Skip to main content
SpringerLink
Log in

Shape representation and description

  • Chapter
Image Processing, Analysis and Machine Vision

  • 2010 Accesses

Abstract

The last chapter was devoted to image segmentation methods which showed how to construct homogeneous regions of images and/or their boundaries. Recognition of image regions is one of the most important steps on the way to understanding image data, and requires an exact region description in a form suitable for a classifier (Chapter 7). This description step should generate a numeric feature vector, or a non-numeric syntactic description word, which characterizes properties (for example, shape) of the described region. Region description is the third of the four levels given in Chapter 3, implying that the description already comprises some abstraction — for example, 3D real objects can be represented in a 2D plane. Nevertheless, shape properties used for object description are usually computed in two dimensions. If we are interested in a 3D object description, we have to process at least two images of the same object taken from different viewpoints (stereo vision), or derive the 3D shape from a sequence of images if the object is in motion. A 2D shape representation is sufficient in the majority of practical applications, but if 3D information is necessary — if, say, a 3D object reconstruction is the processing goal, or the 3D characteristics bear the important information — the object description task is much more difficult; these topics are introduced in Chapter 9. In the following sections we will limit our discussion to 2D shape features and proceed under the assumption that described objects result from the image segmentation process.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K Appel, and W Haken: Every planar map is four colourable: Part I: discharging. Illinois Journal of Mathematics, 21: 429–490, 1977.

    MathSciNet  MATH  Google Scholar 

  2. C Arcelli, and G Sanniti di Baja: Endoskeleton and exoskeleton of digital figures, an effective procedure. In V Cappellini and R Marconi, editors, Advances in Image Processing and Pattern Recognition, pages 224–228, North Holland, Amsterdam, 1986.

    Google Scholar 

  3. H Asada, and M Brady: The curvature primal sketch. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8 (1): 2–14, 1986.

    Article  Google Scholar 

  4. H H Atkinson, Gargantini, I, and T R S Walsh: Counting regions, holes and their nesting level in time proportional to the border. Computer Vision, Graphics, and Image Processing, 29: 196–215, 1985.

    MATH  Google Scholar 

  5. J Babaud, A P Witkin, M Baudin, and R O Duda: Uniqueness of the Gaussian kernel for scale-space filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8 (1): 26–33, 1986.

    Article  MATH  Google Scholar 

  6. D H Ballard, and C M Brown: Computer Vision. Prentice-Hall, Englewood Cliffs, NJ, 1982.

    Google Scholar 

  7. M F Barnsley: Fractals Everywhere. Academic Press, Boston, Ma, 1988.

    Google Scholar 

  8. B Bhanu, and O D Faugeras: Shape matching of two—dimensional objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (2): 137–155, 1984.

    Article  Google Scholar 

  9. B K Bhattacharya, and H E Gindy: A new linear convex hull algorithm for simple polygons. IEEE Transactions on Information Theory, 30: 85–88, 1984.

    Article  MATH  Google Scholar 

  10. B K Bhattacharya, and G T Toussaint: Time-and-storage-efficient implementation of an optimal planar convex hull algorithm. Image and Vision Computing, 1 (3): 140–144, 1983.

    Article  Google Scholar 

  11. M Brady: Representing shape. In M Brady, L A Gerhardt, and H F Davidson, editors, Robotics and Artificial Intelligence, pages 279–300. Springer + NATO, Berlin, 1984.

    Chapter  Google Scholar 

  12. J W Brandt, and V R Algazi: Continuous skeleton computation by Voronoi diagram. CVGIP — Image Understanding, 55 (3), 1992.

    Google Scholar 

  13. E Bribiesca, and A Guzman: How to describe pure form and how to measure differences in shapes using shape numbers. Pattern Recognition, 12 (2): 101–112, 1980.

    Article  Google Scholar 

  14. M H Brill, E B Barrett, and P M Payton: Projective invariants for curves in two and three dimensions. In J L Mundy and A Zisserman, editors, Geometric Invariance in Computer Vision. MIT Press, Cambridge, Ma; London, 1992.

