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2016 | OriginalPaper | Chapter

4. Amoeba Techniques for Shape and Texture Analysis

Author : Martin Welk

Published in: Perspectives in Shape Analysis

Publisher: Springer International Publishing

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Abstract

Morphological amoebas are image-adaptive structuring elements for morphological and other local image filters introduced by Lerallut et al. Their construction is based on combining spatial distance with contrast information into an image-dependent metric. Amoeba filters show interesting parallels to image filtering methods based on partial differential equations (PDEs), which can be confirmed by asymptotic equivalence results. In computing amoebas, graph structures are generated that hold information about local image texture. This chapter reviews and summarises the work of the author and his coauthors on morphological amoebas, particularly their relations to PDE filters and texture analysis. It presents some extensions and points out directions for future investigation on the subject.

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Literature
1.
go back to reference Alvarez, L., Lions, P.-L., Morel, J.-M.: Image selective smoothing and edge detection by nonlinear diffusion. II. SIAM J. Numer. Anal. 29, 845–866 (1992)MathSciNetCrossRefMATH Alvarez, L., Lions, P.-L., Morel, J.-M.: Image selective smoothing and edge detection by nonlinear diffusion. II. SIAM J. Numer. Anal. 29, 845–866 (1992)MathSciNetCrossRefMATH
2.
go back to reference Austin, T.L.: An approximation to the point of minimum aggregate distance. Metron 19, 10–21 (1959)MathSciNetMATH Austin, T.L.: An approximation to the point of minimum aggregate distance. Metron 19, 10–21 (1959)MathSciNetMATH
3.
go back to reference Baccelli, F., Cohen, G., Olsder, G.J., Quadrat, J.: Synchronization and Linearity: An Algebra for Discrete Event Systems. Wiley, Chichester (1992)MATH Baccelli, F., Cohen, G., Olsder, G.J., Quadrat, J.: Synchronization and Linearity: An Algebra for Discrete Event Systems. Wiley, Chichester (1992)MATH
4.
go back to reference Bonchev, D., Trinajstić, N.: Information theory, distance matrix, and molecular branching. J. Chem. Phys. 67 (10), 4517–4533 (1977)CrossRef Bonchev, D., Trinajstić, N.: Information theory, distance matrix, and molecular branching. J. Chem. Phys. 67 (10), 4517–4533 (1977)CrossRef
5.
go back to reference Braga-Neto, U.M.: Alternating sequential filters by adaptive neighborhood structuring functions. In: Maragos, P., Schafer, R.W., Butt, M.A. (eds.) Mathematical Morphology and Its Applications to Image and Signal Processing. Volume 5 of Computational Imaging and Vision, pp. 139–146. Kluwer, Dordrecht (1996)CrossRef Braga-Neto, U.M.: Alternating sequential filters by adaptive neighborhood structuring functions. In: Maragos, P., Schafer, R.W., Butt, M.A. (eds.) Mathematical Morphology and Its Applications to Image and Signal Processing. Volume 5 of Computational Imaging and Vision, pp. 139–146. Kluwer, Dordrecht (1996)CrossRef
6.
go back to reference Burgeth, B., Kleefeld, A.: Morphology for color images via Loewner order for matrix fields. In: Luengo Hendriks, C.L., Borgefors, G., Strand, R. (eds.) Mathematical Morphology and Its Applications to Signal and Image Processing. Volume 7883 of Lecture Notes in Computer Science, pp. 243–254. Springer, Berlin (2013) Burgeth, B., Kleefeld, A.: Morphology for color images via Loewner order for matrix fields. In: Luengo Hendriks, C.L., Borgefors, G., Strand, R. (eds.) Mathematical Morphology and Its Applications to Signal and Image Processing. Volume 7883 of Lecture Notes in Computer Science, pp. 243–254. Springer, Berlin (2013)
7.
