Abstract
We consider the problem of image segmentation and describe an algorithm that is based on the Minimum Description Length (MDL) principle, is fast, is applicable to multiband images, and guarantees closed regions. We construct an objective function that, when minimized, yields a partitioning of the image into regions where the pixel values in each band of each region are described by a polynomial surface plus noise. The polynomial orders and their coefficients are determined by the algorithm. The minimization is difficult because (1) it involves a search over a very large space and (2) there is extensive computation required at each stage of the search. To address the first of these problems we use a region-merging minimization algorithm. To address the second we use an incremental polynomial regression that uses computations from the previous stage to compute results in the current stage, resulting in a significant speed up over the non-incremental technique. The segmentation result obtained is suboptimal in general but of high quality. Results on real images are shown.
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References
N. Abramson. Information Theory and Coding. McGraw-Hill, 1963.
H. Akaike. A new look at statistical model identification. IEEE Trans., AC-19:716–723, 1974.
T.W. Anderson. An Introduction to Multivariate Statistical Analysis. Wiley, New York, second edition, 1984.
James O. Berger. Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, New York, second edition, 1985.
J.M. Beaulieu and M. Goldberg. Hierarchy in picture segmentation: A stepwise optimization approach. IEEE PAMI, 11(2):150–163, February 1989.
P.J. Besl and R.C. Jain. Segmentation through variable-order surface fitting. IEEE Trans PAMI, 10(2):167–192, March 1988.
A. Blake and A. Zisserman. Visual Reconstruction. MIT Press, Cambridge, MA, 1987.
Thomas M. Cover and Joy A. Thomas. Elements of Information Theory. Wiley, New York, 1991.
Trevor Darrell and Alex Pentland. Recovery of minimal descriptions using parallel robust estimation. Technical Report 163, 1991.
Byron Dom and David Steele. 2n — tree classifiers and realtime image segmentation. In MVA ′90: IAPR Workshop on Machine Vision Applications, Tokyo, Japan, 1990. IAPR (for expanded version see IBM Research Report 7558 (70424) 7/2/90).
Trevor Darrel, Stan Sclaroff, and Alex Pentland. Segmentation by minimal description. In ICCV 90, Osaka, Japan, pp. 112-116, 1990.
P. Fua and A.J. Hanson. Extracting generic shapes using model driven optimization. In Proceedings of the Image Understanding Workshop, pp. 994-1004, Boston, 1988.
I.S. Gradshteyn and I.M. Ryzhik. Table of Integrals, Series, and Products. Academic Press, New York, corrected and enlarged edition, 1980.
G.H. Golub and C.F. van Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore, MD, 1983.
R.M. Haralick and L. Shapiro. Image segmentation techniques. Computer Vision, Graphics, and Image Processing, 29:100–132, 1985.
R.M. Haralick and L.G. Shapiro. Computer and Robot Vision, volume 1. Addison-Wesley, 1992.
Edwin T. Jaynes. Prior probabilities. In R.D. Rosenkrantz, editor, E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics, chapter 7. D. Reidel, Boston, 1983 (original paper published in 1968).
T. Kanungo, B. Dom, W. Niblack, and D. Steele. A fast algorithm for MDL-based multi-band image segmentation. In International Conference on Computer Vision and Pattern Recognition. IEEE Computer Society, 1994 (to appear).
K. Keeler. Minimal length encoding of planar subdivision topologies with application to image segmentation. In AAAI 1990 Spring Symposium of the Theory and Application of Minimal Length Encoding, 1990.
Daniel Keren, Ruth Marcus, Michael Werman, and Shmuel Peleg. Segmentation by minimum length encoding. In ICPR 90, pp. 681-683, 1990.
S. Liou, A.H. Chin, and R. Jain. A parallel technique for signal-level perceptual organization. IEEE Trans PAMI, 13(4):317–325, 1991.
Y.G. Leclerc. Constructing simple stable descriptions for image partitioning. International Journal of Computer Vision, 3:73–102, 1989.
Y.G. Leclerc. The Local Structure of Image Intensity Discontinuities. PhD thesis, McGill University, Montréal, Québec, Canada, May 1989.
Y.G. Leclerc. Region grouping using the minimum-description-length principle. In DARPA Image Understanding Workshop, 1990.
C.L. Liu. Elements of Discrete Mathematics. McGraw Hill, New York, 1977.
S. Liou and R. Jain. An approach to three-dimensional image segmentation. CVGIP: Image Understanding, 53(3):237–252, 1991.
Ragnar Nohre. Topics in Descriptive Complexity. PhD thesis, Technical University of Linkoping, 1993. See Chap. 2 Coding Small Data Sets.
Alex Pentland. Part segmentation for objects recognition. Neural Computation, 1:82–91, 1989.
W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery. Numerical Recipes in C (2 ed.). Cambridge University Press, 1992.
J. Rissanen. Modelling by shortest data description. Automatica, 14:465–471, 1978.
J. Rissanen. A universal prior for integers and estimation by minimum description length. The Annals of Statistics, 2(11):211–222, 1983.
J. Rissanen. Stochastic Complexity in Statistical Inquiry, volume 15. World Scientific Series in Computer Science, 1989.
Jorma Rissanen. Fisher information and stochastic complexity. Research Report RJ 9547, IBM Research Division, 1993.
J. Sheinvald, B. Dom, W. Niblack, and D. Steele. Unsupervised image segmentation using the minimum description length principle. In Proceedings of ICPR 92, August 1992. For an expanded version see: IBM Research Report RJ 8474 (76695), (11/1/91).
R. Sedgewick. Algorithms in C. Addison Wesley, 1990.
C.E. Shannon. A mathematical theory of communication. Bell Syst Tech J., (3):379–423, 1948.
G. Strang. Linear Algebra and its Applications. Academic Press, New York, NY, 1980.
R.S. Wallace and T. Kanade. Finding natural clusters having minimum description length. In AAAI 1990 Spring Symposium on the Theory and Application of Minimum Length Methods, Stanford University, Stanford, CA, 1990.
J. Zhang and J.W. Modestino. A model fitting approach to cluster validation with application to stochastic model-based image segmentation. IEEE PAMI, 12(10):1009–1017, October 1990.
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Kanungo, T., Dom, B., Niblack, W., Steele, D. (1996). A Fast Algorithm for MDL-Based Multi-Band Image Segmentation. In: Sanz, J.L.C. (eds) Image Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58288-2_5
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DOI: https://doi.org/10.1007/978-3-642-58288-2_5
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