4.3.2.1 Morphological Operator Decomposition

Zhuang, X.H.[Xin-Hua], Haralick, R.M.[Robert M.],
Morphological Structuring Element Decomposition,
CVGIP(35), No. 3, September 1986, pp. 370-382.
WWW Version. BibRef 8609

Richardson, C.H., and Schafer, R.W.,
A Lower Bound for Structuring Element Decompositions,
PAMI(13), No. 4, April 1991, pp. 365-369.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9104
And:
Symbolic Manipulation and Analysis of Morphological Expressions,
ICASSP90(2173-2176). BibRef

Kanungo, T., Haralick, R.M.,
Vector-Space Solution for a Morphological Shape-Decomposition Problem,
JMIV(2), 1992, pp. 51-82. BibRef 9200
Morphological Decomposition of Restricted Domains: A Vector Space Solution,
CVPR92(627-629).
IEEE Abstract. IEEE Top Reference. BibRef

Camps, O.I., Kanungo, T., Haralick, R.M.,
Gray-scale structuring element decomposition,
IP(5), No. 1, January 1996, pp. 111-120.
IEEE DOI Link 0402
BibRef
Earlier: A1, A3, A2: ICPR92(III:260-263).
IEEE DOI Link 9208
BibRef

Li, D.,
Recursive Operations in Image Algebra,
JMIV(1), 1992, pp. 23-42. BibRef 9200

Li, D.,
Morphological Template Decomposition with Max-Polynomials,
JMIV(1), 1992, pp. 215-221. BibRef 9200

Yang, J.Y., Chen, C.C.,
Decomposition of Additively Separable Structuring Elements with Applications,
PR(26), No. 6, June 1993, pp. 867-875.
WWW Version. BibRef 9306

Zhuang, X.,
Decomposition of Morphological Structuring Elements,
JMIV(4), 1994, pp. 5-18. BibRef 9400
And:
Morphological structuring function decomposition,
CVPR92(566-571).
IEEE Abstract. IEEE Top Reference. 0403
BibRef

Shih, F.Y.C.[Frank Yeong Chyang], Mitchell, O.R.[Owen Robert],
Threshold Decomposition of Gray-Scale Morphology into Binary Morphology,
PAMI(11), No. 1, January 1989, pp. 31-42.
IEEE Abstract. IEEE Top Reference.
WWW Version. See also Rapid Euclidean Distance Transform Using Grayscale Morphology Decomposition. BibRef 8901

Shih, F.Y.C.[Frank Yeong Chyang], Mitchell, O.R.[Owen Robert],
Decomposition of gray-scale morphological structuring elements,
PR(24), No. 3, 1991, pp. 195-203.
WWW Version. 0401
BibRef

Pu, C.C., Shih, F.Y.C.,
Threshold Decomposition of Gray-Scale Soft Morphology into Binary Soft Morphology,
GMIP(57), No. 6, November 1995, pp. 522-526. BibRef 9511
Earlier: A2, A1:
Threshold decomposition of soft morphological filters,
CVPR93(672-673).
IEEE Abstract. IEEE Top Reference. 0403
BibRef

Shih, F.Y.C., Puttagunta, P.[Padmaja],
Recursive soft morphological filters,
IP(4), No. 7, July 1995, pp. 1027-1032.
IEEE DOI Link 0402
BibRef

Shih, F.Y.C.[Frank Y.C.], Wu, Y.T.[Yi-Ta],
Decomposition of arbitrary gray-scale morphological structuring elements,
PR(38), No. 12, December 2005, pp. 2323-2332.
WWW Version. 0510
See also Enhancement of image watermark retrieval based on genetic algorithms. BibRef

Shih, F.Y.C., Wu, H.,
Decomposition of Geometric-Shaped Structuring Elements Using Morphological Transformations on Binary Images,
PR(25), No. 10, October 1992, pp. 1097-1106.
WWW Version. BibRef 9210