go back to reference Burgeth, B., Bruhn, A., Papenberg, N., Welk, M., Weickert, J.: Mathematical morphology for matrix fields induced by the Loewner ordering in higher dimensions. Signal Process. 87 (2), 277–290 (2007)CrossRefMATH Burgeth, B., Bruhn, A., Papenberg, N., Welk, M., Weickert, J.: Mathematical morphology for matrix fields induced by the Loewner ordering in higher dimensions. Signal Process. 87 (2), 277–290 (2007)CrossRefMATH
8.
go back to reference Burgeth, B., Welk, M., Feddern, C., Weickert, J.: Morphological operations on matrix-valued images. In: Pajdla, T., Matas, J. (eds.) Computer Vision – ECCV 2004, Part IV. Volume 3024 of Lecture Notes in Computer Science, pp. 155–167. Springer, Berlin (2004) Burgeth, B., Welk, M., Feddern, C., Weickert, J.: Morphological operations on matrix-valued images. In: Pajdla, T., Matas, J. (eds.) Computer Vision – ECCV 2004, Part IV. Volume 3024 of Lecture Notes in Computer Science, pp. 155–167. Springer, Berlin (2004)
9.
go back to reference Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Proceedings of the Fifth International Conference on Computer Vision, Cambridge, June 1995, pp. 694–699. IEEE Computer Society Press. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Proceedings of the Fifth International Conference on Computer Vision, Cambridge, June 1995, pp. 694–699. IEEE Computer Society Press.
10.
go back to reference Cohen, L.D.: On active contour models and balloons. CVGIP: Image Underst. 53 (2), 211–218 (1991)CrossRefMATH Cohen, L.D.: On active contour models and balloons. CVGIP: Image Underst. 53 (2), 211–218 (1991)CrossRefMATH
11.
go back to reference Cootes, T.F., Taylor, C.J.: Statistical models of appearance for computer vision. Technical report, University of Manchester, Oct 2001 Cootes, T.F., Taylor, C.J.: Statistical models of appearance for computer vision. Technical report, University of Manchester, Oct 2001
12.
go back to reference Dehmer, M.: Information processing in complex networks: graph entropy and information functionals. Appl. Math. Comput. 201, 82–94 (2008)MathSciNetMATH Dehmer, M.: Information processing in complex networks: graph entropy and information functionals. Appl. Math. Comput. 201, 82–94 (2008)MathSciNetMATH
13.
go back to reference Dehmer, M., Emmert-Streib, F., Mehler, A. (eds.): Towards an Information Theory of Complex Networks: Statistical Methods and Applications. Birkhäuser Publishing, Basel (2012) Dehmer, M., Emmert-Streib, F., Mehler, A. (eds.): Towards an Information Theory of Complex Networks: Statistical Methods and Applications. Birkhäuser Publishing, Basel (2012)
14.
go back to reference Dehmer, M., Emmert-Streib, F., Tripathi, S.: Large-scale evaluation of molecular descriptors by means of clustering. PloS ONE 8 (12), e83956 (2013)CrossRef Dehmer, M., Emmert-Streib, F., Tripathi, S.: Large-scale evaluation of molecular descriptors by means of clustering. PloS ONE 8 (12), e83956 (2013)CrossRef
15.
go back to reference Dehmer, M., Sivakumar, L.: Recent developments in quantitative graph theory: information inequalities for networks. PLoS ONE 7 (2), e31395 (2012)CrossRef Dehmer, M., Sivakumar, L.: Recent developments in quantitative graph theory: information inequalities for networks. PLoS ONE 7 (2), e31395 (2012)CrossRef
18.
go back to reference Emmert-Streib, F., Dehmer, M.: Information theoretic measures of UHG graphs with low computational complexity. Appl. Math. Comput. 190, 1783–1794 (2007)MathSciNetMATH Emmert-Streib, F., Dehmer, M.: Information theoretic measures of UHG graphs with low computational complexity. Appl. Math. Comput. 190, 1783–1794 (2007)MathSciNetMATH
19.
