mathematics},
Month = {mar},
Publisher = {Le Livre de Poche},
Series = {La pochoth{\`{e}}que, Encyclop{\'{e}}dies d{'}aujourd{'}hui},
Url = {Paperback},
author = {Reinhardt, F. and Soeder, H.},
title = {Atlas des math{\'{e}}matiques},
year = {1997},
}
@Article{citeulike_813768,
Abstract = {Geometric moments (GMs) have been successfully used in pattern recognition and object orientation determination; however, their computation is too expensive, which limits the application of GMs. In this paper, a new method is proposed to calculate geometric moments. Firstly, the pixel-based calculation of GMs is converted into the line-segment-based calculation, then a new approach is proposed to calculate the line-segment integrals. After line-segment integrals are calculated, Hatamian{'}s filter method is introduced to calculate GMs, which further simplifies the moment calculation. Finally, this method is compared with the known results, which show that our method can calculate any complicated object moments, and also efficiently reduces both addition and multiplication complexity.},
Doi = {10.1016/0031-3203(93)90092-B},
Keywords = {moments},
Month = {jan},
Url = {http://dx.doi.org/10.1016/0031-3203(93)90092-B},
author = {Li, Bing-Cheng},
title = {A new computation of geometric moments},
journal = {Pattern Recognition},
volume = {26},
number = {1},
pages = {109-113},
year = {1993},
}
@Article{citeulike_813454,
Abstract = {The three-dimensional Cartesian geometric moments (for short 3-D moments) are important features for 3-D object recognition and shape description. To calculate the moments of objects in a 3-D image by a straightforward method requires a large number of computing operations. Some authors have proposed fast algorithms to compute the 3-D moments. However, the problem of computation has not been well solved since all known methods require computations of orderN3, assuming that the object is represented by anNxNxNvoxel image. In this paper, we present a discrete divergence theorem which can be used to compute the sum of a function over ann-dimensional discrete region by a summation over the discrete surface enclosing the region. As its corollaries, we give a discrete Gauss{'}s theorem for 3-D discrete objects and a discrete Green{'}s theorem for 2-D discrete objects. Using a fast surface tracking algorithm and the discrete Gauss{'}s theorem, we design a new method to compute the geometric moments of 3-D binary objects as observed in 3-D discrete images. This method reduces the computational complexity significantly, requiring computation ofO(N2). This reduction is demonstrated experimentally on two 3-D objects. We also generalize the method to deal with high-dimensional images. Some 3-D moment invariants and shape features are also discussed.},
Doi = {10.1006/gmip.1997.0418},
Keywords = {green moments},
Month = {mar},
Url = {http://dx.doi.org/10.1006/gmip.1997.0418},
author = {Yang, Luren and Albregtsen, Fritz and Taxt, Torfinn},
title = {Fast Computation of Three-Dimensional Geometric Moments Using a Discrete Divergence Theorem and a Generalization to Higher Dimensions},
journal = {Graphical Models and Image Processing},
volume = {59},
number = {2},
pages = {97-108},
year = {1997},
}
@Article{citeulike_812357,
Abstract = {Various types of moments have been used to recognize image patterns in a number of applications. A number of moments are evaluated and some fundamental questions are addressed, such as image-representation ability, noise sensitivity, and information redundancy. Moments considered include regular moments, Legendre moments, Zernike moments, pseudo-Zernike moments, rotational moments, and complex moments. Properties of these moments are examined in detail and the interrelationships among them are discussed. Both theoretical and experimental results are presented},
Keywords = {moments zernike},
Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=3913},
author = {Teh, C. H. and Chin, R. T.},
title = {On image analysis by the methods of moments},
journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
volume = {10},
number = {4},
pages = {496-513},
year = {1988},
}
@Article{journals/cad/NovotniK04,
Keywords = {zernike},
Url = {http://dx.doi.org/10.1016/j.cad.2004.01.005},
author = {Novotni, M. and Klein, R.},
title = {Shape retrieval using 3D Zernike descriptors},
journal = {Computer-Aided Design},