Shih, F.Y.C., Pu, C.C.,
Morphological Shape Description Using Geometric Spectrum on Multidimensional Binary Images,
PR(25), No. 9, September 1992, pp. 921-927.
WWW Version. BibRef 9209

Park, H.[Hochong], Chin, R.T.,
Optimal decomposition of convex morphological structuring elements for 4-connected parallel array processors,
PAMI(16), No. 3, March 1994, pp. 304-313.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0401
BibRef

Park, H.C., Chin, R.T.,
Decomposition of Arbitrarily Shaped Morphological Structuring Elements,
PAMI(17), No. 1, January 1995, pp. 2-15.
IEEE Abstract. IEEE Top Reference.
WWW Version. See also Note on Park and Chin's Algorithm, A. BibRef 9501

Shih, F.Y.C., King, C.T.[Chung Ta], Pu, C.C.,
Pipeline architectures for recursive morphological operations,
IP(4), No. 1, January 1995, pp. 11-18.
IEEE DOI Link 0402
BibRef

Lucke, L., Chakrabarti, C.,
A digit-serial architecture for gray-scale morphological filtering,
IP(4), No. 3, March 1995, pp. 387-391.
IEEE DOI Link 0402
BibRef

Chen, S.[Su], Haralick, R.M.,
Recursive erosion, dilation, opening, and closing transforms,
IP(4), No. 3, March 1995, pp. 335-345.
IEEE DOI Link 0402
BibRef

Haralick, R.M., Chen, S., Kanungo, T.,
Recursive opening transform,
CVPR92(560-565).
IEEE Abstract. IEEE Top Reference. 0403
BibRef

Morales, A., Acharya, R., Ko, S.J.[Sung-Jea],
Morphological pyramids with alternating sequential filters,
IP(4), No. 7, July 1995, pp. 965-977.
IEEE DOI Link 0402
BibRef

Morales, A., Acharya, R.,
Nonlinear multiscale filtering using mathematical morphology,
CVPR92(572-578).
IEEE Abstract. IEEE Top Reference. 0403
BibRef

Jin, X.C., Ong, S.H., Jayasooriah,
A domain operator for binary morphological processing,
IP(4), No. 7, July 1995, pp. 1042-1046.
IEEE DOI Link 0402
BibRef

Sidiropoulos, N.D., Baras, J.S., Berenstein, C.A.,
Further results on MAP optimality and strong consistency of certain classes of morphological filters,
IP(5), No. 5, May 1996, pp. 762-764.
IEEE DOI Link 0402
BibRef
Earlier:
On morphological openings and closings of signals in shaped noise,
ICIP95(I: 518-521).
IEEE DOI Link 9510
BibRef

Singh, B., Siddiqi, M.U.,
A Simplified Algorithm for Approximate Separable Decomposition of Morphological Templates,
PR(29), No. 9, September 1996, pp. 1519-1522.
WWW Version. Template Decomposition. Separable Templates. Structuring Elements. BibRef 9609
And:
On MAP optimality of gray-scale morphological filters,
ICIP96(III: 29-32).
IEEE DOI Link 9610
BibRef
And:
Statistical optimization of gray-scale morphological filters,
ICIP96(III: 33-36).
IEEE DOI Link 9610
BibRef

Ghosh, P.K.,
The Indecomposability Problem in Binary Morphology: An Algorithmic Approach,
JMIV(6), No. 2-3, June 1996, pp. 169-198. 9608
BibRef

Ghosh, P.K., Haralick, R.M.,
Mathematical Morphological Operations of Boundary-Represented Geometric Objects,
JMIV(6), No. 2-3, June 1996, pp. 199-222. 9608
BibRef

Sussner, P., Ritter, G.X.,
Decomposition of Gray-Scale Morphological Templates Using The Rank Method,
PAMI(19), No. 6, June 1997, pp. 649-658.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9708
BibRef