go back to reference Ferrer, M., Bunke, H.: Graph edit distance–theory, algorithms, and applications. In: Lezoray, O., Grady, L. (eds.) Image Processing and Analysis with Graphs: Theory and Practice, chapter 13, pp. 383–422. CRC Press, Boca Raton (2012) Ferrer, M., Bunke, H.: Graph edit distance–theory, algorithms, and applications. In: Lezoray, O., Grady, L. (eds.) Image Processing and Analysis with Graphs: Theory and Practice, chapter 13, pp. 383–422. CRC Press, Boca Raton (2012)
20.
go back to reference Guichard, F., Morel, J.-M.: Partial differential equations and image iterative filtering. In: Duff, I.S., Watson, G.A. (eds.) The State of the Art in Numerical Analysis. Number 63 in IMA Conference Series (New Series), pp. 525–562. Clarendon Press, Oxford (1997) Guichard, F., Morel, J.-M.: Partial differential equations and image iterative filtering. In: Duff, I.S., Watson, G.A. (eds.) The State of the Art in Numerical Analysis. Number 63 in IMA Conference Series (New Series), pp. 525–562. Clarendon Press, Oxford (1997)
21.
go back to reference Haralick, R.: Statistical and structural approaches to texture. Proc. IEEE 67 (5), 786–804 (1979)CrossRef Haralick, R.: Statistical and structural approaches to texture. Proc. IEEE 67 (5), 786–804 (1979)CrossRef
22.
go back to reference Haralick, R., Shanmugam, K., Dinstein I.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. 3 (6), 610–621 (1973)CrossRef Haralick, R., Shanmugam, K., Dinstein I.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. 3 (6), 610–621 (1973)CrossRef
23.
go back to reference Heijmans, H.J.A.M.: Morphological Image Operators. Academic, Boston (1994)MATH Heijmans, H.J.A.M.: Morphological Image Operators. Academic, Boston (1994)MATH
24.
go back to reference Heijmans, H.J.A.M., Ronse, C.: The algebraic basis of mathematical morphology. I: dilations and erosions. Comput. Vis. Graph. Image Process. 50, 245–295 (1990)MATH Heijmans, H.J.A.M., Ronse, C.: The algebraic basis of mathematical morphology. I: dilations and erosions. Comput. Vis. Graph. Image Process. 50, 245–295 (1990)MATH
25.
go back to reference Heijmans, H.J.A.M., van den Boomgaard, R.: Algebraic framework for linear and morphological scale-spaces. J. Vis. Commun. Image Represent. 13 (1/2), 269–301 (2002)CrossRef Heijmans, H.J.A.M., van den Boomgaard, R.: Algebraic framework for linear and morphological scale-spaces. J. Vis. Commun. Image Represent. 13 (1/2), 269–301 (2002)CrossRef
26.
go back to reference Hosoya, H.: Topological index: a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Jpn 44 (9), 2332–2339 (1971)CrossRef Hosoya, H.: Topological index: a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Jpn 44 (9), 2332–2339 (1971)CrossRef
27.
go back to reference Howarth, P., Rüger, S.: Evaluation of texture features for content-based image retrieval. In: Enser, P., Kompatsiaris, Y., O’Connor, N., Smeaton, A., Smeulders, A. (eds.) Image and Video Retrieval. Volume 3115 of Lecture Notes in Computer Science, pp. 326–334. Springer, Berlin (2004) Howarth, P., Rüger, S.: Evaluation of texture features for content-based image retrieval. In: Enser, P., Kompatsiaris, Y., O’Connor, N., Smeaton, A., Smeulders, A. (eds.) Image and Video Retrieval. Volume 3115 of Lecture Notes in Computer Science, pp. 326–334. Springer, Berlin (2004)
28.
go back to reference Huang, K., Murphy, R.: Automated classification of subcellular patterns in multicell images without segmentation into single cells. In: Proceedings of the 2004 IEEE International Symposium on Biomedical Imaging, Apr 2004, vol. 2, pp. 1139–1142 Huang, K., Murphy, R.: Automated classification of subcellular patterns in multicell images without segmentation into single cells. In: Proceedings of the 2004 IEEE International Symposium on Biomedical Imaging, Apr 2004, vol. 2, pp. 1139–1142
29.