    Google Scholar 

  15. G L Cash, and M Hatamian: Optical character recognition by the method of moments. Computer Vision, Graphics, and Image Processing, 39: 291–310, 1987.

    Google Scholar 

  16. C Chang, and S Chatterjee: Fractal based approach to shape description, reconstruction and classification. In Twenty-Third Annual Asilomar Conference on Signals, Systems and Computers, Pacific Grove, Ca, pages 172–176, IEEE, Los Alamitos, Ca, 1989.

    Google Scholar 

  17. C H Chien, and J K Aggarwal: Model construction and shape recognition from occluding contours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (4): 372–389, 1989.

    Article  Google Scholar 

  18. T F Cootes, D H Cooper, C J Taylor, and J Graham: Trainable method of parametric shape description. Image and Vision Computing, 10 (5), 1992.

    Google Scholar 

  19. P P Cortopassi, and T C R,earick: Computationally efficient algorithm for shape decomposition. In Proceedings - CVPR ‘88: Computer Society Conference on Computer Vision and Pattern Recognition, Ann Arbor, Mi, pages 597–601, IEEE, Los Alamitos, Ca, 1988.

    Google Scholar 

  20. M F Costabile, C Guerra, and G G Pieroni: Matching shapes: A case study in time—varying images. Computer Vision, Graphics, and Image Processing, 29: 296–310, 1985.

    Google Scholar 

  21. J L Crowley: A multiresolution representation for shape. In A Rosenfeld, editor, Multiresolution Image Processing and Analysis, pages 169–189. Springer Verlag, Berlin, 1984.

    Chapter  Google Scholar 

  22. C A DeBoor: A Practical Guide to Splines. Springer Verlag, New York, 1978.

    Google Scholar 

  23. References 245

    Google Scholar 

  24. R O Duda, and P E Hart: Pattern Classification and Scene Analysis. John Wiley and Sons, New York, 1973.

    MATH  Google Scholar 

  25. C R Dyer: Computing the Euler number of an image from its quadtree. Computer Graphics and Image Processing, 13: 270–276, 1980.

    Article  Google Scholar 

  26. G Eichmann, C Lu, M Jankowski, and R Tolimeiri: Shape representation by Gabor expansion. In Hybrid Image and Signal Processing II, Orlando, Fl, pages 86–94, Society for Optical Engineering, Bellingham, Wa, 1990.

    Google Scholar 

  27. K S Fu: Syntactic Methods in Pattern Recognition. Academic Press, New York, 1974.

    MATH  Google Scholar 

  28. K Falconer. Fractal Geometry: Mathematical Foundations and Applications. Wiley, Chichester, New York, 1990.

    Google Scholar 

  29. H Y Feng and T Pavlidis. Decomposition of polygons into simpler components. IEEE Transactions on Computers, 24: 636650, 1975.

    Google Scholar 

  30. C Fermuller, and W Kropatsch: Multiresolution shape description by corners. In Proceedings, 1992 Computer Vision and Pattern Recognition, Champaign, Il, pages 271–276, IEEE, Los Alamitos, Ca, 1992.

    Google Scholar 

  31. L M J Florack, B M Haar-Romeny, J J Koenderink, and M A Viergever: Scale and the differential structure of images. Image and Vision Computing, 10 (6): 376–388, 1992.

    Article  Google Scholar 

  32. D Forsyth, J L Mundy, A Zisserman, C. Coelho, A. Heller, and C. Rothwell: Invariant descriptors for 3D object recognition and pose. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13 (10): 971–991, 1991.

    Article  Google Scholar 

  33. H Freeman: On the enconding of arbitrary geometric configuration. IRE Transactions on Electronic Computers, EC-10(2): 260–268, 1961.

    Google Scholar 

  34. A A Frisch, D A Evans, J P Hudson, and J Boon:Shape discrimination of sand samples using the fractal dimension. In Coastal Sediments ‘87, Proceedings of a Specialty Conference on Advances in Understanding of Coastal Sediment Processes, New Orleans, LA, pages 138–153, ASCE, Dallas, Tx, 1987.