Sussner, P., Ritter, G.X.,
Rank-Based Decompositions of Morphological Templates,
IP(9), No. 8, August 2000, pp. 1420-1430.
IEEE DOI Link 0008
BibRef

Vanrell, M., Vitria, J.,
Optimal 3x3 Decomposable Disks for Morphological Transformations,
IVC(15), No. 11, November 1997, pp. 845-854.
WWW Version. 9712
BibRef
Earlier:
3X3 decomposition of circular structuring elements,
ICIP96(III: 5-8).
IEEE DOI Link 9610
BibRef

Anelli, G.[Giovanni], Broggi, A.[Alberto], Destri, G.[Giulio],
Decomposition of Arbitrarily Shaped Binary Morphological Structuring Elements Using Genetic Algorithms,
PAMI(20), No. 2, February 1998, pp. 217-224.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9803
BibRef
Earlier:
Experiments on the decomposition of arbitrarily shaped binary morphological structuring elements,
CIAP97(I: 543-550).
WWW Version. 9709
BibRef

Broggi, A., Conte, G., Lavagno, L., Gregoretti, F., Sansoe, C., Burzio, G., Reyneri, L.M.,
PAPRICA-3: a real-time morphological image processor,
ICIP94(III: 654-658).
IEEE DOI Link 9411
BibRef

Hashimoto, R.F.[Ronaldo Fumio], Barrera, J.[Junior], Ferreira, C.E.[Carlos Eduardo],
A Combinatorial Optimization Technique for the Sequential Decomposition of Erosions and Dilations,
JMIV(13), No. 1, August 2000, pp. 17-33.
WWW Version. 0006
BibRef

Hashimoto, R.F.[Ronaldo Fumio], Barrera, J.[Junior],
From the Sup-Decomposition to Sequential Decompositions,
JMIV(15), No. 3, November 2001, pp. 197-216.
WWW Version. 0111
BibRef

Boutalis, Y.S., Tsirikolias, K., Metrtzios, B.G., Andreadis, I.T.,
Implementation of morphological filters using coordinate logic operations,
PR(35), No. 1, January 2002, pp. 187-198.
WWW Version. 0111
BibRef

Gatos, B.[Basilios], Perantonis, S.J.[Stavros J.], Papamarkos, N.[Nikos], Andreadis, I.[Ioannis],
Fast Implementation Of Morphological Operations Using Binary Image Block Decomposition,
IJIG(4), No. 2, April 2004, pp. 183-202. 0404
BibRef

Engbers, E.A., van den Boomgaard, R., Smeulders, A.W.M.,
Decomposition of Separable Concave Structuring Functions,
JMIV(15), No. 3, November 2001, pp. 181-195.
WWW Version. 0111
BibRef

van den Boomgaard, R., Smeulders, A.W.M.,
The morphological structure of images,
ICPR92(III:268-271).
IEEE DOI Link 9208
BibRef

Hanbury, A.G., Serra, J.,
Morphological operators on the unit circle,
IP(10), No. 12, December 2001, pp. 1842-1850.
IEEE DOI Link 0201
BibRef

Hanbury, A.G.[Allan G.], Serra, J.[Jean],
Colour Image Analysis in 3D-Polar Coordinates,
DAGM03(124-131).
HTML Version. 0310
BibRef
Earlier:
Mathematical Morphology in the HLS Colour Space,
BMVC01(Poster Session 2. and Demonstrations).
HTML Version. Ecole des Mines de Paris 0110
BibRef

Hanbury, A.G.,
The morphological top-hat operator generalised to multi-channel images,
ICPR04(I: 672-675).
IEEE DOI Link 0409
BibRef

Hanbury, A.G.[Allan G.],
Morphological Distinguished Regions,
CIARP07(202-211).
Springer DOI Link 0711
BibRef

Soille, P.[Pierre],
On morphological operators based on rank filters,
PR(35), No. 2, February 2002, pp. 527-535.
WWW Version. 0201
BibRef

