Abstract
Historically, mathematical morphology has primarily focused on the processing and analysis of two-dimensional image data. In this paper, we survey a number of other areas where mathematical morphology finds fruitful application, such as computer graphics and solid modeling; path planning; filtering, segmentation and visualization of volume data; or visual exploration of high-dimensional data. We also mention techniques for accelerating morphological computations by using graphics hardware (GPU computing).
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Bekker, H., Brink, A.A., Roerdink, J.B.T.M.: Reducing the time complexity and identifying ill-posed problem instances of Minkowski sum based similarity calculations. International Journal of Computational Geometry and Applications 19(5), 441–456 (2009)
Bertrand, G.: On the dynamics. Image Vision Comput. 25(4), 447–454 (2007)
Braga-Neto, U., Goutsias, J.: A theoretical tour of connectivity in image processing and analysis. J. Math. Imag. Vision 19, 5–31 (2003)
ten Caat, M., Lorist, M.M., Bezdan, E., Roerdink, J.B.T.M., Maurits, N.M.: High-density EEG coherence analysis using functional units applied to mental fatigue. J. Neuroscience Methods 171(2), 271–278 (2008), doi:10.1016/j.jneumeth.2008.03.022
ten Caat, M., Maurits, N.M., Roerdink, J.B.T.M.: Data-driven visualization and group analysis of multichannel EEG coherence with functional units. IEEE Trans. Visualization and Computer Graphics 14(4), 756–771 (2008)
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In: Proc. 5th Int. Conf. Computer Vision, pp. 694–699 (1995)
Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Processing 10, 266–277 (2001)
Crippa, A., Maurits, N.M., Roerdink, J.B.T.M.: Graph averaging as a means to compare multichannel EEG coherence networks and its application to the study of mental fatigue and neurodegenerative disease. Computers & Graphics 35(2), 265–274 (2011)
Everts, M.H., Bekker, H., Roerdink, J.B.T.M., Isenberg, T.: Depth-Dependent Halos: Illustrative Rendering of Dense Line Data. IEEE Transactions on Visualization and Computer Graphics 15(6), 1299–1306 (2009)
Ferdosi, B.J., Buddelmeijer, H., Trager, S., Wilkinson, M.H.F., Roerdink, J.B.T.M.: Finding and visualizing relevant subspaces for clustering high-dimensional astronomical data using connected morphological operators. In: Proceedings of IEEE Conference on Visual Analytics Science and Technology (IEEE VAST), pp. 35–42 (October 2010)
Foley, J.D., Dam, A.V., Feiner, S.K.: Computer Graphics: Principles and Practice. Addison-Wesley, Reading (1990)
Ghosh, P.K.: A mathematical model for shape description using Minkowski operators. Comp. Vis. Graph. Im. Proc. 44, 239–269 (1988)
Glassner, A.S. (ed.): An Introduction to Ray Tracing. Academic Press, New York (1989)
Goutsias, J., Heijmans, H.J.A.M.: Multiresolution signal decomposition schemes. Part 1: Linear and morphological pyramids. IEEE Trans. Image Processing 9(11), 1862–1876 (2000)
Gouzènes, L.: Strategies for solving collision-free trajectories problems for mobile and manipulator robots. Intern. J. Robotics Res. 3, 51–65 (1984)
Hansen, C.D., Johnson, C.R. (eds.): The Visualization Handbook. Elsevier, Butterworth-Heinemann (2005)
Heijmans, H.J.A.M., Ronse, C.: he algebraic basis of mathematical morphology. Part I: dilations and erosions. Comp. Vis. Graph. Im. Proc. 50, 245–295 (1989)
Heijmans, H.J.A.M., Tuzikov, A.: Similarity and symmetry measures for convex shapes using Minkowski addition. IEEE Trans. Patt. Anal. Mach. Intell. 20(9), 980–993 (1998)
Heijmans, H.J.A.M.: Morphological Image Operators. Advances in Electronics and Electron Physics 25(suppl.) (1994)
Hopf, M., Ertl, T.: Accelerating Morphological Analysis with Graphics Hardware. In: Workshop on Vision, Modelling, and Visualization VMV 2000, pp. 337–345 (2000)
Jalba, A.C., Roerdink, J.B.T.M.: An efficient morphological active surface model for volumetric image segmentation. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) Proc. 9th International Symposium on Mathematical Morphology and its Application to Signal and Image Processing, Groningen, August 24-27, pp. 193–204 (2009)
Kindlmann, G.L., Westin, C.F.: Diffusion tensor visualization with glyph packing. IEEE Trans. Vis. Comput. Graph 12(5), 1329–1336 (2006)
van der Laan, W.J., Jalba, A.C., Roerdink, J.B.T.M.: Multiresolution MIP rendering of large volumetric data accelerated on graphics hardware. In: Proc. Eurographics/IEEE VGTC Symposium on Visualization (EuroVis), pp. 243–250 (2007)
Leung, A., Lhoták, O., Lashari, G.: Automatic parallelization for graphics processing units. In: Proceedings of the 7th International Conference on Principles and Practice of Programming in Java, PPPJ 2009, pp. 91–100. ACM, New York (2009)
Lindholm, E., Nickolls, J., Oberman, S., Montrym, J.: NVIDIA Tesla: A unified graphics and computing architecture. IEEE Micro. 28(2), 39–55 (2008)
