PrelucrareaPrelucrarea ImaginilorImaginilor CursCurs 88 MorphologicalMorphological ImageImage ProcessingProcessing
Utilizate in extragerea componentelor unei imagini la reprezentare si descriere:
Extragere contur
Schelet
Invelitoare convexa
Filtrare
Subtiere
Curatare
...
2/21 GrayGray--ScaleScale imagesimages -- EroziuneEroziune,, DilatareDilatare
Functiile pentru valorile nuantelor de gri:
XX(x,y) Æ obiect BB(x,y) Æ element structural
DilatareaDilatarea luilui XX prin BB, notată cu XX ℗℗ BB este:
(XX ℗ B)B (s,t) = MaxMax{XX(s-x,y-t)++BB(x,y) / ((s-x),(y-t))∈XX, (x,y)∈BB}
EroziuneaEroziunea lui X de către BB, notată cu XXΘΘBB este:
(XX Θ B)B (s,t) = MinMin{XX(s+x,y+t)--BB(x,y) / ((s+x),(y+t))∈XX, (x,y)∈BB}
3/21 …… GrayGray--ScaleScale imagesimages - Eroziune, Dilatare ... proprietăţi: ExempluExemplu:: X,X, XX ℗ B,B, XX Θ BB ::
Dualitate (eroziunea şi dilatarea sunt duale faţă de complementare notată cu XC): (X(XC ℗℗ ⌐B)B) (s,t) == (X(X ΘΘ B)B)C (s,t) ,, unde: XXC == --XX (x,y) si ⌐BB == BB (-x,-y).. 4/21 … Morphological Image Processing - Transformări uzuale derivate
Deschiderea lui X faţă de B, notată cu XB este :
XB = (X Θ B) ℗ B; B Închiderea lui X faţă de B, notată cu X este: XB = (X ℗ B) Θ B;
Dualitate (Deschiderea şi Închiderea ) :
B C C ((X ) = (X(X )) (⌐B) 5/21 … Morphological Image Processing - Transformări uzuale derivate
Netezire morfologica :
B gg = (XB) ;
Efect: atenuare a nuantelor deschise/inchise si a zgomotului:
6/21 … Morphological Image Processing - Transformări uzuale derivate
Gradientul morfologic :
gg = (X ℗ B) – (X Θ B);
Top-Hat :
hh = X - XB;
7/21 … Morphological Image Processing - Transformări uzuale derivate
Segmentare texturala :
Se aplica operatorul de inchidere utilizand succesiv elemente structurale mai mari decat elementele de textura mici;
Se aplica operatorul de deschidere utilizand un element structural mai mare decat distanta dintre elemntele de textura mari;
Avand o regiune deschisa in stanga si una inchisa in dreapta, vom folosi un prag simplu pentru a rezulta granita dintre cele doua texturi.
8/21 … Morphological Image Processing - Transformări uzuale derivate
Granulometrie – determina distributia dimensiunii particulelor dintr-o imagine :
Se aplica operatorul de deschidere utilizand succesiv elemente structurale tot mai mari;
Se calculeaza diferenta dintre imagine initiala si cea obtinuta prin deschidere la fiecare pas;
In final aceste diferente sunt normalizate si utilizate la construirea histogramei.