    Google Scholar 

  35. R L Graham, and F F Yao: Finding the convex hull of a simple polygon. Journal of Algorithms, 4: 324–331, 1984.

    Article  MathSciNet  Google Scholar 

  36. L D Griffin, A C F Colchester, and G P Robinson: Scale and segmentation of grey-level images using maximum gradient paths. Image and Vision Computing, 10 (6): 389–402, 1992.

    Article  Google Scholar 

  37. T R Grimmins: A complete set of Fourier descriptors for two—dimensional shapes. IEEE Transactions on Systems, Man and Cybernetics, 12 (6): 923–927, 1982.

    Google Scholar 

  38. Z Guo, and R W Hall: Fast fully parallel thinning algo- rithms. CVGIP — Image Understanding, 55 (3): 317–328, 1992.

    Article  MATH  Google Scholar 

  39. L Gupta, and M D Srinath: Contour sequence moments for the classification of closed planar shapes. Pattern Recognition, 20 (3): 267–272, 1987.

    Article  Google Scholar 

  40. Gupta et al. 90] L Gupta, M R Sayeh, and R Tammana: Neural network approach to robust shape classification. Pattern Recognition,23(6):563568, 1990.

    Google Scholar 

  41. J E Hoperoft, D P Huttenlocher, and P C Wayner:Affine invariants for model-based recognition. In J L Mundy and A Zisserman, editors, Geometric Invariance in Computer Vision. MIT Press, Cambridge, Ma; London, 1992.

    Google Scholar 

  42. M K Hu: Visual pattern recognition by moment invariants. IRE Transactions Information Theory, 8 (2): 179–187, 1962.

    Article  MATH  Google Scholar 

  43. Y Ikebe, and S Miyamoto: Shape design, representation, and restoration with splines. In K S Fu and H Kunii, editors, Picture Engineering. Springer Verlag, Berlin, 1982.

    Google Scholar 

  44. A K Jain: Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs, NJ, 1989.

    MATH  Google Scholar 

  45. R Jakubowski: Extraction of shape features for syntactic recognition of mechanical parts. IEEE Transactions on Systems, Man and Cybernetics, 15 (5): 642–651, 1985.

    Article  MATH  Google Scholar 

  46. R Jakubowski: Decomposition of complex shapes for their structural recognition. Information Sciences, 50 (1): 35–71, 1990.

    Article  MATH  Google Scholar 

  47. R D Juday, editor. Digital and Optical Shape Representation and Pattern Recognition, Orlando, Fl, Bellingham, Wa, 1988. SPIE.

    Google Scholar 

  48. K Kanatani: Group-Theoretical Methods in Image Understanding. Springer Verlag, Berlin, 1990.

    Book  MATH  Google Scholar 

  49. N Kiryati, and D Maydan: Calculating geometric properties from Foutier representation. Pattern Recognition, 22 (5): 469–475, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  50. M W Koch, and R L Kashyap: Using polygons to recognize and locate partially occluded objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9 (4): 483–494, 1987.

    Article  Google Scholar 

  51. J J Koenderink, and A J van Doom: Dynamic shape. Technical report, Dept. Medical and Physiological Physics, State University, Utrecht, The Netherlands, 1986.

    Google Scholar 

  52. R Krishnapuram, and L F Chen: Iterative neural networks for skeletonization and thinning. In Intelligent Robots and Computer Vision IX: Neural, Biological, and 3D Methods, Boston, Ma, pages 271–281, Soc for Optical Engineering, Bellingham, Wa, 1991.

    Google Scholar 

  53. A Krzyzak, S Y Leung, and C Y Suen: Reconstruction of two-dimensional patterns from Fourier descriptors. Machine Vision and Applications, 2 (3): 123–140, 1989.

    Article  Google Scholar 

  54. L Lam, S W Lee, and C Y Suen: Thinning methodologies - a comprehensive survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (9): 869–885, 1992.