go back to reference Ivanciuc, O., Balaban, T.-S., Balaban, A.: Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices. J. Math. Chem. 12 (1), 309–318 (1993) Ivanciuc, O., Balaban, T.-S., Balaban, A.: Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices. J. Math. Chem. 12 (1), 309–318 (1993)
30.
go back to reference Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. In: Proceedings of the Fifth International Conference on Computer Vision, Cambridge, June 1995, pp. 810–815. IEEE Computer Society Press Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Gradient flows and geometric active contour models. In: Proceedings of the Fifth International Conference on Computer Vision, Cambridge, June 1995, pp. 810–815. IEEE Computer Society Press
31.
go back to reference Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Conformal curvature flows: from phase transitions to active vision. Arch. Ration. Mech. Anal. 134, 275–301 (1996)MathSciNetCrossRefMATH Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A., Yezzi, A.: Conformal curvature flows: from phase transitions to active vision. Arch. Ration. Mech. Anal. 134, 275–301 (1996)MathSciNetCrossRefMATH
32.
go back to reference Lerallut, R., Decencière, É., Meyer, F.: Image processing using morphological amoebas. In: Ronse, C., Najman, L., Decencière, E. (eds.) Mathematical Morphology: 40 Years on. Volume 30 of Computational Imaging and Vision, pp. 13–22. Springer, Dordrecht (2005)CrossRef Lerallut, R., Decencière, É., Meyer, F.: Image processing using morphological amoebas. In: Ronse, C., Najman, L., Decencière, E. (eds.) Mathematical Morphology: 40 Years on. Volume 30 of Computational Imaging and Vision, pp. 13–22. Springer, Dordrecht (2005)CrossRef
33.
go back to reference Lerallut, R., Decencière, É., Meyer, F.: Image filtering using morphological amoebas. Image Vis. Comput. 25 (4), 395–404 (2007)CrossRef Lerallut, R., Decencière, É., Meyer, F.: Image filtering using morphological amoebas. Image Vis. Comput. 25 (4), 395–404 (2007)CrossRef
34.
go back to reference Leventon, M.E., Grimson, W.E.L., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Proceedings of the 2000 IEEE International Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 316–323, Hilton Head Island, June 2000 Leventon, M.E., Grimson, W.E.L., Faugeras, O.: Statistical shape influence in geodesic active contours. In: Proceedings of the 2000 IEEE International Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 316–323, Hilton Head Island, June 2000
35.
go back to reference Malladi, R., Sethian, J., Vemuri, B.: Shape modeling with front propagation: a level set approach. IEEE Trans. Pattern Anal. Mach. Intell. 17, 158–175 (1995)CrossRef Malladi, R., Sethian, J., Vemuri, B.: Shape modeling with front propagation: a level set approach. IEEE Trans. Pattern Anal. Mach. Intell. 17, 158–175 (1995)CrossRef
36.
go back to reference Maragos, P.: Lattice image processing: a unification of morphological and fuzzy algebraic systems. J. Math. Imaging Vis. 22, 333–353 (2005)MathSciNetCrossRef Maragos, P.: Lattice image processing: a unification of morphological and fuzzy algebraic systems. J. Math. Imaging Vis. 22, 333–353 (2005)MathSciNetCrossRef
37.
go back to reference Maragos, P., Vachier, C.: Overview of adaptive morphology: trends and perspectives. In: Proceedings of the 2009 IEEE International Conference on Image Processing, Cairo, Nov 2009, pp. 2241–2244 Maragos, P., Vachier, C.: Overview of adaptive morphology: trends and perspectives. In: Proceedings of the 2009 IEEE International Conference on Image Processing, Cairo, Nov 2009, pp. 2241–2244
38.
