Moment-Preserving Piecewise Linear Approximations of Signals and Images

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 19, Issue 1, 1997, Pages 84-91

[No Author Info available]

Author keywords

[No Author keywords available]

Indexed keywords

ANALOG TO DIGITAL CONVERSION; ERRORS; FOURIER TRANSFORMS; FUNCTIONS; GEOMETRY; IMAGE PROCESSING; PATTERN RECOGNITION; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; SIGNAL PROCESSING;

DISCRETE COSINE TRANSFORM; MOMENT PRESERVING APPROXIMATION; SINGLE VARIABLE FUNCTIONS; TWO DIMENSIONAL;

APPROXIMATION THEORY;

EID: 0030853029     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.566816     Document Type: Article

References (36)

1. K. Åström, "Fundamental Limitations on Projective Invariants of Planar Curves,"IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, pp. 77-80,1995.
2. A. Blake and C. Marinos, "Shape from Texture-Estimation, Isotropy and Moments,"Artificial Intelligence, vol. 45, pp. 323-380, 1990.
3. H. Dirilten and T.G. Newman, "Pattern Matching Under Affine Transformations,"IEEE Trans. Computers, vol. 26, pp. 314-317, 1977.
4. A.P. Reeves and A. Rostampur, "Shape Analysis of Segmented Objects Using Moments,"Proc. CoJ. PR1P, Dallas, Aug. 1981, pp. 171-174.
5. A.P. Reeves, "Three-Dimensional Shape Analysis Using Moments and Fourier Descriptors,"IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, pp. 937-943,1988.
6. T.H. Reiss, Recognizing Planar Objects Using Invariant Image Features. Berlin/Heidelberg: Springer-Verlag, 1993.
7. A. Rosenfeld and A. Kak, Digital Picture Processing. New York: Academic Press, pp. 405-417.
8. I. Rothe, K.' Vöss, H. Suesse, and J. Rothe, "A General Method to Determine Invariants," Technical Report 503, Univ. Rochester, Rochester, New York, Apr. 1994.
9. I. Rothe, K. Voss, and H. Suesse, "The Method of Normalization to Determine Invariants,"IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, pp. 366-376,1996.
10. R. Saafee, K.C. Smith, B. Benhabib, and I. Tchoukanov, "Application of Moment and Fourier Descriptors to the Accurate Estimation of Elliptical Shape Parameters,"IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, pp. 2,465-2,468,1992.
11. D. Sinclair and A. Blake, "Isoperimetric Normalization of Planar Curves,"IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, pp. 769-777,1994.
12. H. Suesse, K. Voss, and I. Rothe, "Invariant Standard Positions of Ordered Sets of Points,"Pwc. Sixth Int'i Conf., CAIP '95, Lecture Notes in Computer Science 970, pp. 9-16, Prague, 1995.
13. K. Udagawa, J. Toriwaki, and K. Sugino, "Normalization and Recognition of Two-Dimensional Patterns with Linear Distortion by Moments,"Electr. Commun. Japan, vol. 47, pp. 34-46,1964. , [14] K. Voss and H. Suesse, Adaptive Modelle und Invarianten für zweidimensionale Bilder. Aachen: Shaker Verlag, 1995.
14. K.P.W. Wang, "Affine-Invariant Moment Method of ThreeDimensional Object Identification," dissertation, Syracuse Univ., 1977.
15. Discrete Cosine Transform, Discrete Transforms and Their Applications. Van Nostrand Reinhold Co., Inc.
16. H. Ahmed, T. Natarajan, and K.R. Rao, Discrete Cosine Transform, Discrete Transforms and Their Applications. Van Nostrand Reinhold Co., Inc., pp. 9-12,1985.
17. R.L. Cosgrif, Identification of Shape, Ohio State Univ. Research Foundation, Columbus, Ohio., Report 820-11, ASTIA AD 254 792, Dec. 1960.
18. C. de Boor, A Practical Guide to Splines. New York: Springer-Verlag, 1978.
19. J. G. Dunham, "Optimum Uniform Piecewise Linear Approximation of Planar Curves,"IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 67-75,1986.
20. B. Gluss, "A Line Segment Curve-Fitting Algorithm Related to Optimal Encoding of Information," Information and Control, vol. 5, pp. 261-267,1962.
21. G.H. Granlund, "Fourier Preprocessing for Hand Print Character Recognition,"IEEE Trans. Computers, vol. 21, pp. 195-201,1972.
22. F. B. Hildebrand, Introduction to Numerical Analysis, 2nd Ed. Dover Publications, 1987.
23. Y. Kurozumi and W.A. Davis, "Polygonal Approximation by the Minimax Method,"Computer Graphics and Image Processing, vol. 19, pp. 248-264,1982.
24. D.G. Lowe, "Three-Dimensional Object Recognition from Single Two-Dimensional Images,"Artificial Intelligence, vol. 31, pp. 355395,1987.
25. U. Montanari, "A Note on Minimal Length Polygonal Approximation to a Digitized Contour,"Comm. A.C.M., vol. 13, no. 1, pp. 41-47, Jan. 1970.
26. [II] T.B. Nguyen, Moment-Preserving Piecewise Linear Approximations of Signals and Images, master's thesis, Carleton Univ., Ottawa, Ontario, Canada, 1994.
27. T. Pavlidis and S.L. Horowitz, "Segmentation of Plane Curves,"IEEE Trans. Computers, vol. 23, no. 8, pp. 860-870, Aug. 1974.
28. G.M. Phillips, "Algorithm for Piecewise Straight Line Approximations,"ComputerJ., vol. 11, pp. 211-212,1968.
29. P. Prusinkiewicz and M. Christopher, "Hologram-Like Transmission of Pictures,"The Visual Computer. Springer Verlag, pp. 185193,1985.
30. U. Ramer, "An Iterative Procedure for the Polygonal Approximation of Plane Curves,"Computer Graphics and Image Processing, vol. l, pp. 244-256,1972.
31. K.R. Rao and P. Yip, Discrete Cosine Transform-Algorithms, Advantages, Applications. Academic Press, Inc., 1990.
32. P.L. Rosin and G.A.W. West, "Techniques for Segmenting Image Curves into Meaningful Descriptions,"Pattern Recognition, vol. 24, no. 7, pp. 643-652,1991.
33. N.I. Akhiezer, "The Classical Moment Problem,"Univ. Mathematical Monographs. Oliver & Boyd Ltd., 1965.
34. H. Stone, "Approximation of Curves by Line Segments,"Mathematics of Computation, vol. 15, pp. 40-47,1961.
35. S.L. Tanimoto, "Image Transmission with Gross Information First,"Computer Graphics and Image Processing, vol. 9, pp. 72-76, 1979.
36. C.T. Zahn and R.Z. Roskies, "A Fourier Description for Plane Close Curves,"IEEE Trans. Computers, vol. 21, pp. 269-281,1972.