• Deschiderea corespunzatoare unei anumite dimensiuni are efect maxim in regiunile care contin particule avand acea dimensiune. 9/21 BibliografieBibliografie • Image Analysis and Mathematical Morphology by Jean Serra, ISBN 0126372403 (1982) • Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances by Jean Serra, ISBN 0-12-637241-1 (1988) • An Introduction to Morphological Image Processing by Edward R. Dougherty, ISBN 0-8194-0845-X (1992) • Morphological Image Analysis; Principles and Applications by Pierre Soille, ISBN 3540-65671-5 (1999) • Mathematical Morphology and its Application to Signal Processing, J. Serra and Ph. Salembier (Eds.), proceedings of the 1st international symposium on mathematical morphology (ISMM'93), ISBN 84-7653-271-7 (1993) • Mathematical Morphology and Its Applications to Image Processing, J. Serra and P. Soille (Eds.), proceedings of the 2nd international symposium on mathematical morphology (ISMM'93), ISBN 0-7923-3093-5 (1994) • Mathematical Morphology and its Applications to Image and Signal Processing, Henk J.A.M. Heijmans and Jos B.T.M. Roerdink (Eds.), proceedings of the 4th international symposium on mathematical morphology (ISMM'98), ISBN 0-7923- 5133-9 (1998) • Mathematical Morphology: 40 Years On, Christian Ronse, Laurent Najman, and Etienne Decencière (Eds.), ISBN-10: 1-4020-3442-3 (2005) • Mathematical Morphology and its Applications to Signal and Image Processing, Gerald J.F. Banon, Junior Barrera, Ulisses M. Braga-Neto (Eds.), proceedings of the 8th international symposium on mathematical morphology (ISMM'07), ISBN 978-85-17-00032-4 (2007) 10/21 AdreseAdrese WebWeb
• Online course on mathematical morphology, by Jean Serra (in English, French, and Spanish) • Center of Mathematical Morphology, Paris School of Mines • History of Mathematical Morphology, by Georges Matheron and Jean Serra • Morphology Digest, a newsletter on mathematical morphology, by Pierre Soille • Lectures on Image Processing: A collection of 18 lectures in pdf format from Vanderbilt University. Lectures 16-18 are on Mathematical Morphology, by Alan Peters • Mathematical Morphology; from Computer Vision lectures, by Robyn Owens • Free SIMD Optimized Image processing library • Java applet demonstration • FILTERS : a free open source image processing library • Fast morphological erosions, dilations, openings, and closings • Retrieved from http://en.wikipedia.org/wiki/Mathematical_morphology • Morphological operations for color image processing, J. Electron. Imaging, Vol. 8, 279 (1999); DOI:10.1117/1.482677 11/21 AA newnew approachapproach toto morphologicalmorphological colorcolor imageimage processingprocessing
G. Louverdis, M. I. Vardavoulia, I. Andreadis , and Ph. Tsalides Laboratory of Electronics, Section of Electronics and Information Systems Technology, Department of Electrical & Computer Engineering, Democritus University of Thrace, GR-67100 Xanthi, Greece Received 10 December 2000; revised 1 June 2001; accepted 5 July 2001 Available online 12 April 2002. Abstract This paper presents a new approach to the generalization of the concepts of grayscale morphology to color images. A new vector ordering scheme is proposed, infimum and supremum operators are defined, and the fundamental vector morphological operations are extracted. The basic properties of the presented vector morphology are described and its similarities to grayscale morphological operators are pointed out. The main advantages of the proposed methodology are that is vector preserving and provides improved results in many morphological applications. Furthermore, experimental results demonstrate the applicability of the proposed technique in a number of image processing and analysis problems, such as noise removal, edge detection and skeleton extraction. Author Keywords: Vector ordering; Mathematical morphology; Color images
Article Outline 1. Introduction 2. A new vector ordering in the HSV color space 3. Definitions of new infimum and supremum operators 4. Morphological operators for color images 4.1. Basic definitions 4.2. Vector erosion 4.3. Vector dilation 4.4. Basic properties of vector erosion and dilation 4.4.1. The adjunction property 4.4.2. Other properties 5. Morphological filtering for color images 6. Other applications 6.1. Boundary extraction 6.2. Color image skeletonization 7. Conclusions References Vitae
12/21 MorphologicalMorphological operationsoperations forfor colorcolor imageimage processingprocessing
J. Electron. Imaging, Vol. 8, 279 (1999); DOI:10.1117/1.482677
Mary L. Comer and Edward J. Delp Purdue University, Video and Image Processing Laboratory, School of Electrical Engineering, West Lafayette, Indiana
In this paper operations based on mathematical morphology which have been developed for binary and grayscale images are extended to color images. We investigate two approaches for "color morphology"—a vector approach and a component-wise approach. New vector morphological filtering operations are defined, and a set-theoretic analysis of these vector operations is presented. We also present experimental results comparing the performance of the vector approach and the component-wise approach for multiscale color image analysis and for noise suppression in color images.
