Ridges for image analysis
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
Representation of object shape by medial structures has been an important aspect of image analysis. Methods for describing objects in a binary image by medial axes are well understood. Many attempts have been made to construct similar medial structures for objects in gray scale images. In particular, researchers have studied images by analyzing the graphs of the intensity data and identifying ridge and valley structures on those surfaces. In this paper we review many of the definitions for ridges. Computational vision models require that medial structures should remain invariant under certain transformations of the spatial locations and intensities. For each ridge definition we point out which invariances the definition satisfies. We also give extensions of the concepts so that we can located-dimensional ridge structures withinn-dimensional images. A comparison of the ridge structures produced by the different definitions is given both by mathematical examples and by an application to a 2-dimensional MR image of a head.
- H. Blum, “Biological shape and visual science (Part I),”J. Theoret. Biol. vol. 38, pp. 205–287, 1973.
- H. Blum and R.N. Nagel, “Shape description using weighted symmetric axis features,”Pattern Recognition, vol. 10, pp. 167–180, 1978.
- L.A. Bucchi, “Ridge detection on surfaces,” M.S. dissertation, Dept. of Math., Univ. of North Carolina at Chapel Hill, 1991.
- J.W. Bruce, P.J. Giblin, and C.G. Gibson, “Symmetry sets,”Proc. Roy. Soc. Edinburgh, 101A, pp. 163–186, 1985.
- A.C.F. Colchester, “Network representation of 2D and 3D images,” in3D Imaging in Medicine, K.H. Hoehne, H. Fuchs and S. Pizer (eds.), Springer-Verlag, Berlin, pp. 45–62, 1990.
- J.L. Crowley and A.C. Parker, “A representation for shape based on peaks and ridges in the difference of lowpass transform,”IEEE Trans. PAMI, vol. PAMI-6, no. 2, pp. 156–170, 1984.
- D. Eberly and S.M. Pizer, “Ridge flow models for image segmentation,”Dept. of Comp. Sci., Univ. of North Carolina, technical report TR93-056, 1993. (Also, to appear in SPIE Proc. Med. Imag. 1994.)
- B.M. ter Haar Romeny, L.M.J. Florak, J.J. Koenderink, and M.A. Viergever, “Scale-space: Its natural operators and differential invariants,” inInformation Processing in Medical Imaging (IPMI), Proc. 12 th Int. Conf., Colchester and Hawkes (eds.), Springer-Verlag, Berlin, 1991.
- L.M.J. Florack, B.M. ter Haar Romeny, J.J. Koenderink, and M.A. Viergever,General intensity transformations and second order invariants, inTheory & Applications of Image Analysis, World Scientific, Series inMachine Perception and Artificial Intelligence, vol. 2, pp. 22–29, P. Johansen and S. Olsen (eds.), Singapore.
- L.M.J. Florack, B.M. ter Haar Romeny, J.J. Koenderink, and M.A. Viergever, “Images: Regular tempered distributions”, inShape in Picture,NATO ASI Series F, A. Toet and O. Ying-Lie (eds.), Springer-Verlag, Berlin, 1993.
- W. Fulks,Advanced Calculus, 3rd edition, John Wiley and Sons: New York, 1978.
- R. Haralick, “Ridges and valleys in digital images,”CVGIP, vol. 22, pp. 28–38, 1983.
- R.A. Horn and C.R. Johnson,Matrix Analysis, Cambridge University Press: Cambridge, England, 1991.
- J.M. Gauch, “The multiresolution intensity axis of symmetry and its application to image segmentation,” Ph.D. dissertation, Dept. of Comp. Sci., Univ. of North Carolina, technical report TR89-047, 1989.
- L.D. Griffin, A.C.F. Colchester, and G.P. Robinson, “Scale and segmentation of gray-level images using maximum gradient paths,” inLecture Notes in Computer Science 511:Information Processing in Medical Imaging, 12 th International Conference, Wye, UK, pp. 256–272, 1991.
- J. Koenderink,Solid Shape, MIT Press: Cambridge, MA, 1991.
- J. Koenderink and A.J. van Doorn, “Local features of smooth shapes: Ridges and Courses,”SPIE Proc. 2031: Geometric Methods in Computer Vision II, San Diego, pp. 2–13, 1993.
- B.S. Morse, “Ridges of height functions in scale space,” preprint, 1993.
- L.R. Nackman, “Three-dimensional shape description using the symmetric axis transform,” Ph.D. dissertation, Dept. of Comp. Sci., Univ. North Carolina, Chapel Hill, 1982.
- L.R. Nackman, “Two-dimensional critical point configuration graphs,”IEEE Trans. PAMI, vol. PAMI-6, no. 4, pp. 442–450, 1984.
- C.E. Pearson (ed.),Handbook of Applied Mathematics, Van Nostrand Reinhold: New York, 1983.
- S.M. Pizer, C.A. Burbeck, J.M. Coggins, D.S. Fritsch, and B.S. Morse, “Object shape before boundary shape: scalespace medial axis,” Dept. of Comp. Sci., Univ. of North Carolina, technical report TR92-023, 1992.
- C. Scharlach, “Ridges and the description of image structure,” inGeometry and Topology of Submanifolds V, Proc. Conf. on Diff. Geom. and Vision, F. Dillen and L. Verstraelen (eds.), World Scientific, Singapore (to appear), 1992.
- J-P. Thirion and A. Gourdon, “The 3D marching lines algorithm and its application to crest line extraction,”INRIA Research Report, Robotique, Image et Vision, Programme 4, No. 1672, pp. 1–28, 1992.
- Ridges for image analysis
Journal of Mathematical Imaging and Vision
Volume 4, Issue 4 , pp 353-373
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Industry Sectors
- Author Affiliations
- 1. Department of Computer Science, University of North Carolina, 27599-3175, Chapel Hill, NC, USA
- 2. Department of Mathematics, University of North Carolina, 27599-3250, Chapel Hill, NC, USA
- 3. Fachbereich Mathematik MA 8-3, Technische Universität Berlin, Straβe des 17. Juni 136, D-10623, Berlin, Germany