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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K Appel, and W Haken: Every planar map is four colourable: Part I: discharging. Illinois Journal of Mathematics, 21: 429–490, 1977.
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.
H Asada, and M Brady: The curvature primal sketch. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8 (1): 2–14, 1986.
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.
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.
D H Ballard, and C M Brown: Computer Vision. Prentice-Hall, Englewood Cliffs, NJ, 1982.
M F Barnsley: Fractals Everywhere. Academic Press, Boston, Ma, 1988.
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.
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.
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.
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.
J W Brandt, and V R Algazi: Continuous skeleton computation by Voronoi diagram. CVGIP — Image Understanding, 55 (3), 1992.
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.
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.
G L Cash, and M Hatamian: Optical character recognition by the method of moments. Computer Vision, Graphics, and Image Processing, 39: 291–310, 1987.
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.
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.
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.
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.
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.
J L Crowley: A multiresolution representation for shape. In A Rosenfeld, editor, Multiresolution Image Processing and Analysis, pages 169–189. Springer Verlag, Berlin, 1984.
C A DeBoor: A Practical Guide to Splines. Springer Verlag, New York, 1978.
References 245
R O Duda, and P E Hart: Pattern Classification and Scene Analysis. John Wiley and Sons, New York, 1973.
C R Dyer: Computing the Euler number of an image from its quadtree. Computer Graphics and Image Processing, 13: 270–276, 1980.
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.
K S Fu: Syntactic Methods in Pattern Recognition. Academic Press, New York, 1974.
K Falconer. Fractal Geometry: Mathematical Foundations and Applications. Wiley, Chichester, New York, 1990.
H Y Feng and T Pavlidis. Decomposition of polygons into simpler components. IEEE Transactions on Computers, 24: 636650, 1975.
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.
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.
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.
H Freeman: On the enconding of arbitrary geometric configuration. IRE Transactions on Electronic Computers, EC-10(2): 260–268, 1961.
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.
R L Graham, and F F Yao: Finding the convex hull of a simple polygon. Journal of Algorithms, 4: 324–331, 1984.
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.
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.
Z Guo, and R W Hall: Fast fully parallel thinning algo- rithms. CVGIP — Image Understanding, 55 (3): 317–328, 1992.
L Gupta, and M D Srinath: Contour sequence moments for the classification of closed planar shapes. Pattern Recognition, 20 (3): 267–272, 1987.
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.
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.
M K Hu: Visual pattern recognition by moment invariants. IRE Transactions Information Theory, 8 (2): 179–187, 1962.
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.
A K Jain: Fundamentals of Digital Image Processing. Prentice-Hall, Englewood Cliffs, NJ, 1989.
R Jakubowski: Extraction of shape features for syntactic recognition of mechanical parts. IEEE Transactions on Systems, Man and Cybernetics, 15 (5): 642–651, 1985.
R Jakubowski: Decomposition of complex shapes for their structural recognition. Information Sciences, 50 (1): 35–71, 1990.
R D Juday, editor. Digital and Optical Shape Representation and Pattern Recognition, Orlando, Fl, Bellingham, Wa, 1988. SPIE.
K Kanatani: Group-Theoretical Methods in Image Understanding. Springer Verlag, Berlin, 1990.
N Kiryati, and D Maydan: Calculating geometric properties from Foutier representation. Pattern Recognition, 22 (5): 469–475, 1989.
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.
J J Koenderink, and A J van Doom: Dynamic shape. Technical report, Dept. Medical and Physiological Physics, State University, Utrecht, The Netherlands, 1986.
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.
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.
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.
D T Lee: On finding the convex hull of a simple polygon. International Journal of Computer and Information Sciences, 12: 87–98, 1983.
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.
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.
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.
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.
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.
E A Lord, and C B Wilson: The Mathematical Description of Shape and Form. Halsted Press, Chichester, UK, 1984.
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.
S Maitra: Moment invariants. Proceedings IEEE, 67 (4): 697–699, 1979.
B B Mandelbrot: The Fractal Geometry of Nature. Freeman, New York, 1983.
P Maragos: Pattern spectrum and multiscale shape representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11: 701–716, 1989.
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.
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.
S Marshall: Review of shape coding techniques. Image and Vision Computing, 7 (4): 281–194, 1989.
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.
References 249
D McCallum, and D Avis: A linear algorithm for finding the convex hull of a simple polygon. Information Processing Letters, 9: 201–206, 1979.
D S McKenzie, and S R Protheroe: Curve description using the inverse Hough transform. Pattern Recognition, 23 (3–4): 283–290, 1990.
A V Melkman: On-line construction of the convex hull of a simple polyline. Information Processing Letters, 25 (1): 11–12, 1987.
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.
B Moayer, and K S Fu: A tree system approach for fingerprint pattern recognition. IEEE Transactions on Computers, 24 (4): 436–450, 1975.
J L Mundy, and A Zisserman: Geometric Invariance in Computer Vision. MIT Press, Cambridge, Ma; London, 1992.