13/21 SoftSoft MorphologicalMorphological ColorColor ImageImage Processing:Processing: AA FuzzyFuzzy ApproachApproach
Gerasimos Louverdis and Ioannis Andreadis a) Soft Erosion Soft erosion of f by g at a point x is defined as follows: ( f Θ [β, a, k])(x) = min(k) (ΜSn1), for x: D[gx]⊆ D[f] where ΜSn1 denotes the following multi-set of the HSV color space: ΜSn1 = { k◊( f (z1) –ax (z1))} ∪ { f (z2) – βx (z2)} for z1 ∈ D [ f ] ∩ D [ ax] and z2 ∈ D [ f ] ∩ D [ βχ] b) Soft Dilation Soft dilation of f by g at a point x is defined as follows: ( f ℗ [β, a, k])(x) = max(k) (ΜSn2), for x: D[f] ∩ D[g’-x]≠∅ In this case ΜSn2 denotes the following multi-set of the HSV color space: ΜSn2 = { k◊( f (z1) + a-x (-z1))} ∪ { f (z2) + β-x (-z2)} for z1 ∈ D [ f ] ∩ D [ a’-x] and z2 ∈ D [ f ] ∩ D [ β’-x]
14/21 TemaTema
RealizaRealizaţţii următoarele TransformTransformăăriri MorfologiceMorfologice :
o)o) EroziuneaEroziunea şii DilatareaDilatarea a)a) DeschidereaDeschiderea b)b) ÎÎnchidereanchiderea c)c) NetezireNetezire d)d) GradientGradient e)e) TopTop--Hat,Hat, f)f) SegmentareSegmentare TexturalaTexturala g)g) HistogramaHistograma GranulometricaGranulometrica
h)h) oo transformaretransformare colorcolor (la alegere) 15/21 Bibliografie
4.3.2.2 Gray Scale Morphology Chapter Contents (Back) Gray Scale Morphology. Sternberg, S.R., Grayscale Morphology, CVGIP(35), No. 3, 1987, pp. 333-355. WWW Version. BibRef 8700 Earlier: with added A1, A3: Haralick, R.M., Zhuang, X., CVPR86(543-550). Basically an introduction to what grayscale morphology. BibRef Heijmans, H.J.A.M., Theoretical Aspects of Gray-Level Morphology, PAMI(13), No. 6, June 1991, pp. 568-582. IEEE Abstract. WWW Version. BibRef 9106 Heijmans, H.J.A.M., A Note on the Umbra Transform in Gray-Scale Morphology, PRL(14), 1993, pp. 877-881. BibRef 9300 Dougherty, E.R., Euclidean Gray-Scale Granulometries: Representation and Umbra Inducement, JMIV(1), 1992, pp. 7-21. BibRef 9200 Dougherty, E.R., Optimal Mean-Absolute-Error Filtering of Gray-Scale Signals by the Morphological Hit-or-Miss Transform, JMIV(4), 1994, pp. 255-271. BibRef 9400 Dougherty, E.R., The Dual Representation of Gray-Scale Morphological Filters,CVPR89(172-177). IEEE Abstract. BibRef 8900 Dougherty, E.R., Hausdorf-metric interpretation of convergence in the Matheron topology for binary mathematical morphology,ICPR90(I: 870-875). IEEE DOI Link 9006 BibRef Zhao, D., Dougherty, E.R., 16/21 Bibliografie
Morphological Hit-or-Miss Transformation for Shape Recognition, JVCIR(2), 1991, pp. 230-243. BibRef 9100 Dougherty, E.R., Zhao, D., Model-Based Characterization of Statistically Optimal Design for Morphological Shape Recognition Algorithms via the Hit-or-Miss Transform, JVCIR(3), 1992, pp. 147-160. BibRef 9200 Dougherty, E.R., Optimal Mean-Square N-Observation Digital Morphological Filters: I. Optimal Binary Filters, CVGIP(55), No. 1, January 1992, pp. 36-54. WWW Version. BibRef 9201 Optimal Mean-Square N-Observation