This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Image Manipulation Using M-filters in a Pyramidal Computer Model
November 1995 (vol. 17 no. 11)
pp. 1110-1115

Abstract—This paper presents how morphological transformations can be related to representations of a set on different lattices. A hierarchical definition of structuring element conveys to a class of multigrid transformations Ψk that handle changes on discrete representations of regions. The transformations correspond to upward and downward processes in a hierarchical structure. Based on multigrid transformations, a method to delineate not-perfectly-isolated objects in an nxn image requiring O(log n) time is presented. The approach considers grey level regions as sets and processes through a pyramid to carry out geometric manipulations. Extending the concept of boundary to cope with hierarchical representations of a set, a second method which identifies the boundaries in an image is discussed.

[1] A.D. Gross,A. Rosenfeld,“Multiresolution object detection and delineation,” Computer Vision, Graphics, and Image Processing, vol. 39, pp. 102-115, 1987.
[2] T.H. Hong and A. Rosenfeld,“Compact region extraction using weighted pixel linking in a pyramid,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 2, pp. 222-228, Mar. 1984.
[3] T.H. Hong and M. Shneier,“Extracting compact objects using linked pyramids,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 2, pp. 229-237, Mar. 1984.
[4] W.I. Grosky and R. Jain,“A pyramid-based approach to segmentation applied to region matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 5, pp. 639-650, Sept. 1986.
[5] V. Cantoni and S. Levialdi,“Contour labeling by pyramidal processing,” Intermediate Level Image Processing, M.J.B. Duff, ed., pp. 181-191, Academic Press, 1986.
[6] P.J. Burt and E.H. Adelson,“The Laplacian pyramid as a compact image code,” IEEE Trans. Communications, vol. 31, no. 4, pp. 337-345, Apr. 1983.
[7] J. Princen,J. Illingworth,, and J. Kittler,“A hierarchical approach to line extraction,” Computer Vision’89 and Pattern Recognition Proc. , pp. 92-97, IEEE CS, 1989.
[8] P. Meer,E.S. Baugher,, and A. Rosenfeld,“Frequency domain analysis and synthesis of image pyramid generating kernels,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 4, pp. 512-522, July 1987.
[9] P. Maragos and R.W. Schafer,“Morphological filters-Part I: Their set-theoretic analysis and relations to linear shift-invariant,” IEEE Trans. Acoustic, Speech, and Signal Processing, vol. 35, no. 8, pp. 1,153-1,169, Aug. 1987.
[10] P. Maragos and R.W. Schafer,“Morphological filters-Part II: Their relations to median order-statistic and stack filters,” IEEE Trans. Acoustic, Speech, and Signal Processing, vol. 35, no. 8, pp. 1,170-1,184, Aug. 1987.
[11] P. Maragos,“A representation theory for morphological image and signal,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 586-599, June 1989.
[12] M. Chen and P. Yan,“A multiscaling approach based on morphological filtering,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 694-700, July 1989.
[13] A. Morales and R. Acharya,“Nonlinear multiscale filtering using mathematical morphology,” Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 572-578,Champaign, Ill., June15-18, 1992.
[14] A. Toet,“A hierarchical morphological image decomposition,” Pattern Recognition Letters, vol. 11, no. 4, pp. 267-274, Apr. 1990.
[15] G. Grätzer,General Lattice Theory.New York: Acadamic Press, 1978.
[16] D. Karis and K.M. Dobroth, "Automating Services with Speech Recognition over the Public Switched Telephone Network: Human Factors Considerations," IEEE J. of Selected Areas in Communications, Vol. 9, No. 4, 1991, pp. 574-585.
[17] C. Ronse,“Why mathematical morphology needs complete lattices,” Signal Processing, vol. 21, pp. 129-154, 1990.
[18] J. Serra,“Introduction to mathematical morphology,” Computer Vision, Graphics, and Image Processing, vol. 35, pp. 283-305, 1986.
[19] J. Serra,Image Analysis and Mathematical Morphology, vol. 1. San Diego: Academic Press, 1982.
[20] R.M. Haralick,S.R. Sternberg,, and X. Zhuang,“Image analysis using mathematical morphology,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 4, pp. 532-550, July 1988.
[21] H.J.A.M. Heijmans, "Theoretical Aspects of Gray-Level Morphology," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 6, pp. 568-582, June 1991.
[22] X. Zhuang and R. Haralick, “Morphological Structuring Element Decomposition,” Computer Vision, Graphics, and Image Processing, vol. 35, pp. 370–382, 1986.
[23] J.L. Stephen,K. Jacobson,, and H. Brian,“Quantitative precision of an automated, fluorescence-based image cytometer,” Analytical Quantitative Cytology and Histology, vol. 4, no. 3, pp. 187-202, June 1992.
[24] F. Meyer,“Automatic screening of cytological specimens,” Computer Vision, Graphics, and Image Processing, vol. 35, pp. 356-369, 1986.
[25] S. Sternberg, “Grayscale Morphology,” Computer Graphics and Image Processing, vol. 35, pp. 333-355, 1986.

Index Terms:
Mathematical morphology, multiresolution, image pyramids, image segmentation, parallel algorithms.
Citation:
M.e. Montiel, A.s. Aguado, M.a. Garza-Jinich, J. Alarcón, "Image Manipulation Using M-filters in a Pyramidal Computer Model," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 11, pp. 1110-1115, Nov. 1995, doi:10.1109/34.473240
Usage of this product signifies your acceptance of the Terms of Use.