Digital representation schemes for 3D curves

Pattern Recognition

Volumn 30, Issue 11, 1997, Pages 1803-1816

  Jonas, Amnon ^a,b   Kiryati, Nahum ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b Phasecom Ltd   (Israel)

Author keywords

3 D discrete curve; Chain code; Cube quantization; Digital line; Grid intersect quantization; Three dimensional digitization scheme

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); IMAGE CODING; IMAGE PROCESSING; THREE DIMENSIONAL;

CHAIN CODE; CUBE QUANTIZATION; DIGITAL LINE; DIGITAL REPRESENTATION; GRID INTERSECT QUANTIZATION; THREE DIMENSIONAL CURVES;

IMAGE ANALYSIS;

EID: 0031268095     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0031-3203(97)00011-3     Document Type: Article

References (49)

1. H. Freeman, Boundary encoding and processing, in Picture Processing and Psychopictorics, B. S. Lipkin and A. Rosefeld, eds, pp. 241-266. Academic Press, New York (1970).
2. H. Freeman, Computer processing of line-drawing images, Comput. Surveys 6, 57-97 (1974).
3. F. C. A. Groen and P. W. Verbeek, Freeman-code probabilities of object boundary quantized contours, Comput. Graphics Image Process. 7, 391-402 (1978).
4. C. E. Kim, On cellular straight line segments, Comput. Graphics Image Process. 18, 369-381 (1982).
5. J. Koplowitz, On the performance of chain codes for quantization of line drawings, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-3, 180-185 (1981).
6. U. Montanari, On limit properties in digitization schemes, J. ACM 17, 348-360 (1970).
7. U. Montanari, A note on minimal length polygonal approximation to a digitized contour, Comm. ACM 13, 41-47 (1970).
8. D. L. Neuhoff and K. G. Castor, A rate and distortion analysis of chain codes for line drawings, IEEE Trans. Inform. Theory IT-31, 53-68 (1985).
9. D. Proffitt and D. Rosen, Metrication errors and coding efficiency of chain-encoding schemes for the representation of lines and edges, Comput. Graphics Image Process. 10, 318-332 (1979).
10. J. A. Saghri and H. Freeman, Analysis of the precision of generalized chain codes for the representation of planar curves, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-3, 533-539 (1981).
11. A. M. Vossepoel and A. W. M. Smeulders, Vector code probability and metrication error in the representation of straight lines of finite length, Comput. Graphics Image Process. 20, 347-364 (1982).
12. Z. Kulpa, More about areas and perimeters of quantized objects, Comput. Vision Graphics Image Process. 22, 268-276 (1983).
13. L. Dorst and A. W. M. Smeulders, Length estimators for digitized contours, Comput. Vision Graphics Image Process. 40, 311-333 (1987).
14. J. Koplowitz and A. M. Bruckstein, Design of perimeter estimators for digitized planar shapes, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-11, 611-622 (1989).
15. A. M. Bruckestein, Self-similarity properties of digitized straight lines, Contemp. Math. 119, 1-20 (1991).
16. L. Dorst and R. P. W. Duin, Spirograph theory: A framework for calculations on digitized straight lines, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-6, 632-639 (1984).
17. L. Dorst and A. W. M. Smeulders, Discrete representation of straight lines, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-6, 450-463 (1984).
18. L. Dorst and A. W. M. Smeulders, Discrete straight line segments: Parameters primitives and properties, Contemp. Math. 119, 45-62 (1991).
19. S. H. Y. Hung, On the straightness of digital arcs, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-7, 203-215 (1985).
20. V. A. Kovalevsky, New definition and fast recognition of digital straight segments and arcs, Proc. Tenth Int. Conf. on Pattern Recognition, II, pp. 31-34 (1990).
21. M. Lindenbaum and J. Koplowitz, A new parameterization of digital straight lines, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-13, 847-852 (1991).