Digital Morphological Filters: II. Optimal Gray-Scale Filters, CVGIP(55), No. 1, January 1992, pp. 55-72. WWW Version. BibRef Dougherty, E.R., Unification of Nonlinear Filtering in the Context of Binary Logical Calculus, Part II: Gray-Scale Filters, JMIV(2), 1992, pp. 185-192. See also Unification of Nonlinear Filtering in the Context of Binary Logical Calculus, Part I: Binary Filters. BibRef 9200 Dougherty, E.R., Application of the Hausdorff Metric in Gray-Scale Mathematical Morphology via Truncated Umbrae,JVCIR(2), 1991, pp. 177-187. BibRef 9100 Dougherty, E.R.[Edward R.], 17/21 Bibliografie A Lattice-Based Minimal Gray-Scale Switching Algorithm for Obtaining the Optimal Increasing Filter from the Optimal Filter,JMIV(21), No. 1, July 2004, pp. 43-52. WWW Version. 0409 BibRef Takriti, S., Gader, P.D., Local Decomposition of Gray-Scale Morphological Templates, JMIV(2), 1992, pp. 39-50. BibRef 9200 Hawkes, P.W., Manipulation of Multivalued Images in Image Algebra, JMIV(2), 1992, pp. 83-85. BibRef 9200 Sapiro, G.[Guillermo], Kimmel, R.[Ron], Shaked, D.[Doron], Kimia, B.B.[Benjamin B.], Bruckstein, A.M.[Alfred M.], Implementing continuous-scale morphology via curve evolution, PR(26), No. 9, September 1993, pp. 1363-1372. WWW Version. 0401 BibRef Gader, P.D., Separable Decompositions and Approximations of Greyscale Morphological Templates, CVGIP(53), No. 3, May 1991, pp. 288-296. WWW Version. BibRef 9105 Jones, R., Svalbe, I., Algorithms for the Decomposition of Gray-Scale Morphological Operations, PAMI(16), No. 6, June 1994, pp. 581-588. IEEE Abstract. WWW Version. BibRef 9406 Earlier: Basis decomposition of morphological operations, ICPR92(III:264-267). IEEE DOI Link 9208 BibRef Albiol, A., Serra, J., 18/21 Morphological Image Enlargements,JVCIR(8), 1997, pp. 367-383. Bibliografie BibRef 9700 Deng, T.Q.[Ting-Quan], Heijmans, H.J.A.M.[Henk J.A.M.], Grey-Scale Morphology Based on Fuzzy Logic,JMIV(16), No. 2, March 2002, pp. 155- 171. WWW Version. 0202 BibRef Naegel, B.[Benoît], Passat, N.[Nicolas], Ronse, C.[Christian], Grey-level hit-or-miss transforms--Part I: Unified theory,PR(40), No. 2, February 2007, pp. 635-647. WWW Version. 0611Mathematical morphology; Hit-or-miss transform; Grey-level interval operator; Morphological probing BibRef Naegel, B.[Benoît], Passat, N.[Nicolas], Ronse, C.[Christian], Grey-level hit-or-miss transforms--part II: Application to angiographic image processing, PR(40), No. 2, February 2007, pp. 648-658. WWW Version. 0611Mathematical morphology; Hit-or-miss transform; Grey-level interval operator; Angiographic image processing BibRef Angulo, J.[Jesus], Morphological colour operators in totally ordered lattices based on distances: Application to image filtering, enhancement and analysis,CVIU(107), No. 1-2, July- August 2007, pp. 56-73. WWW Version. 0706 Colour mathematical morphology; Colour distance; Multivariate ordering; Colour feature extraction; Colour noise removal; Colour contrast enhancement; LSH; L*a*b* BibRef Verdú-Monedero, R.