volume = {36},
number = {11},
pages = {1047-1062},
year = {2004},
}
@InProceedings{bb33207,
BookTitle = {Scandinavian Conference on Image Analysis},
Keywords = {zernike},
author = {Canterakis, N.},
title = {3D Zernike Moments and Zernike Affine Invariants for 3D Image Analysis and Recognition},
year = {1999},
}
@Article{citeulike_761605,
Abstract = {Computerized image analysis makes statements about the continuous world by looking at a discrete representation. Therefore, it is important to know precisely which information is preserved during digitization. We analyze this question in the context of shape recognition. Existing results in this area are based on very restricted models and thus not applicable to real imaging situations. We present generalizations in several directions: first, we introduce a new shape similarity measure that approximates human perception better. Second, we prove a geometric sampling theorem for arbitrary dimensional spaces. Third, we extend our sampling theorem to two-dimensional images that are subjected to blurring by a disk point spread function. Our findings are steps towards a general sampling theory for shapes that shall ultimately describe the behavior of real optical systems.},
Doi = {10.1016/j.imavis.2004.06.003},
Keywords = {digitization resolution sampling},
Month = {feb},
Url = {http://dx.doi.org/10.1016/j.imavis.2004.06.003},
author = {Stelldinger, Peer and Kothe, Ullrich},
title = {Towards a general sampling theory for shape preservation},
journal = {Image and Vision Computing},
volume = {23},
number = {2},
pages = {237-248},
year = {2005},
}
@Book{citeulike_707502,
Doi = {10.1007/11774938_23},
Keywords = {digital hyperplane iwcia2006 recognition},
Month = {jan},
Url = {http://dx.doi.org/10.1007/11774938_23},
author = {Coeurjolly, David and Brimkov, Valentin},
title = {Computational Aspects of Digital Plane and Hyperplane Recognition},
volume = {4040},
year = {2006},
}
@Article{citeulike_695920,
Address = {New York, NY, USA},
Doi = {10.1145/358172.358409},
Issn = {0001-0782},
Keywords = {axis hma medial quadtree},
Month = {sep},
Publisher = {ACM Press},
Url = {http://portal.acm.org/citation.cfm?id=358409},
author = {Samet, Hanan},
title = {A quadtree medial axis transform},
journal = {Commun. ACM},
volume = {26},
number = {9},
pages = {680-693},
year = {1983},
}
@InProceedings{chirkov,
Address = {N. Novgorod, Nizhegorod University Press},
BookTitle = {"2nd International Conference{``}Mathematical Algorithms{"}", citeulike-article-id = "695492", editor = "V.E.AlekseevandM.A.AntonetsandV.N.Shevchenko", keywords = "bibtex-importintergeriwcia2006programming", pages = "169{--}174", priority = "2", title = "Ontherelationofupperboundsonthenumberofverticesoftheconvexhulloftheintegerpointsofapolyhedronwithitsmetriccharacteristics(inRussian},
author = {Chirkov, A. V.},
}
@Proceedings{citeulike_677853,
Abstract = {This paper proposes a novel hypergraph skeletal representation for 3D shape based on a formal derivation of the generic structure of its medial axis. By classifying each skeletal point by its order of contact, we shout that generically the medial axis consists of five types of points which are then organized into sheets, curves, and points: (i) sheets (manifolds with boundary) which are the locus of bitangent spheres with regular tangency<sup>1</sup> A<sub>1</sub><sup>2</sup>. Two types of curves (ii) the intersection curve of three sheets and the locus of centers of tritangent spheres, A<sub>1</sub><sup>3</sup>, and (iii) the boundary of sheets which are the locus of centers of spheres whose radius equals the larger principle curvature, i.e., higher order contact A<sub>3</sub> points; and two types of points (iv) centers of quad-tangent spheres, A<sub>1</sub><sup>4</sup>, and, (v) centers of spheres with one regular tangency and one higher order tangency, A<sub>1 </sub>A<sub>3</sub> The geometry of the 3D medial axis thus consists of sheets (A<sub>1</sub><sup>2</sup>) bounded by one type of curve (A<sub>3 </sub>) on their free end, which corresponds to ridges on the surface, and attached to two other sheets at another type of curves (A<sub>1</sub><sup>3</sup>), which support a generalized cylinder description. The A<sub>3</sub> curves can only end in A<sub>1</sub>A<sub>3</sub> points where they must meet an A<sub>1</sub> <sup>3</sup> curve. The A<sub>1</sub><sup>3</sup> curves can