Lürig, C., Ertl, T.: Hierarchical volume analysis and visualization based on morphological operators. In: Proc. IEEE Visualization 1998, pp. 335–341. IEEE Computer Society Press, Los Alamitos (1998)
Lysenko, M., Nelaturi, S., Shapiro, V.: Group morphology with convolution algebras. In: Proceedings of the 14th ACM Symposium on Solid and Physical Modeling, SPM 2010, pp. 11–22. ACM, New York (2010)
Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: A level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 17, 158–175 (1995)
Maragos, P.: Differential morphology and image processing. IEEE Transactions on Image Processing 5(6), 922–937 (1996)
Menon, J.P., Marisa, R.J., Zagajac, J.: More powerful solid modeling through ray representations. IEEE Computer Graphics and Applications 14(3), 22–35 (1994)
Roerdink, J.B.T.M.: Mathematical morphology with non-commutative symmetry groups. In: Dougherty, E.R. (ed.) Mathematical Morphology in Image Processing, ch. 7, pp. 205–254. Marcel Dekker, New York (1993)
Roerdink, J.B.T.M.: Solving the empty space problem in robot path planning by mathematical morphology. In: Serra, J., Salembier, P. (eds.) Proc. Workshop ‘Mathematical Morphology and its Applications to Signal Processing’, Barcelona, Spain, May 12-14, pp. 216–221 (1993)
Roerdink, J.B.T.M.: The generalized tailor problem. In: Maragos, P., Shafer, R.W., Butt, M.A. (eds.) Mathematical Morphology and its Applications to Image and Signal Processing, pp. 57–64. Kluwer Acad. Publ., Dordrecht (1996)
Roerdink, J.B.T.M.: Group morphology. Pattern Recognition 33(6), 877–895 (2000)
Roerdink, J.B.T.M., Blaauwgeers, G.S.M.: Visualization of Minkowski operations by computer graphics techniques. In: Serra, J., Soille, P. (eds.) Mathematical Morphology and its Applications to Image Processing, pp. 289–296. Kluwer Acad. Publ., Dordrecht (1994)
Roerdink, J.B.T.M.: Morphological pyramids in multiresolution MIP rendering of large volume data: Survey and new results. J. Math. Imag. Vision 22(2/3), 143–157 (2005)
Roerdink, J.B.T.M., Bekker, H.: Similarity measure computation of convex polyhedra revisited. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 389–399. Springer, Heidelberg (2002)
Ronse, C., Heijmans, H.J.A.M.: The algebraic basis of mathematical morphology. Part II: openings and closings. Comp. Vis. Graph. Im. Proc.: Image Understanding 54, 74–97 (1991)
Ronse, C.: Partial partitions, partial connections and connective segmentation. Journal of Mathematical Imaging and Vision 32(2), 97–125 (2008)
Rossignac, J.R., Requicha, A.A.G.: Offsetting operations in solid modeling. Computer Aided Geometric Design 3, 129–148 (1986)
Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Transactions on Image Processing 7, 555–570 (1998)
Schroeder, W., Martin, K., Lorensen, B.: The Visualization Toolkit: an Object Oriented Approach to 3D Graphics, 4th edn. Kitware, Inc. (2006)
Serra, J. (ed.): Image Analysis and Mathematical Morphology. Theoretical Advances, vol. II. Academic Press, New York (1988)
Serra, J.: Connectivity on complete lattices. J. Math. Imag. Vision 9(3), 231–251 (1998)
Soille, P.: Constrained connectivity for hierarchical image decomposition and simplification. IEEE Trans. Pattern Anal. Mach. Intell. 30(7), 1132–1145 (2008)
Suri, J., Liu, K., Singh, S., Laxminarayan, S., Zeng, X., Reden, L.: Shape recovery algorithms using level sets in 2-D/3-D medical imagery: A state of the art review. IEEE Trans. on Inf. Tech. in Biomed. 6, 8–28 (2002)
Tuzikov, A.V., Roerdink, J.B.T.M., Heijmans, H.J.A.M.: Similarity measures for convex polyhedra based on Minkowski addition. Pattern Recognition 33(6), 979–995 (2000)
Tuzikov, A.V., Sheynin, S.: Symmetry measure computation for convex polyhedra. Journal of Mathematical Imaging and Vision 16(1), 41–56 (2002)
Weickert, J., Hagen, H. (eds.): Visualization and Processing of Tensor Fields. Springer, Berlin (2006)
Westenberg, M.A., Roerdink, J.B.T.M.: Frequency domain volume rendering by the wavelet X-ray transform. IEEE Trans. Image Processing 9(7), 1249–1261 (2000)
Westenberg, M.A., Roerdink, J.B.T.M., Wilkinson, M.H.F.: Volumetric attribute filtering and interactive visualization using the Max-tree representation. IEEE Trans. Image Processing 16(12), 2943–2952 (2007)
Wilkinson, M.H.F.: Attribute-space connectivity and connected filters. Image and Vision Computing 25, 426–435 (2007)
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Roerdink, J.B.T.M. (2011). Mathematical Morphology in Computer Graphics, Scientific Visualization and Visual Exploration. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds) Mathematical Morphology and Its Applications to Image and Signal Processing. ISMM 2011. Lecture Notes in Computer Science, vol 6671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21569-8_32
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DOI: https://doi.org/10.1007/978-3-642-21569-8_32
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