22. M. D. McIlory, A note on discrete representation of lines, AT&T Tech. J. 64, 481-490 (1984).
23. A. Rosenfeld, Digital straight line segments, IEEE Trans. Comput. C-23, 1264-1269 (1974).
24. L. D. Wu, On the chain code of a line, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-4, 347-353 (1982).
25. I. Debled-Rennesson and J. P. Reveillès, A linear algorithm for segmentation of digital curves, Proc. Third Int. Workshop on parallel image analysis theory and applications, pp. 47-75, Washington (March 1994).
26. C. E. Kim, Three-dimensional digital segments, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-5, 231-234 (1983).
27. R. Klette, The m-dimensional grid point space, Comput. Vision Graphics Image Process. 30, 1-12 (1985).
28. I. Stojmenović and R. Tošić, Digitization schemes and the recognition of digital straight lines, hyperplanes and flats in arbitrary dimensions, Contemp. Math. 119, 197-212 (1991).
29. T. M. Amarunnishad and P. P. Das, Estimation of length for digitized straight lines in three dimensions, Pattern Recognition Lett. 11, 207-213 (1990).
30. S. Chattopadhyay and P. P. Das, Estimation of the original length of a straight line segment from its digitization in three dimensions, Pattern Recognition 25, 787-798 (1992).
31. N. Kiryati and K, übler, O. On chain code probabilities and length estimators for digitized three-dimensional curves, Pattern Recognition 28, 361-372 (1995).
32. C. G. Lekkerkerker, Geometry of Numbers. Wolters-Noordhoff, Amsterdam (1969).
33. G. Borgefors, Distance transformations in arbitrary dimensions, Comput. Vision Graphics Image Process. 27, 321-345 (1984).
34. A. Rosenfeld, Connectivity in digital pictures, J. ACM 17, 146-170 (1970).
35. P. P. Das, P. P. Chakrabarti and B. N. Chatterji, Generalized distances in digital geometry, Inform. Sci. 42, 51-67 (1987).
36. A. Rosenfeld and J. L. Pfaltz, Distance functions on digital pictures, Pattern Recognition 1, 33-61 (1968).
37. T. Pavlidis, Algorithms for Graphics and Image Processing. Springer, Berlin (1982).
38. A. Rosenfeld, Adjacency in digital pictures, Inform. and Control 26, 24-33 (1974).
39. A. Rosenfeld, Three-dimensional digital topology, Inform. and Control 50, 119-127 (1981).
40. J. K. Udupa, S. N. Srihari and G. T. Herman, Boundary detection in multidimensions, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-4, 41-50 (1982).
41. J. E. Bresenham, Algorithm for computer control of a digital plotter, IBM Systems J. 4, 25-30 (1965).
42. H. Freeman and J. A. Saghri, Comparative analysis of line-drawing modeling schemes, Comput. Graphics Image Process. 12, 203-223 (1980).
43. D. K. Scholten and S. G. Wilson, Chain coding with a hexagonal lattice, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-5, 526-533 (1983).
44. T. A. Anderson and C. E. Kim, Representation of digital line segments and their preimages, Comput. Vision Graphics Image Process. 30, 279-288 (1985).
45. C. E. Kim, Three-dimensional digital planes, IEEE Trans. Pattern Analysis Mach. Intell. PAMI-6, 639-645 (1984).
46. X. Luo and L. Wu, The generalized chord property of digital plane element, Proc. Eighth Int. Conf. on Pattern Recognition, pp. 1159-1161 (1986).
47. A. L. D. Beckers and A. W. M. Smeulders, Optimization of length measurements for isotropic distance transformation in three dimensions, CVGIP: Image Understanding 55, 296-306 (1992).
48. A. Jonas and N. Kiryati, Length estimation in 3-D using cube quantization, Proc. SPIE Vision Geometry III 2356, 220-230 (1994) To appear in J. Mathematical Imaging and Vision.
49. A. Jonas and N. Kiryati, Length estimation in 3-D using cube quantization, Proc. SPIE Vision Geometry III 2356, 220-230 (1994) To appear in J. Mathematical Imaging and Vision.