Soille, P.[Pierre], Talbot, H.[Hugues],
Directional Morphological Filtering,
PAMI(23), No. 11, November 2001, pp. 1313-1329.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0112
How to efficiently implement them. BibRef

Hashimoto, R.F.[Ronaldo Fumio], Barrera, J.[Junior],
A Note on Park and Chin's Algorithm,
PAMI(24), No. 1, January 2002, pp. 139-144.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0201
See also Decomposition of Arbitrarily Shaped Morphological Structuring Elements. BibRef

Meijster, A.[Arnold], Wilkinson, M.H.F.[Michael H.F.],
A Comparison of Algorithms for Connected Set Openings and Closings,
PAMI(24), No. 4, April 2002, pp. 484-494.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0204
BibRef
Earlier:
Fast Computation of Morphological Area Pattern Spectra,
ICIP01(III: 668-671).
IEEE Abstract. IEEE Top Reference. 0108
Implementation of operators. BibRef

Wilkinson, M.H.F.[Michael H.F.],
Connected filtering by reconstruction: Basis and new advances,
ICIP08(2180-2183).
IEEE DOI Link 0810
BibRef

Gil, J.Y.[Joseph Yossi], Kimmel, R.[Ron],
Efficient Dilation, Erosion, Opening, and Closing Algorithms,
PAMI(24), No. 12, December 2002, pp. 1606-1617.
IEEE Abstract. IEEE Top Reference. 0212
BibRef

Sussner, P.[Peter],
Generalizing Operations of Binary Autoassociative Morphological Memories Using Fuzzy Set Theory,
JMIV(19), No. 2, September 2003, pp. 81-93.
WWW Version. 0308
BibRef

Sussner, P.[Peter], Valle, M.E.[Marcos Eduardo],
Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality,
JMIV(32), No. 2, October 2008, pp. xx-yy.
Springer DOI Link 0804
BibRef

Jonker, P.P.[Pieter P.],
Morphological operations in recursive neighbourhoods,
PRL(25), No. 5, 5 April 2004, pp. 527-541.
WWW Version. 0403
BibRef

Herskovits, E.H., Peng, H., Davatzikos, C.,
A Bayesian Morphometry Algorithm,
MedImg(23), No. 6, June 2004, pp. 723-737.
IEEE Abstract. IEEE Top Reference. 0406
BibRef

Chen, R., Herskovits, E.H.,
Graphical-Model-Based Morphometric Analysis,
MedImg(24), No. 10, October 2005, pp. 1237-1248.
IEEE DOI Link 0510
BibRef

Heijmans, H.J.A.M.[Henk J.A.M.], Buckley, M.[Michael], Talbot, H.[Hugues],
Path Openings and Closings,
JMIV(22), No. 2-3, May 2005, pp. 107-119.
Springer DOI Link 0505
BibRef
Earlier:
Path-based morphological openings,
ICIP04(V: 3085-3088).
IEEE DOI Link 0505
BibRef

Shih, F.Y.C.[Frank Y.C.], Wu, Y.T.[Yi-Ta],
Decomposition of binary morphological structuring elements based on genetic algorithms,
CVIU(99), No. 2, August 2005, pp. 291-302.
WWW Version. 0506
BibRef

Chien, S.Y., Ma, S.Y., Chen, L.G.,
Partial-Result-Reuse Architecture and Its Design Technique for Morphological Operations With Flat Structuring Elements,
CirSysVideo(15), No. 9, September 2005, pp. 1156-1169.
IEEE DOI Link 0509
BibRef

Burgeth, B.[Bernhard], Weickert, J.[Joachim],
An Explanation for the Logarithmic Connection between Linear and Morphological System Theory,
IJCV(64), No. 2-3, September 2005, pp. 157-169.
Springer DOI Link 0510
BibRef
Earlier:
An Explanation for the Logarithmic Connection between Linear and Morphological Systems,
ScaleSpace03(325-339).
HTML Version. 0310
BibRef