either meet one A<sub>3</sub> curve or meet three other A<sub>1</sub><sup>3</sup> curve at an A<sub>1</sub><sup>4</sup> point. This formal result leads to a compact representation for 3D shape, referred to as the medial axis hypergraph representation consisting of nodes (A<sub>1</sub><sup>4</sup> and A<sub>1</sub>A<sub>3</sub> points), links between pairs of nodes (A <sub>1</sub><sup>3</sup> and A<sub>3</sub> curves) and hyperlinks between groups of links (A<sub>1</sub><sup>2</sup> sheets). The description of the local geometry at nodes by itself is sufficient to capture qualitative aspects of shapes, in analogy to 2D. We derive a pointwise reconstruction formula to reconstruct a surface from this medial axis hypergraph. Thus, the hypergraph completely characterizes 3D shape and lays the theoretical foundation for its use in recognition, morphing, design and manipulation of shapes},
Keywords = {axis medial},
Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=855870},
author = {Giblin, P. and Kimia, B. B.},
title = {A formal classification of 3D medial axis points and their local geometry},
volume = {1},
pages = {566-573},
year = {2000},
}
@Article{citeulike_677854,
Abstract = {This paper proposes a novel hypergraph skeletal representation for 3D shape based on a formal derivation of the generic structure of its medial axis. By classifying each skeletal point by its order of contact, we show that, genetically, the medial axis consists of five types of points, which are then organized into sheets, curves, and points: 1) sheets (manifolds with boundary) which are the locus of bitangent spheres with regular tangency A/sub 1//sup 2/ (A/sub k//sup n/ notation means n distinct k-fold tangencies of the sphere of contact, as explained in the text); two types of curves, 2) the intersection curve of three sheets and the locus of centers of tritangent spheres, A/sub 1//sup 3/, and 3) the boundary of sheets, which are the locus of centers of spheres whose radius equals the larger principal curvature, i.e., higher order contact A/sub 3/ points; and two types of points, 4) centers of quad-tangent spheres, A/sub 1//sup 4/, and 5) centers of spheres with one regular tangency and one higher order tangency, A/sub 1/A/sub 3/. The geometry of the 3D medial axis thus consists of sheets (A/sub 1//sup 2/) bounded by one type of curve (A/sub 3/) on their free end, which corresponds to ridges on the surface, and attached to two other sheets at another type of curve (A/sub 1//sup 3/), which support a generalized cylinder description. The A/sub 3/ curves can only end in A/sub 1/ A/sub 3/ points where they must meet an A/sub 1//sup 3/ curve. The A/sub 1//sup 3/ curves meet together in fours at an A/sub 1//sup 4/ point. This formal result leads to a compact representation for 3D shape, referred to as the medial axis hypergraph representation consisting of nodes (A/sub 1//sup 4/ and A/sub 1/ A/sub 3/ points), links between pairs of nodes (A/sub 1//sup 3/ and A/sub 3/ curves) and hyperlinks between groups of links (A/sub 1//sup 2/ sheets). The description of the local geometry at nodes by itself is sufficient to capture qualitative aspects of shapes, in analogy to 2D. We derive a pointwise reconstruction formula to reconstruct a surface from this medial axis hypergraph together with the radius function. Thus, this information completely characterizes 3D shape and lays the theoretical foundation for its use in recognition, morphing, design, and man- ipulation of shapes.},
Keywords = {axis medial},
Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1262192},
author = {Giblin, P. and Kimia, B. B.},
title = {A formal classification of 3D medial axis points and their local geometry},
journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
volume = {26},
number = {2},
pages = {238-251},
year = {2004},
}
@Article{citeulike_677703,
Abstract = {A naive digital plane is a subset of points verifying h[less-than-or-equals, slant]ax+by+czh+max |a|,|b|,|c| , where . Given a finite unstructured subset of , the problem of the digital plane recognition is to determine whether there exists a naive digital plane containing it. This question is rather classical in the field of digital geometry (also called discrete geometry). We suggest in this paper a new algorithm to solve it. Its asymptotic complexity is bounded by O(n7) but its behavior seems to be linear in practice. It uses an original strategy of optimization in a set of triangular facets (triangles). The code is short and elementary (less than 300 lines) and available on http://www.loria.fr/ debled/plane.},