go back to reference Matheron, G.: Eléments pour une théorie des milieux poreux. Masson, Paris (1967) Matheron, G.: Eléments pour une théorie des milieux poreux. Masson, Paris (1967)
39.
go back to reference Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)CrossRef Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)CrossRef
41.
go back to reference Plavšić, D., Nikolić, S., Trinajstić, N.: On the Harary index for the characterization of chemical graphs. J. Math. Chem. 12 (1), 235–250 (1993)MathSciNetCrossRef Plavšić, D., Nikolić, S., Trinajstić, N.: On the Harary index for the characterization of chemical graphs. J. Math. Chem. 12 (1), 235–250 (1993)MathSciNetCrossRef
42.
go back to reference Quadrat, J.-P.: Max-plus algebra and applications to system theory and optimal control. In: Chatterji, S.D. (ed.) Proceedings of the International Congress of Mathematicians, pp. 1511–1522. Birkhäuser, Basel (1995)CrossRef Quadrat, J.-P.: Max-plus algebra and applications to system theory and optimal control. In: Chatterji, S.D. (ed.) Proceedings of the International Congress of Mathematicians, pp. 1511–1522. Birkhäuser, Basel (1995)CrossRef
43.
go back to reference Sanfeliu, A., Fu, K.-S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Trans. Syst. Man Cybern. 13 (3), 353–362 (1983)CrossRefMATH Sanfeliu, A., Fu, K.-S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Trans. Syst. Man Cybern. 13 (3), 353–362 (1983)CrossRefMATH
44.
go back to reference Sapiro, G.: Vector (self) snakes: a geometric framework for color, texture and multiscale image segmentation. In: Proceedings of the 1996 IEEE International Conference on Image Processing, Lausanne, Sept 1996, vol. 1, pp. 817–820 Sapiro, G.: Vector (self) snakes: a geometric framework for color, texture and multiscale image segmentation. In: Proceedings of the 1996 IEEE International Conference on Image Processing, Lausanne, Sept 1996, vol. 1, pp. 817–820
45.
go back to reference Serra, J.: Image Analysis and Mathematical Morphology, vol. 1. Academic, London (1982)MATH Serra, J.: Image Analysis and Mathematical Morphology, vol. 1. Academic, London (1982)MATH
46.
go back to reference Serra, J.: Image Analysis and Mathematical Morphology, vol. 2. Academic, London (1988) Serra, J.: Image Analysis and Mathematical Morphology, vol. 2. Academic, London (1988)
48.
go back to reference Spence, C., Fancourt, C.: An iterative method for vector median filtering. In: Proceedings of the 2007 IEEE International Conference on Image Processing, vol. 5, pp. 265–268 (2007) Spence, C., Fancourt, C.: An iterative method for vector median filtering. In: Proceedings of the 2007 IEEE International Conference on Image Processing, vol. 5, pp. 265–268 (2007)
49.
go back to reference Tesař, L., Shimizu, A., Smutek, D., Kobatake, H., Nawano, S.: Medical image analysis of 3D CT images based on extension of Haralick texture features. Comput. Med. Imaging Graph. 32 (6), 513–520 (2008)CrossRef Tesař, L., Shimizu, A., Smutek, D., Kobatake, H., Nawano, S.: Medical image analysis of 3D CT images based on extension of Haralick texture features. Comput. Med. Imaging Graph. 32 (6), 513–520 (2008)CrossRef
50.
go back to reference Tukey, J.W.: Exploratory Data Analysis. Addison–Wesley, Menlo Park (1971)MATH Tukey, J.W.: Exploratory Data Analysis. Addison–Wesley, Menlo Park (1971)MATH
51.
go back to reference Verly, J.G., Delanoy, R.L.: Adaptive mathematical morphology for range imagery. IEEE Trans. Image Process. 2 (2), 272–275 (1993)CrossRef Verly, J.G., Delanoy, R.L.: Adaptive mathematical morphology for range imagery. IEEE Trans. Image Process. 2 (2), 272–275 (1993)CrossRef
52.