Luengo Hendriks, C.L., van Vliet, L.J.,
Using Line Segments as Structuring Elements for Sampling-Invariant Measurements,
PAMI(27), No. 11, November 2005, pp. 1826-1831.
IEEE DOI Link 0510
BibRef
Earlier:
Discrete Morphology with Line Structuring Elements,
CAIP03(722-729).
WWW Version. 0311
In order to get higher resolution structuring elements. BibRef

Hendriks, C.L.L.[Cris L. Luengo], van Vliet, L.J.[Lucas J.],
Basic Morphological Operations, Band-Limited Images and Sampling,
ScaleSpace03(313-324).
HTML Version. 0310
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Luengo Hendriks, C.L., van Kempen, G.M.P., van Vliet, L.J.,
Improving the accuracy of isotropic granulometries,
PRL(28), No. 7, May 2007, pp. 865-872.
WWW Version. 0703
Sieve; Scale-space; Mathematical morphology; Image analysis; Size distribution BibRef

Yang, H.T.[Hsin-Tai], Lee, S.J.[Shie-Jue],
Decomposition of morphological structuring elements with integer linear programming,
VISP(152), No. 2, April 2005, pp. 148-154.
WWW Version. 0510
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Earlier:
Optimal decomposition of morphological structuring elements,
ICIP96(III: 1-4).
IEEE DOI Link 9610
BibRef

Darbon, J.[Jérôme], Sigelle, M.[Marc],
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization,
JMIV(26), No. 3, December 2006, pp. 261-276.
Springer DOI Link 0701
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Earlier:
A Vectorial Self-dual Morphological Filter Based on Total Variation Minimization,
ISVC05(388-395).
Springer DOI Link 0512
BibRef
And:
A Fast and Exact Algorithm for Total Variation Minimization,
IbPRIA05(I:351).
Springer DOI Link 0509
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Darbon, J.[Jérôme], Sigelle, M.[Marc],
Image Restoration with Discrete Constrained Total Variation Part II: Levelable Functions, Convex Priors and Non-Convex Cases,
JMIV(26), No. 3, December 2006, pp. 277-291.
Springer DOI Link 0701
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Earlier:
Exact Optimization of Discrete Constrained Total Variation Minimization Problems,
IWCIA04(548-557).
WWW Version. 0505
BibRef

Darbon, J.[Jérôme],
Global Optimization for First Order Markov Random Fields with Submodular Priors,
IWCIA08(xx-yy).
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Darbon, J.[Jérôme],
A Note on the Discrete Binary Mumford-Shah Model,
MIRAGE07(283-294).
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Talbot, H.[Hugues], Appleton, B.[Ben],
Efficient complete and incomplete path openings and closings,
IVC(25), No. 4, April 2007, pp. 416-425.
WWW Version. 0702
Algebraic morphological operators; Attributes; Complexity BibRef

Beucher, S.[Serge],
Numerical residues,
IVC(25), No. 4, April 2007, pp. 405-415.
WWW Version. 0702
Image analysis; Mathematical morphology; Residues; Ultimate opening; Quasi-distance; Image segmentation; Hierarchy BibRef

Strauss, O.[Olivier], Comby, F.[Frederic],
Variable structuring element based fuzzy morphological operations for single viewpoint omnidirectional images,
PR(40), No. 12, December 2007, pp. 3578-3596.
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Omnidirectional images; Single viewpoint; Mathematical morphology; Choquet and Sugeno fuzzy integrals; Standardized fuzzy partition; Sampling; Variable structuring element; Filtering BibRef

Kim, W.J.[Wook-Joong], Kim, S.D.[Seong-Dae], Radha, H.[Hyder],
3D binary morphological operations using run-length representation,
SP:IC(23), No. 6, July 2008, pp. 442-450.
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Dilation; Erosion; 3D morphological filter BibRef