Doi = {10.1016/j.dam.2005.02.026},
Keywords = {digital plane recognition},
Month = {oct},
Url = {http://dx.doi.org/10.1016/j.dam.2005.02.026},
author = {Gerard, Y. and Debled-Rennesson, I. and Zimmermann, P.},
title = {An elementary digital plane recognition algorithm},
journal = {Discrete Applied Mathematics},
volume = {151},
number = {1-3},
pages = {169-183},
year = {2005},
}
@Book{citeulike_667664,
Doi = {10.1007/11590316_62},
Keywords = {irregular isothetic pourantoine},
Month = {dec},
Url = {http://dx.doi.org/10.1007/11590316_62},
author = {Bhowmick, Partha and Biswas, Arindam and Bhattacharya, Bhargab},
title = {Isothetic Polygonal Approximations of a 2D Object on Generalized Grid},
volume = {3776},
year = {2005},
}
@Article{citeulike_636693,
Abstract = {Medial Axis (MA), also known as Centres of Maximal Disks, is a useful representation of a shape for image description and analysis. MA can be computed on a distance transform, where each point is labelled to its distance to the background. Recent algorithms allow one to compute Squared Euclidean Distance Transform (SEDT) in linear time in any dimension. While these algorithms provide exact measures, the only known method to characterise MA on SEDT, using local tests and Look-Up Tables (LUT), is limited to 2D and small distance values [Borgefors, et al., Seventh Scandinavian Conference on Image Analysis, 1991]. We have proposed [Remy, et al., Pat. Rec. Lett. 23 (2002) 649] an algorithm which computes the LUT and the neighbourhood to be tested in the case of chamfer distances. In this article, we adapt our algorithm for SEDT in arbitrary dimension and show that results have completely different properties.},
Doi = {10.1016/j.imavis.2004.06.007},
Keywords = {edt nd},
Month = {feb},
Url = {http://dx.doi.org/10.1016/j.imavis.2004.06.007},
author = {Remy, E. and Thiel, E.},
title = {Exact medial axis with euclidean distance},
journal = {Image and Vision Computing},
volume = {23},
number = {2},
pages = {167-175},
year = {2005},
}
@Article{megiddo_LP,
Address = {New York, NY, USA},
Doi = {10.1145/2422.322418},
Issn = {0004-5411},
Keywords = {computationalgeometry hyperplane lp},
Month = {jan},
Publisher = {ACM Press},
Url = {http://portal.acm.org/citation.cfm?id=322418},
author = {Megiddo, Nimrod},
title = {Linear Programming in Linear Time When the Dimension Is Fixed},
journal = {J. ACM},
volume = {31},
number = {1},
pages = {114-127},
year = {1984},
}
@Article{citeulike_620178,
Address = {New York, NY, USA},
Doi = {10.1145/1118890.1118893},
Issn = {0360-0300},
Keywords = {art3d indexation representations},
Month = {dec},
Publisher = {ACM Press},
Url = {http://portal.acm.org/citation.cfm?id=1118890.1118893},
author = {Bustos, Benjamin and Keim, Daniel A. and Saupe, Dietmar and Schreck, Tobias and Vrani\ć, Dejan V.},
title = {Feature-based similarity search in 3D object databases},
journal = {ACM Comput. Surv.},
volume = {37},
number = {4},
pages = {345-387},
year = {2005},
}
@Article{citeulike_617169,
Abstract = {Two new methods for computing the rectilinearity of polygons are presented. They provide shape measures and estimates of canonical orientations which can be used in applications such as shape retrieval, object classification, image segmentation, etc. Examples are presented demonstrating their use in skew correction of scanned documents, deprojection of aerial photographs of buildings, and scale selection for curve simplification. Furthermore, testing has been carried out on synthetic data and with human subjects to verify that the measures do indeed produce perceptually meaningful results.},
Doi = {10.1016/j.cviu.2005.01.003},
Keywords = {polygon rectilinearity},
Month = {aug},
Url = {http://dx.doi.org/10.1016/j.cviu.2005.01.003},
author = {Rosin, Paul L. and Zunic, Jovisa},
title = {Measuring rectilinearity},
journal = {Computer Vision and Image Understanding},
volume = {99},
number = {2},
pages = {175-188},
year = {2005},
}
@Article{citeulike_613266,
