Abstract
In contrast to morphological transformations described so far, the hit-or-miss transformation involves SEs composed of two sets. The first has to fit the object under study while the second has to miss it. Hence, the name fit-and-miss would have been more appropriate. Hit-or-miss transformations extract all image pixels satisfying a given neighbourhood configuration such as that corresponding to an isolated background or foreground pixel. Adding to an image all pixels having a given configuration leads to the thickening operator while subtracting them from the image defines the thinning operator.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliographical notes and references
C. Arcelli and G. Sanniti di Baja. A one pass two-operation process to detect the skeletal pixels on the 4-distance transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (4): 411–414, April 1989.
G. Banon and J. Barrera. Minimal representation for translation-invariant set mappings by mathematical morphology. SIAM Journal on Applied Mathematics, 51: 1782–1798, 1991.
G. Bertrand. Simple points, topological numbers and geodesic neighborhoods in cubic grids. Pattern Recognition Letters, 15: 1003–1011, 1994.
G. Bertrand, J.-C. Everat, and M. Couprie. Image segmentation through operators based upon topology. Journal of Electronic Imaging, 6 (4): 395–405, 1997.
S. Beucher. Ligne de partage des eaux: comment l’expliquer en termes de transformation fonctionnelle ? Technical Report N-699, Ecole des Mines de Paris, May 1981.
S. Beucher. Segmentation d’Images et Morphologie Mathématique. PhD thesis, Ecole des Mines de Paris, June 1990.
S. Beucher. Digital skeletons in Euclidean and geodesic spaces. Signal Processing, 38 (1): 127–141, July 1994.
D. Bloomberg and P. Maragos. Generalized hit-miss operations. In P. Gader, editor, Image Algebra and Morphological Image Processing, volume SPIE-1350, pages 116–128, 1990.
H. Blum. A transformation for extracting new descriptors of shape. In W. WathenDunn, editor, Models for the Perception of Speech and Visual Form, pages 362380, Cambridge, MA, 1967. M.I.T. Press.
H. Blum. Biological shape and visual science (part 1). Journal of Theoretical Biology, 38: 205–287, 1973.
G. Borgefors, I. Nyström, and G. Sanniti di Baja. Computing skeletons in three dimensions. Pattern Recognition, 32 (7): 1225–1236, 1999.
L. Calabi and W. E. Hartnett. Shape recognition, prairie fires, convex deficiencies and skeletons. Amer. Math. Monthly, 75: 335–342, 1968.
D. Casasent and R. Sturgill. Optical hit-or-miss morphological transforms for ATR. In A. Tescher, editor, Applications of Digital Image Processing XII, volume SPIE-1153, pages 500–510, 1990.
T. Crimmins and W. Brown. Image algebra and automatic shape recognition. IEEE Transactions on Aerospace and Electronic Systems, 21 (1): 60–69, January 1985.
H. Freeman. Computer processing of line-drawing images. Computing Surveys, 6: 57–97, March 1974.
Y. Ge and J. Fitzpatrick. On the generation of skeletons from discrete Euclidean distance maps. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (11): 1055–1066, November 1996.
V. Goetcherian. From binary to grey tone image processing using fuzzy logic concepts. Pattern Recognition, 12: 7–15, 1980.
M. Golay. Hexagonal parallel pattern transformation. IEEE Transactions on Computers, 18 (8): 733–740, August 1969.
S. Gray. Local properties of binary images in two dimensions. IEEE Transactions on Computers, 20 (5): 551–561, May 1971.
C. Hilditch. Linear skeletons form square cupboards. In B. Mertzer and D. Michie, editors, Machine Intelligence, volume 4, chapter 22, pages 403–420. University Press, Edinburgh, 1969.
P. Jonker. Skeletons in N dimensions using shape primitives. Pattern Recognition Letters, 23 (6): 677–686, April 2002.
T. Kong. On topology preservation in 2-D and 3-D thinning. International Journal of Pattern Recognition and Artificial Intelligence, 9 (5): 813–844, 1995.
R. Kresch and D. Malah. Multi-parameter skeleton decomposition. In J. Serra and P. Soille, editors, Mathematical Morphology and its Applications to Image Processing, pages 141–148. Kluwer Academic Publishers, 1994.
L. Lam, S.-W. Lee, and C. Suen. Thinning methodologies: a comprehensive survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (9): 869–885, 1992.
C. Lantuéjoul. La Squelettisation et son Application aux Mesures Topologiques des Mosaïques Polycristallines. PhD thesis, Ecole des Mines de Paris, 1978.