Hedberg, H., Dokladal, P., Owall, V.,
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IP(18), No. 3, March 2009, pp. 562-572.
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Gao, H., Tham, J.Y., Xue, P., Lin, W.,
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WWW Version. 0905
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Fabrizio, J.[Jonathan], Marcotegui, B.[Beatriz],
Fast Implementation of the Ultimate Opening,
ISMM09(272-281).
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Porter, R.[Reid], Zimmer, G.B.[G. Beate], Hush, D.[Don],
Stack Filter Classifiers,
ISMM09(282-294).
Springer DOI Link 0908
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Levillain, R.[Roland], Géraud, T.[Thierry], Najman, L.[Laurent],
Milena: Write Generic Morphological Algorithms Once, Run on Many Kinds of Images,
ISMM09(295-306).
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Tankyevych, O.[Olena], Talbot, H.[Hugues], Dokladál, P.[Petr], Passat, N.[Nicolas],
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ISMM09(137-148).
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Welk, M.[Martin], Breuß, M.[Michael], Vogel, O.[Oliver],
Differential Equations for Morphological Amoebas,
ISMM09(104-114).
Springer DOI Link 0908
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Baba-Ali, M.[Mehdi], Damiand, G.[Guillaume], Skapin, X.[Xavier], Marcheix, D.[David],
Insertion and Expansion Operations for n-Dimensional Generalized Maps,
DGCI08(xx-yy).
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Imiya, A.[Atsushi], Kameda, Y.[Yusuke], Ohnishi, N.[Naoya],
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DGCI08(xx-yy).
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Chandra, S.[Shekhar], Svalbe, I.[Imants], Guédon, J.P.[Jean-Pierre],
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Numerical Invariantization for Morphological PDE Schemes,
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de A. Araujo, R., Madeiro, F., Ferreira, T.A.E., de Sousa, R.P., Pessoa, L.F.C.,
Improved Evolutionary Hybrid Method for Designing Morphological Operators,
ICIP06(2417-2420). 0610

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Narayanan, A.[Ajay],
Fast Binary Dilation/Erosion Algorithm Using Kernel Subdivision,
ACCV06(II:335-342).
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Evans, A.N.,
Morphological gradient operators for colour images,
ICIP04(V: 3089-3092).
IEEE DOI Link 0505
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Gao, X., Ramesh, V., Boult, T.,
Statistical Characterization of Morphological Operator Sequences,
ECCV02(IV: 590 ff.).
HTML Version. 0205
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Sasportas, R., Klein, J.C.,
Morphological filters implementation based on a co-design approach,
CIAP99(154-161).
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Li, C.K.[Chi-Kwong], Lam, R.[Ringo], Ip, H.[Horace],
Approaches to Decompose Flat Structuring Element for Fast Overlapping Search Morphological Algorithm,
ICPR98(Vol II: 1461-1463).
IEEE DOI Link 9808
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Banerji, A., Goutsias, J.,
Statistical inference for a stochastic multiresolution image decomposition scheme,
ICIP98(I: 625-629).
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Heijmans, H.J.A.M.[Henk J. A. M.],
Morphological grain operators for binary images,
CAIP97(392-399).
WWW Version. 9709
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Khoudour, L., Duvieubourg, L., Meunier, B., Wan, Y.F.[Yue Feng], Deparis, J.P.,
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ICIP96(III: 57-60).
IEEE DOI Link 9610
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Gong, W.[Wei], Shi, Q.[Qinyun], Cheng, M.D.[Min-De],
Morphological filters without distorting image,
ICPR92(III:684-687).
IEEE DOI Link 9208
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Gong, W.[Wei],
On decomposition of structure element for mathematical morphology,
ICPR88(II: 836-838).
IEEE DOI Link 8811
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Chapter on Computational Vision, Regularization, Connectionist, Morphology, Scale-Space, Perceptual Grouping, Wavelets, Color, Sensors, Optical, Laser, Radar continues in
Color Morphology, Gray Scale Morphology .