    Article  Google Scholar 

  55. D T Lee: On finding the convex hull of a simple polygon. International Journal of Computer and Information Sciences, 12: 87–98, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  56. J G Leu: View-independent shape representation and matching. In IEEE International Conference on Systems Engineering, Fairborn, Oh, pages 601–604, IEEE, Piscataway, NJ, 1989.

    Google Scholar 

  57. F Leymarie, and M D Levine: Shape features using curvature morphology. In Visual Communications and Image Processing IV, Philadelphia, Pa, pages 390–401, SPIE, Bellingham, Wa, 1989.

    Google Scholar 

  58. X Li, and Z Zhiying: Group direction difference chain codes for the representation of the border. In Digital and Optical Shape Representation and Pattern Recognition, Orlando, FI, pages 372–376, SPIE, Bellingham, Wa, 1988.

    Google Scholar 

  59. C C Lin, and R Chellappa: Classification of partial 2D shapes using Fourier descriptors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9 (5): 686–690, 1987.

    Article  Google Scholar 

  60. C Lipari, and C A Harlow: Representation and recognition of elongated regions in aerial images. In Applications of Artificial Intelligence VI, Orlando, Fl, pages 557–567, SPIE, Bellingham, Wa, 1988.

    Google Scholar 

  61. E A Lord, and C B Wilson: The Mathematical Description of Shape and Form. Halsted Press, Chichester, UK, 1984.

    Google Scholar 

  62. A C P Loui, A N Venetsanopoulos, and K C Smith: Two-dimensional shape representation using morphological correlation functions. In Proceedings of the 1990 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 90, Albuquerque, NM, pages 2165–2168, IEEE, Piscataway, NJ, 1990.

    Google Scholar 

  63. S Maitra: Moment invariants. Proceedings IEEE, 67 (4): 697–699, 1979.

    Article  Google Scholar 

  64. B B Mandelbrot: The Fractal Geometry of Nature. Freeman, New York, 1983.

    Google Scholar 

  65. P Maragos: Pattern spectrum and multiscale shape representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11: 701–716, 1989.

    Article  MATH  Google Scholar 

  66. P A Maragos, and R W Schafe: Morphological skeleton representation and coding of binary images. IEEE Transactions on Acoustics, Speech and Signal Processing, 34 (5): 1228–1244, 1986.

    Article  Google Scholar 

  67. S Marshall: Application of image contours to three aspects of image processing; compression, shape recognition and stereopsis. In Third International Conference on Image Processing and its Applications, Coventry, England, pages 604–608, IEE, Michael Faraday House, Stevenage, England, 1989.

    Google Scholar 

  68. S Marshall: Review of shape coding techniques. Image and Vision Computing, 7 (4): 281–194, 1989.

    Article  Google Scholar 

  69. S J Maybank: The projection of two non-coplanar conics. In J L Mundy and A Zisserman, editors, Geometric Invariance in Computer Vision. MIT Press, Cambridge, Ma; London, 1992.

    Google Scholar 

  70. References 249

    Google Scholar 

  71. D McCallum, and D Avis: A linear algorithm for finding the convex hull of a simple polygon. Information Processing Letters, 9: 201–206, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  72. D S McKenzie, and S R Protheroe: Curve description using the inverse Hough transform. Pattern Recognition, 23 (3–4): 283–290, 1990.

    Article  Google Scholar 

  73. A V Melkman: On-line construction of the convex hull of a simple polyline. Information Processing Letters, 25 (1): 11–12, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  74. J I Minnix, E S McVey, and R M Inigo: Multistaged neural network architecture for position invariant shape recognition. In Visual Communications and Image Processing ‘80, Lausanne, Switzerland, pages 58–68, SPIE, Bellingham, Wa, 1990.

    Google Scholar 

  75. B Moayer, and K S Fu: A tree system approach for fingerprint pattern recognition. IEEE Transactions on Computers, 24 (4): 436–450, 1975.