M Nagao, and T Matsuyama: A Structural Analysis of Complex Aerial Photographs. Plenum Press, New York, 1980.
T Nishizeki, and N Chiba: Planar Graphs: Theory and Algorithms. North Holland, Amsterdam-New York-Tokyo, 1988.
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.
A V Oppenheim, A S Willsky, and I T Young: Signals and Systems. Prentice-Hall, Englewood Cliffs, NJ, 1983.
T Pavlidis: Structural Pattern Recognition. Springer Verlag, Berlin, 1977.
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.
Papoulis 91] A Papoulis: Probability, Random Variables, and Stochastic Processes. McGraw Hill, New York, 3rd edition, 1991.
T Pavlidis: A review of algorithms for shape analysis. Computer Graphics and Image Processing, 7: 243–258, 1978.
T Pavlidis: Algorithms for shape analysis of contours and waveforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (4): 301–312, 1980.
E Persoon, and K S Fu: Shape discrimination using Fourier descriptors. IEEE Transactions on Systems, Man and Cybernetics, 7: 170–179, 1977.
I Pitas, and A N Venetsanopoulos: Morphological shape decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (1): 38–45, 1990.
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.
Pratt 91] W K Pratt, Digital Image Processing. John Wiley and Sons, New York, 2nd edition, 1991.
L Quan, P Gros, and R Mohr: Invariants of a pair of conics revisited. Image and Vision Computing, 10 (5): 319–323, 1992.
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.
A Rosenfeld: Digital straight line segments. IEEE Transactions on Computers, 23: 1264–1269, 1974.
A Rosenfeld: Picture Languages — Formal Models for Picture Recognition. Academic Press, New York, 1979.
Rosenfeld and Kak 82] A Rosenfeld, and A C Kak: Digital Picture Processing. Academic Press, New York, 2nd edition, 1982.
P L Rosin, and G A W West: Segmentation of edges into lines and arcs. Image and Vision Computing, 7 (2): 109–114, 1989.
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.
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.
J Sklansky: Measuring concavity on a rectangular mosaic. IEEE Transactions on Computers, 21 (12): 1355–1364, 1972.
T L Saaty, and P C Kainen: The Four Colour Problem. McGraw Hill, New York, 1977.
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.
H Samet: Computing perimeters of images represented by quadtrees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3: 683–687, 1981.
H Samet: A tutorial on quadtree research. In A Rosenfeld, editor, Multiresolution Image Processing and Analysis, pages 212–223. Springer Verlag, Berlin, 1984.
H Samet: Reconstruction of quadtree medial axis transforms. Computer Vision, Graphics, and Image Processing, 29: 311–328, 1985.
E Saund: Symbolic construction of a 2D scale-space image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12: 817830, 1990.
Savini 88] M Savini: Moments in image analysis. Alta Frequenza,57(2):145152, 1988.
L Shapiro: A structural model of shape. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (2): 111–126, 1980.
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.
M Shridhar, and A Badreldin: High accuracy character recognition algorithms using Fourier and topological descriptors. Pattern Recognition, 17 (5): 515–524, 1984.
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.
S Smith, and A Jain: Cord distribution for shape matching. Computer Graphics and Image Processing, 20: 259–265, 1982.
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.
W Stallings: Approaches to Chinese character recognition. Pattern Recognition, 8 (1): 87–98, 1976.
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.
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.
I Tomek: Two algorithms for piecewise linear continuous approximation of functions of one variable. IEEE Transactions on Computers, 23 (4): 445–448, 1974.
G Toussaint: A historical note on convex hull finding algorithms. Pattern Recognition Letters, 3 (1): 21–28, 1985.
G Toussaint: A counter-example to a convex hull algorithm for polygons. Pattern Recognition, 24 (2): 183–184, 1991.
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.
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.
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.
D Vernon: Two-dimensional object recognition using partial contours. Image and Vision Computing, 5 (1): 21–27, 1987.
T P Wallace: Comments on algorithms for shape analysis of contours and waveforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3 (5), 1981.
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.
I Weiss. Projective invariants of shapes. In Proceedings of Image Understanding Workshop, volume 2, pages 1125–1134, Cambridge, Ma, 1988.
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.
H Weyl: The Classical Groups and Their Invariants. Princeton University Press, Princeton, NJ, 1946.
R Wilson and R Nelson. Graph Colourings. Longman Scientific and Technical; Wiley, Essex, England and New York, 1990.
P H Winston: editor. The Psychology of Computer Vision. McGraw Hill, New York, 1975.
A P Witkin: Scale space filtering. In A P Pentland, editor, From Pixels to Predicates, pages 5–19. Ablex Publishing Corporation, Norwood, NJ, 1986.
J Woodwark: Computing Shape: An Introduction to the Representation of Component and Assembly Geometry for Computer-Aided Engineering. Butterworths, London-Boston, 1986.
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.
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.
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.
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.
Author information
Authors and Affiliations
Rights 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