C. Lantuéjoul. Skeletonization in quantitative metallography. In R. Haralick and J.-C. Simon, editors, Issues in Digital Image Processing, volume 34 of NATO ASI Series E, pages 107–135, Alphen aan den Rijn, 1980. Sijthoff & Noordhoff.
S. Lobregt, P. Verbeek, and F. Groen. Three-dimensional skeletonization: principle and algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (1): 75–77, January 1980.
P. Maragos and R. Schafer. Morphological skeletons representation and coding of binary images. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34 (5): 1228–1244, October 1986.
M. Matheron. Examples of topological properties of skeletons. In J. Serra, editor, Image Analysis and Mathematical Morphology. Volume 2: Theoretical Advances, chapter 11, pages 217–238. Academic Press, 1988.
F. Meyer. Skeletons in digital spaces. In J. Serra, editor, Image Analysis and Mathematical Morphology. Volume 2: Theoretical Advances, chapter 13, pages 257–296. Academic Press, London, 1988.
F. Meyer. Skeletons and perceptual graphs. Signal Processing, 16: 335–363, 1989.
F. Meyer. Digital Euclidean skeletons. In M. Kunt, editor, Visual Communications and Image Processing’90, volume SPIE-1360, pages 251–262, Lausanne, 1990. Society of Photo-Instrumentation Engineers.
U. Montanari. A method for obtaining skeletons using a quasi-Euclidean distance. Journal of the ACM, 15 (4): 600–624, October 1968.
S. Peleg and A. Rosenfeld. A min-max medial axis transform. IEEE Transactions on Pattern Analysis and Machine Intelligence, 3: 208–210, March 1981.
R. Peyrard, P. Soille, J.-C. Klein, and A. Tuzikov. A dedicated hardware system for the extraction of grid patterns on stamped metal sheets. In I. Pitas, editor, Proc. of 1995 IEEE Workshop on Nonlinear Signal and Image Processing, pages 867–870, Neos Marmaras, June 1995.
C. Pudney. Distance-ordered homotopic thinning: a skeletonization algorithm for 3D digital images. Computer Vision and Image Understanding, 72 (3): 404–413, December 1998.
V. Ranwez and P. Soille. Order independent homotopic thinning. In G. Bertrand, M. Couprie, and L. Perroton, editors, Proc. of Discrete Geometry for Computer Imagery’99, volume 1568 of Lecture Notes in Computer Science, pages 337–346. Springer-Verlag, 1999.
V. Ranwez and P. Soille. Order independent homotopic thinning for binary and grey tone anchored skeletons. Pattern Recognition Letters, 23 (6): 687–702, April 2002.
C. Ronse. A topological characterization of thinning Theoretical Computer Science, 43: 31–41, 1986.
C. Ronse. Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images. Discrete Applied Mathematics, 21: 67–79, 1988.
C. Ronse. A lattice-theoretical morphological view on template extraction in images. Journal of Visual Communication and Image Representation, 7 (3): 273–295, September 1996.
A. Rosenfeld. Connectivity in digital pictures. Journal of the ACM, 17 (1): 146–160, 1970.
M. Schmitt. One pixel thick skeletons. In J. Serra and P. Soille, editors, Mathematical Morphology and its Applications to Image Processing, pages 257–264. Kluwer Academic Publishers, 1994.
J. Serra. Image Analysis and Mathematical Morphology. Academic Press, London, 1982.
S. Svensson, G. Borgefors, and I. Nyström. On reversible skeletonization using anchor-points from distance transforms. Journal of Visual Communication and Image Representation, 10: 379–397, 1999.
H. Talbot and L. Vincent. Euclidean skeletons and conditional bisectors. In P. Maragos, editor, Visual Communications and Image Processing, volume SPIE-1818, pages 862–876, 1992.
A. Toet. A hierarchical morphological image decomposition. Pattern Recognition Letters, 11: 267–274, April 1990.
C. Vachier, F. Meyer, C. Gratin, and H. Talbot. Filtrage par décomposition morphologique: application à l’extraction de structures rectilignes. In Reconnaissance des Formes et Intelligence Artificielle,pages 255–263, Paris, 1994. GRETSI.
L. Vincent. Efficient computation of various types of skeletons. In M. Loew, editor, Medical Imaging V: Image Processing, volume SPIE-1445, pages 297–311, 1991.
S. Wilson. Vector morphology and iconic neural networks. IEEE Transactions on Systems, Man, and Cybernetics, 19 (6): 1636–1644, 1989.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Soille, P. (2004). Hit-or-miss and Skeletons. In: Morphological Image Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05088-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-05088-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07696-1
Online ISBN: 978-3-662-05088-0
eBook Packages: Springer Book Archive