    Google Scholar 

  76. J L Mundy, and A Zisserman: Geometric Invariance in Computer Vision. MIT Press, Cambridge, Ma; London, 1992.

    Google Scholar 

  77. M Nagao, and T Matsuyama: A Structural Analysis of Complex Aerial Photographs. Plenum Press, New York, 1980.

    Google Scholar 

  78. T Nishizeki, and N Chiba: Planar Graphs: Theory and Algorithms. North Holland, Amsterdam-New York-Tokyo, 1988.

    MATH  Google Scholar 

  79. R Ogniewicz, and M Ilg: Voronoi skeletons: Theory and applications. In Proceedings, 1992 Computer Vision and Pattern Recognition, Champaign, Il, pages 63–69, IEEE, Los Alamitos, Ca, 1992.

    Google Scholar 

  80. A V Oppenheim, A S Willsky, and I T Young: Signals and Systems. Prentice-Hall, Englewood Cliffs, NJ, 1983.

    MATH  Google Scholar 

  81. T Pavlidis: Structural Pattern Recognition. Springer Verlag, Berlin, 1977.

    MATH  Google Scholar 

  82. D W Paglieroni, and A K Jain: Control point transforms for shape representation and measurement. Computer Vision, Graphics, and Image Processing, 42 (1): 87–111, 1988.

    Google Scholar 

  83. Papoulis 91] A Papoulis: Probability, Random Variables, and Stochastic Processes. McGraw Hill, New York, 3rd edition, 1991.

    Google Scholar 

  84. T Pavlidis: A review of algorithms for shape analysis. Computer Graphics and Image Processing, 7: 243–258, 1978.

    Article  Google Scholar 

  85. T Pavlidis: Algorithms for shape analysis of contours and waveforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (4): 301–312, 1980.

    Article  Google Scholar 

  86. E Persoon, and K S Fu: Shape discrimination using Fourier descriptors. IEEE Transactions on Systems, Man and Cybernetics, 7: 170–179, 1977.

    Article  MathSciNet  Google Scholar 

  87. I Pitas, and A N Venetsanopoulos: Morphological shape decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (1): 38–45, 1990.

    Article  Google Scholar 

  88. S M Pizer, W R Oliver, and S H Bloomberg, Hierarchical shape description via the multiresolution symmetric axis transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 9 (4): 505–511, 1987.

    Article  Google Scholar 

  89. Pratt 91] W K Pratt, Digital Image Processing. John Wiley and Sons, New York, 2nd edition, 1991.

    Google Scholar 

  90. L Quan, P Gros, and R Mohr: Invariants of a pair of conics revisited. Image and Vision Computing, 10 (5): 319–323, 1992.

    Article  Google Scholar 

  91. H Rom, and G Medioni: Hierarchical decomposition and axial shape description. In Proceedings, 1992 Computer Vision and Pattern Recognition, Champaign, II, pages 49–55, IEEE, Los Alamitos, Ca, 1992.

    Google Scholar 

  92. A Rosenfeld: Digital straight line segments. IEEE Transactions on Computers, 23: 1264–1269, 1974.

    Article  MathSciNet  MATH  Google Scholar 

  93. A Rosenfeld: Picture Languages — Formal Models for Picture Recognition. Academic Press, New York, 1979.

    MATH  Google Scholar 

  94. Rosenfeld and Kak 82] A Rosenfeld, and A C Kak: Digital Picture Processing. Academic Press, New York, 2nd edition, 1982.

    Google Scholar 

  95. P L Rosin, and G A W West: Segmentation of edges into lines and arcs. Image and Vision Computing, 7 (2): 109–114, 1989.

    Article  Google Scholar 

  96. C A Rothwell, A Zisserman, D A Forsyth, and J L Mundy: Fast recognition using algebraic invariants. In J L Mundy and A Zisserman, editors, Geometric Invariance in Computer Vision. MIT Press, Cambridge, Ma; London, 1992.