[Rafael], Angulo, J.[Jesús], Spatially-Variant Directional Mathematical Morphology Operators Based on a Diffused Average Squared Gradient Field,ACIVS08(xx-yy). 19/21 Bibliografie Efficient 2-D Grayscale Morphological Transformations With Arbitrary Flat Structuring Elements,IP(17), No. 1, January 2008, pp. 1-8. IEEE DOI Link 0712 BibRef Earlier: Efficient 2-D Gray-Scale Dilations and Erosions with Arbitrary Flat Structuring Elements,ICIP06(1573-1576). 0610 IEEE DOI Link BibRef Montenegro, A., Calixto, E.P., Conci, A., Clua, E., Introducing a new metric for automatic true color images granulometry, WSSIP08(389-392). IEEE DOI Link 0806color morphology to detect grain size. BibRef Dokládal, P.[Petr], Dokládalová, E.[Eva], Earlier: A1, Only: Grey-level morphology combined with an artificial neural networks aproach for multimodal segmentation of the hippocampus, CIAP03(277-282). IEEE Abstract. 0310 BibRef Raducanu, B., Grana, M., Grey-Scale Morphology with Spatially-Variant Rectangles in Linear Time, ACIVS08(xx-yy). Springer DOI Link 0810 BibRef Tobar, M.C., Platero, C., González, P.M., Asensio, G., Mathematical Morphology in the HSI Colour Space, IbPRIA07(II: 467-474). Springer DOI Link 0706 BibRef Breuß, M.[Michael], Burgeth, B.[Bernhard], Weickert, J.[Joachim], Anisotropic Continuous-Scale Morphology, IbPRIA07(II: 515-522). Springer DOI Link 0706 BibRef Nachtegael, M., Sussner, P., Mélange, T., Kerre, E.E., An Interval-Valued Fuzzy Morphological Model Based on Lukasiewicz-Operators, ACIVS08(xx-yy). Springer DOI Link 0810 BibRef de Witte, V.[Valérie], Schulte, S.[Stefan], Nachtegael, M.[Mike], van der Weken, D.[Dietrich], Kerre, E.E.[Etienne E.]20, /21 Bibliografie
Vector Morphological Operators for Colour Images, ICIAR05(667-675). Springer DOI Link 0509 BibRef Hult, R.[Roger], Agartz, I.[Ingrid], Segmentation of Multimodal MRI of Hippocampus Using 3D Grey-Level Morphology Combined with Artificial Neural Networks, SCIA05(272-281). Springer DOI Link 0506 BibRef A Grayscale Hit-or-miss Transform Based on Level Sets, ICIP00(Vol II: 931-933). IEEE Abstract. 0008 BibRef Koppen, M., Nowack, C., Rosel, G., Pareto-Morphology for Color Image Processing, SCIA99(Image Analysis I). BibRef 9900 Bastian, W., Petrou, M., Leng, X., Greyscale Morphology with a Non-Linear Structuring Element, DSP95(366-371). BibRef 9500 Costa, W.S., Haralick, R.M., Predicting expected gray level statistics of opened signals, CVPR92(554-559). IEEE Abstract. 0403The opening of a model signal with a convex, zero-height structuring element is studied empirically. BibRef Wu, M.J.[Min-Jin], Fuzzy morphology and image analysis, ICPR88(I: 453-455). IEEE DOI Link 8811 BibRef Chapter on Computational Vision, Regularization, Connectionist, Morphology, Scale-Space, Perceptual Grouping, Wavelets, Color, Sensors, Optical, Laser, Radar continues in Morphology for Range and 3-D data . 21/21