Abstract = {Digital geometry is very different from Euclidean geometry in many ways and the intersection of two digital lines or planes is often used to illustrate those differences. Nevertheless, while digital lines and planes are widely studied in many areas, very few works deal with the intersection of such objects. In this paper, we investigate the geometrical and arithmetical properties of those objects. More precisely, we give some new results about the connectivity, periodicity, and minimal parameters of the intersection of two digital lines or planes.},
Doi = {10.1016/j.gmod.2004.05.002},
Keywords = {digital intersection line},
Month = {jul},
Url = {http://dx.doi.org/10.1016/j.gmod.2004.05.002},
author = {Sivignon, Isabelle and Dupont, Florent and Chassery, Jean-Marc},
title = {Digital Intersections: minimal carrier, connectivity, and periodicity properties},
journal = {Graphical Models},
volume = {66},
number = {4},
pages = {226-244},
year = {2004},
}
@Article{citeulike_612352,
Abstract = {A simple online algorithm for partitioning of a digital curve into digital straight-line segments of maximal length is given. The algorithm requires <e1>O</e1>(<e1>N</e1>) time and <e1>O</e1>(1) space and is therefore optimal. Efficient representations of the digital segments are obtained as byproducts. The algorithm also solves a number-theoretical problem concerning nonhomogeneous spectra of numbers},
Keywords = {decomposition dss lines segmentation},
Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=232082},
author = {Linderbaum, M. and Bruckstein, A.},
title = {On recursive, O(N) partitioning of a digitized curve into digital straight segments},
journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
volume = {15},
number = {9},
pages = {949-953},
year = {1993},
}
@Article{citeulike_612351,
Abstract = {The number of digital straight lines on an <e1>N</e1>?e1>N </e1> grid is shown. A digital straight line is equivalent to a linear dichotomy of points on a square grid. The result is obtained by determining a way of counting the number of linearly separable dichotomies of points on the plane that are not necessarily in general position. The analysis is easily modified to provide a simple solution to a similar problem considered by C. Berenstein and D. Lavine (1988) on the number of digital straight lines from a fixed starting point},
Keywords = {dss lines},
Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=50392},
author = {Koplowitz, J. and Lindenbaum, M. and Bruckstein, A.},
title = {The number of digital straight lines on an $N\times N$ grid},
journal = {Information Theory, IEEE Transactions on},
volume = {36},
number = {1},
pages = {192-197},
year = {1990},
}
@InProceedings{aupperle88a,
BookTitle = {Proceedings of the 26th Annual Allerton Conf. Comm. Control Comput.},
Keywords = {axis bibtex-import covering decomposition graph image medial np-completeness polygons processing squares theory},
author = {Aupperle, L. J. and Conn, H. E. and Keil, J. M. and O{'}Rourke, J.},
title = {Covering orthogonal polygons with squares},
pages = {97-106},
year = {1988},
}
@Article{p3sat,
Keywords = {3sat np p3sat},
Url = {http://locus.siam.org/SICOMP/volume-11/art_0211025.html},
author = {Lichtenstein, David},
title = {Planar Formulae and Their Uses},
journal = {SIAM Journal on Computing},
volume = {11},
number = {2},
pages = {329-343},
year = {1982},
}
@Article{citeulike_611322,
Abstract = {A new analytical description model, called the standard model, for the discretization of Euclidean linear objects (point, m-flat, m-simplex) in dimension n is proposed. The objects are defined analytically by inequalities. This allows a global definition independent of the number of discrete points. A method is provided to compute the analytical description for a given linear object. A discrete standard model has many properties in common with the supercover model from which it derives. However, contrary to supercover objects, a standard object does not have bubbles. A standard object is (n-1)-connected, tunnel-free and bubble-free. The standard model is geometrically consistent. The standard model is well suited for modelling applications.},
Doi = {10.1016/S1524-0703(03)00004-3},
Keywords = {digitization line model},
Month = {may},
Url = {http://dx.doi.org/10.1016/S1524-0703(03)00004-3},
author = {Andres, Eric},
title = {Discrete linear objects in dimension n: the standard model},
journal = {Graphical Models},
volume = {65},
number = {1-3},
pages = {92-111},
year = {2003},
}
@Article{citeulike_611269,
Abstract = {A digital arc is called \‘straight\’ if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970{'}s, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many algorithms for determining whether a digital arc is straight have been defined. This paper reviews the literature on digital straightness and discusses its relationship to other concepts of geometry, the theory of words, and number theory.},
Doi = {10.1016/S1571-0661(04)80976-9},
Keywords = {discrete dss line},
Month = {aug},
Url = {http://dx.doi.org/10.1016/S1571-0661(04)80976-9},
author = {Rosenfeld, A. and Klette, R.},
title = {Digital Straightness},
journal = {Electronic Notes in Theoretical Computer Science},
volume = {46},
pages = {1-32},
year = {2001},
}
@Article{citeulike_611268,
Abstract = {A digital arc is called \‘straight\’ if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970s, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many algorithms for determining whether a digital arc is straight have been defined. This paper reviews the literature on digital straightness and discusses its relationship to other concepts of geometry, the theory of words, and number theory.},
Doi = {10.1016/j.dam.2002.12.001},
Keywords = {dss},
Month = {apr},
Url = {http://dx.doi.org/10.1016/j.dam.2002.12.001},
author = {Klette, R. and Rosenfeld, A.},
title = {Digital straightness{--}a review},
journal = {Discrete Applied Mathematics},
volume = {139},
number = {1-3},
pages = {197-230},
year = {2004},
}
@Book{citeulike_602537,
Abstract = {This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added.},
Isbn = {3-540-65620-0},
Keywords = {computationalgeometry},
Month = {feb},
Publisher = {Springer},
Url = {http://www.amazon.ca/exec/obidos/redirect?tag=citeulike04-20\&path=ASIN/3540656200},
author = {Berg, Mark de and Kreveld, Marc van and Overmars, Mark and Schwarzkopf, Otfried},
title = {Computational Geometry},
year = {2000},
}
@Article{citeulike_605834,
Abstract = {In this article, we present a discrete definition of the classical visibility in computational geometry based on digital straight lines. We present efficient algorithms to compute the set of pixels in a non-convex domain that are visible from a source pixel. Based on these definitions, we define discrete geodesic paths in discrete domain with obstacles. This allows us to introduce a new geodesic metric in discrete geometry.},
Doi = {10.1016/j.patrec.2003.12.002},
Keywords = {geodesic visibility},
Month = {apr},
Url = {http://dx.doi.org/10.1016/j.patrec.2003.12.002},
author = {Coeurjolly, D. and Miguet, S. and Tougne, L.},
title = {2D and 3D visibility in discrete geometry: an application to discrete geodesic paths},
journal = {Pattern Recognition Letters},
volume = {25},
number = {5},
pages = {561-570},
year = {2004},
}
@Article{citeulike_605833,
Abstract = {This paper concerns the digital circle recognition problem, especially in the form of the circular separation problem. General fundamentals, based on classical tools, as well as algorithmic details, are given (the latter by providing pseudo-code for major steps of the algorithm). After recalling the geometrical meaning of the separating circle problem, we present an incremental algorithm to segment a discrete curve into digital arcs.},
Doi = {10.1016/j.dam.2003.08.003},
Keywords = {arc digital recognition},
Month = {apr},
Url = {http://dx.doi.org/10.1016/j.dam.2003.08.003},
author = {Coeurjolly, D. and Gerard, Y. and Reveilles, and Tougne, L.},
title = {An elementary algorithm for digital arc segmentation},
journal = {Discrete Applied Mathematics},
volume = {139},
number = {1-3},
pages = {31-50},
year = {2004},
}
@Article{citeulike_605832,
Abstract = {On the classical discrete grid, the analysis of digital straight lines (DSL for short) has been intensively studied for nearly half a century. In this article, we are interested in a discrete geometry on irregular grids. More precisely, our goal is to define geometrical properties on irregular isothetic grids that are tilings of the Euclidean plane with different sized axis parallel rectangles. On these irregular isothetic grids, we define digital straight lines with recognition algorithms and a process to reconstruct an invertible polygonal representation of an irregular discrete curve.},
Doi = {10.1016/j.cag.2005.10.009},
Keywords = {irregular isothetic lines straight},
Month = {feb},
Url = {http://dx.doi.org/10.1016/j.cag.2005.10.009},