    Google Scholar 

  97. C A Rothwell, A Zisserman, J L Mundy, and D A Forsyth: Efficient model library access by projectively invariant indexing functions. In Proceedings, 1992 Computer Vision and Pattern Recognition, Champaign, Il, pages 109–114, IEEE, Los Alamitos, Ca, 1992.

    Google Scholar 

  98. J Sklansky: Measuring concavity on a rectangular mosaic. IEEE Transactions on Computers, 21 (12): 1355–1364, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  99. T L Saaty, and P C Kainen: The Four Colour Problem. McGraw Hill, New York, 1977.

    Google Scholar 

  100. R Safaee-Rad, B Benhabib, K C Smith, and K M Ty: Position, rotation, and scale-invariant recognition of 2 dimensional objects using a gradient coding scheme. In IEEE Pacific RIM Conference on Communications, Computers and Signal Processing, Victoria, BC, Canada, pages 306–311, IEEE, Piscataway, NJ, 1989.

    Google Scholar 

  101. H Samet: Computing perimeters of images represented by quadtrees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3: 683–687, 1981.

    Article  Google Scholar 

  102. H Samet: A tutorial on quadtree research. In A Rosenfeld, editor, Multiresolution Image Processing and Analysis, pages 212–223. Springer Verlag, Berlin, 1984.

    Chapter  Google Scholar 

  103. H Samet: Reconstruction of quadtree medial axis transforms. Computer Vision, Graphics, and Image Processing, 29: 311–328, 1985.

    Google Scholar 

  104. E Saund: Symbolic construction of a 2D scale-space image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12: 817830, 1990.

    Google Scholar 

  105. Savini 88] M Savini: Moments in image analysis. Alta Frequenza,57(2):145152, 1988.

    Google Scholar 

  106. L Shapiro: A structural model of shape. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (2): 111–126, 1980.

    Article  Google Scholar 

  107. H Shariat: A model-based method for object recognition. In IEEE International Conference on Robotics and Automation, Cincinnati, Oh, pages 1846–1851, IEEE, Los Alamitos, Ca, 1990.

    Google Scholar 

  108. M Shridhar, and A Badreldin: High accuracy character recognition algorithms using Fourier and topological descriptors. Pattern Recognition, 17 (5): 515–524, 1984.

    Article  MATH  Google Scholar 

  109. A W M Smeulders, A M Vossepoel, J Vrolijk, J S Ploem, and C J Cornelisse: Some shape parameters for cell recognition. In Proceedings of Pattern Recognition in Practice, pages 131–142, North Holland, Amsterdam, 1980.

    Google Scholar 

  110. S Smith, and A Jain: Cord distribution for shape matching. Computer Graphics and Image Processing, 20: 259–265, 1982.

    Article  Google Scholar 

  111. L H Staib, and J S Duncan: Boundary finding with parametrically deformable models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (11): 1061–1075, 1992.

    Article  Google Scholar 

  112. W Stallings: Approaches to Chinese character recognition. Pattern Recognition, 8 (1): 87–98, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  113. J Strackee, and N J D Nagelkerke: On closing the Fourier descriptor presentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 5 (6): 660–661, 1983.

    Article  MATH  Google Scholar 

  114. K R Tampi, and C S Sridhar: Shape detection using word like image description. In Proceedings of the 1990 International Conference on Acoustics, Speech, and Signal Processing - ICASSP 90 Albuquerque, NM, pages 2041–2043, IEEE, Piscataway, NJ, 1990.

    Google Scholar 

  115. I Tomek: Two algorithms for piecewise linear continuous approximation of functions of one variable. IEEE Transactions on Computers, 23 (4): 445–448, 1974.

    Article  MATH  Google Scholar 

  116. G Toussaint: A historical note on convex hull finding algorithms. Pattern Recognition Letters, 3 (1): 21–28, 1985.

    Article  Google Scholar 

  117. G Toussaint: A counter-example to a convex hull algorithm for polygons. Pattern Recognition, 24 (2): 183–184, 1991.

    Article  MathSciNet  Google Scholar 

  118. W H Tsai, and S S Yu: Attributed string matching with merging for shape recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7 (4): 453–462, 1985.