go back to reference Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnés est minimum. Tôhoku Mathematics Journal 43, 355–386 (1937)MATH Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnés est minimum. Tôhoku Mathematics Journal 43, 355–386 (1937)MATH
53.
go back to reference Welk, M.: Amoeba active contours. In: Bruckstein, A.M., ter Haar Romeny, B., Bronstein, A.M., Bronstein, M.M. (eds.) Scale Space and Variational Methods in Computer Vision. Volume 6667 of Lecture Notes in Computer Science, pp. 374–385. Springer, Berlin (2012) Welk, M.: Amoeba active contours. In: Bruckstein, A.M., ter Haar Romeny, B., Bronstein, A.M., Bronstein, M.M. (eds.) Scale Space and Variational Methods in Computer Vision. Volume 6667 of Lecture Notes in Computer Science, pp. 374–385. Springer, Berlin (2012)
54.
go back to reference Welk, M.: Relations between amoeba median algorithms and curvature-based PDEs. In: Kuijper, A., Pock, T., Bredies, K., Bischof, H. (eds.) Scale Space and Variational Methods in Computer Vision. Volume 7893 of Lecture Notes in Computer Science, pp. 392–403. Springer, Berlin (2013) Welk, M.: Relations between amoeba median algorithms and curvature-based PDEs. In: Kuijper, A., Pock, T., Bredies, K., Bischof, H. (eds.) Scale Space and Variational Methods in Computer Vision. Volume 7893 of Lecture Notes in Computer Science, pp. 392–403. Springer, Berlin (2013)
55.
go back to reference Welk, M.: Discrimination of image textures using graph indices. In: Dehmer, M., Emmert-Streib, F. (eds.) Quantitative Graph Theory: Mathematical Foundations and Applications, chapter 12, pp. 355–386. CRC Press, Boca Raton (2014) Welk, M.: Discrimination of image textures using graph indices. In: Dehmer, M., Emmert-Streib, F. (eds.) Quantitative Graph Theory: Mathematical Foundations and Applications, chapter 12, pp. 355–386. CRC Press, Boca Raton (2014)
57.
go back to reference Welk, M., Breuß, M.: Morphological amoebas and partial differential equations. In: Hawkes, P.W. (ed.) Advances in Imaging and Electron Physics, vol. 185, pp. 139–212. Elsevier/Academic, Amsterdam (2014) Welk, M., Breuß, M.: Morphological amoebas and partial differential equations. In: Hawkes, P.W. (ed.) Advances in Imaging and Electron Physics, vol. 185, pp. 139–212. Elsevier/Academic, Amsterdam (2014)
59.
go back to reference Welk, M., Feddern, C., Burgeth, B., Weickert, J.: Median filtering of tensor-valued images. In: Michaelis, B., Krell, G. (eds.) Pattern Recognition. Volume 2781 of Lecture Notes in Computer Science, pp. 17–24. Springer, Berlin (2003) Welk, M., Feddern, C., Burgeth, B., Weickert, J.: Median filtering of tensor-valued images. In: Michaelis, B., Krell, G. (eds.) Pattern Recognition. Volume 2781 of Lecture Notes in Computer Science, pp. 17–24. Springer, Berlin (2003)
60.
go back to reference Welk, M., Weickert, J., Becker, F., Schnörr, C., Feddern, C., Burgeth, B.: Median and related local filters for tensor-valued images. Signal Process. 87, 291–308 (2007)CrossRefMATH Welk, M., Weickert, J., Becker, F., Schnörr, C., Feddern, C., Burgeth, B.: Median and related local filters for tensor-valued images. Signal Process. 87, 291–308 (2007)CrossRefMATH
61.
go back to reference Wiener, H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69 (1), 17–20 (1947)CrossRef Wiener, H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69 (1), 17–20 (1947)CrossRef
Metadata
Title
Amoeba Techniques for Shape and Texture Analysis
Author
Martin Welk
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-24726-7_4

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