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 may work or IEEE-CS DOI may work. 0402 BibRef
Earlier: A1, A3, A2: ICPR92(III:260-263).
IEEE DOI may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 0402 BibRef
Earlier:
On morphological openings and closings of signals in shaped noise,
ICIP95(I: 518-521).
IEEE DOI may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 9610 BibRef
And:
Statistical optimization of gray-scale morphological filters,
ICIP96(III: 33-36).
IEEE DOI may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 9208 BibRef

Hanbury, A.G., Serra, J.,
Morphological operators on the unit circle,
IP(10), No. 12, December 2001, pp. 1842-1850.
IEEE DOI may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 0409 BibRef

Hanbury, A.G.[Allan G.],
Morphological Distinguished Regions,
CIARP07(202-211).
WWW Version. 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. 0112How 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. 0108Implementation of operators. 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.
WWW Version. 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 may work or IEEE-CS DOI may work. 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.
WWW Version. 0505 BibRef
Earlier:
Path-based morphological openings,
ICIP04(V: 3085-3088).
IEEE DOI may work or IEEE-CS DOI may work. 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 may work or IEEE-CS DOI may work. 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.
WWW Version. 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 may work or IEEE-CS DOI may work. 0510 BibRef
Earlier:
Discrete Morphology with Line Structuring Elements,
CAIP03(722-729).
WWW Version. 0311In 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 BibRef

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. 0703Sieve; 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 BibRef
Earlier:
Optimal decomposition of morphological structuring elements,
ICIP96(III: 1-4).
IEEE DOI may work or IEEE-CS DOI may work. 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.
WWW Version. 0701 BibRef
Earlier:
A Vectorial Self-dual Morphological Filter Based on Total Variation Minimization,
ISVC05(388-395).
WWW Version. 0512 BibRef
And:
A Fast and Exact Algorithm for Total Variation Minimization,
IbPRIA05(I:351).
WWW Version. 0509 BibRef

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.
WWW Version. 0701 BibRef
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).
WWW Version. 0804 BibRef

Darbon, J.[Jérôme],
A Note on the Discrete Binary Mumford-Shah Model,
MIRAGE07(283-294).
WWW Version. 0703 BibRef

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. 0702Algebraic morphological operators; Attributes; Complexity BibRef

Beucher, S.[Serge],
Numerical residues,
IVC(25), No. 4, April 2007, pp. 405-415.
WWW Version. 0702Image 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.
WWW Version. 0709Omnidirectional 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.
WWW Version. 0806Dilation; Erosion; 3D morphological filter BibRef

Imiya, A.[Atsushi], Kameda, Y.[Yusuke], Ohnishi, N.[Naoya],
Decomposition and Construction of Neighbourhood Operations Using Linear Algebra,
DGCI08(xx-yy).
WWW Version. 0804 BibRef

Chandra, S.[Shekhar], Svalbe, I.[Imants], Guédon, J.P.[Jean-Pierre],
An Exact, Non-iterative Mojette Inversion Technique Utilising Ghosts,
DGCI08(xx-yy).
WWW Version. 0804 BibRef

Welk, M.[Martin], Kim, P.[Pilwon], Olver, P.J.[Peter J.],
Numerical Invariantization for Morphological PDE Schemes,
SSVM07(508-519).
WWW Version. 0705 BibRef

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
IEEE DOI may work or IEEE-CS DOI may work. BibRef

Narayanan, A.[Ajay],
Fast Binary Dilation/Erosion Algorithm Using Kernel Subdivision,
ACCV06(II:335-342).
WWW Version. 0601 BibRef

Evans, A.N.,
Morphological gradient operators for colour images,
ICIP04(V: 3089-3092).
IEEE DOI may work or IEEE-CS DOI may work. 0505 BibRef

Roerdink, J.B.T.M.[Jos B.T.M.],
A New Class of Morphological Pyramids for Multiresolution Image Analysis,
WTRCV02(165-175). 0204 BibRef

Gao, X., Ramesh, V., Boult, T.,
Statistical Characterization of Morphological Operator Sequences,
ECCV02(IV: 590 ff.).
HTML Version. 0205 BibRef

Sasportas, R., Klein, J.C.,
Morphological filters implementation based on a co-design approach,
CIAP99(154-161).
IEEE DOI may work or IEEE-CS DOI may work. 9909 BibRef

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 may work or IEEE-CS DOI may work. 9808 BibRef

Banerji, A., Goutsias, J.,
Statistical inference for a stochastic multiresolution image decomposition scheme,
ICIP98(I: 625-629).
IEEE DOI may work or IEEE-CS DOI may work. 9810 BibRef

Heijmans, H.J.A.M.[Henk J. A. M.],
Morphological grain operators for binary images,
CAIP97(392-399).
WWW Version. 9709 BibRef

Khoudour, L., Duvieubourg, L., Meunier, B., Wan, Y.F.[Yue Feng], Deparis, J.P.,
A new fast algorithm using an adaptative structuring element applied to a counting device,
ICIP96(III: 57-60).
IEEE DOI may work or IEEE-CS DOI may work. 9610 BibRef

Gong, W.[Wei], Shi, Q.[Qinyun], Cheng, M.D.[Min-De],
Morphological filters without distorting image,
ICPR92(III:684-687).
IEEE DOI may work or IEEE-CS DOI may work. 9208 BibRef

Gong, W.[Wei],
On decomposition of structure element for mathematical morphology,
ICPR88(II: 836-838).
IEEE DOI may work or IEEE-CS DOI may work. 8811 BibRef

Chapter on Computational Vision, Regularization, Connectionist, Morphology, Scale-Space, Perceptual Grouping, Wavelets, Color, Sensors, Optical, Laser, Radar continues in
Gray Scale Morphology .