    Article  Google Scholar 

  119. J L Turney, T N Mudge, and R A Volz: Recognizing partially occluded parts. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7 (4): 410–421, 1985.

    Article  Google Scholar 

  120. L J Van Gool, T Moons, E. Pauwels, and A. Oosterlinck: Semi-differential invariants. In J L Mundy and A Zisserman, editors, Geometric Invariance in Computer Vision. MIT Press, Cambridge, Ma; London, 1992.

    Google Scholar 

  121. D Vernon: Two-dimensional object recognition using partial contours. Image and Vision Computing, 5 (1): 21–27, 1987.

    Article  MathSciNet  Google Scholar 

  122. T P Wallace: Comments on algorithms for shape analysis of contours and waveforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3 (5), 1981.

    Google Scholar 

  123. T P Wallace, and P A Wintz: An efficient three-dimensional aircraft recognition algorithm using normalized Fourier descriptors. Computer Graphics and Image Processing, 13: 99–126, 1980.

    Article  Google Scholar 

  124. I Weiss. Projective invariants of shapes. In Proceedings of Image Understanding Workshop, volume 2, pages 1125–1134, Cambridge, Ma, 1988.

    Google Scholar 

  125. I Weiss: Noise resistant projective and affine invariants. In Proceedings, 1992 Computer Vision and Pattern Recognition, Champaign, Il, pages 115–121, IEEE, Los Alamitos, Ca, 1992.

    Google Scholar 

  126. H Weyl: The Classical Groups and Their Invariants. Princeton University Press, Princeton, NJ, 1946.

    MATH  Google Scholar 

  127. R Wilson and R Nelson. Graph Colourings. Longman Scientific and Technical; Wiley, Essex, England and New York, 1990.

    Google Scholar 

  128. P H Winston: editor. The Psychology of Computer Vision. McGraw Hill, New York, 1975.

    Google Scholar 

  129. A P Witkin: Scale space filtering. In A P Pentland, editor, From Pixels to Predicates, pages 5–19. Ablex Publishing Corporation, Norwood, NJ, 1986.

    Google Scholar 

  130. J Woodwark: Computing Shape: An Introduction to the Representation of Component and Assembly Geometry for Computer-Aided Engineering. Butterworths, London-Boston, 1986.

    Google Scholar 

  131. D M Wuescher, and K L Boyer: Robust contour decomposition using a constant curvature criterion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13 (10): 41–51, 1991.

    Article  Google Scholar 

  132. A L Yuille, and T A Poggio: Scaling theorems for zero-crossings. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8 (1): 15–25, 1986.

    Article  MATH  Google Scholar 

  133. Z Zhou, and A N Venetsanopoulos: Generic ribbons: A morphological approach towards natural shape decomposition. In Visual Communications and Image Processing IV, Philadelphia, Pa, pages 170–180, Soc for Optical Engineering, Bellingham, Wa, 1989.

    Google Scholar 

  134. Q Zhu, and L Poh: Transformation-invariant recursive subdivision method for shape analysis. In 9th International Conference on Pattern Recognition, Rome, Italy, pages 833–835, IEEE, New York, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Iowa, Iowa City, Iowa, USA

    Milan Sonka PhD

  2. Czech Technical University, Prague, Czech Republic

    Vaclav Hlavac PhD

  3. University of Leeds, Leeds, England

    Roger Boyle DPhil, MBCS, CEng

Authors
  1. Milan Sonka PhD
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vaclav Hlavac PhD
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roger Boyle DPhil, MBCS, CEng
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Milan Sonka, Vaclav Hlavac and Roger Boyle

About this chapter

Cite this chapter

Sonka, M., Hlavac, V., Boyle, R. (1993). Shape representation and description. In: Image Processing, Analysis and Machine Vision. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3216-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-3216-7_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-412-45570-4

  • Online ISBN: 978-1-4899-3216-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation