Abstract
The expressiveness of a lot of image analysis algorithms depends on the question whether shape information is preserved during digitization. Most existing approaches to answer this are restricted to binary images and only consider nearest neighbor reconstruction. This paper generalizes this to grayscale images and to several reconstruction methods. It is shown that a certain class of images can be sampled with regular and even irregular grids and reconstructed with different interpolation methods without any change in the topology of the level sets of interest.
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References
Acton, S.T.: A PDE technique for generating locally monotonic images. In: Proceedings of the IEEE International Conference on Image Processing (1998)
Florncio, D.A.F., Schafer, R.W.: Homotopy and Critical Morphological Sampling. In: Proceedings of SPIE Visual Communications and Image Processing, pp. 97–109 (1995)
Florncio, D.A.F., Schafer, R.W.: Critical Morphological Sampling and its Applications to Image Coding. In: Serra, J., Soille, P. (eds.) Mathematical Morphology and Its Applications to Image Processing, Computational Imaging and Vision, vol. 2, pp. 109–116. Kluwer Academic Publishers, Dordrecht (1994)
Haralick, R.M., Zhuang, X., Lim, C., Lee, J.S.J.: The Digital Morphological Sampling Theorem. IEEE Transactions on Acoustics, Speech and Signal Processing 37, 2067–2090 (1989)
Heijmans, H.J.A.M., Toet, A.: Morphological Sampling. Computer Vision, Graphics and Image Processing: Image Understanding 54, 384–400 (1991)
Herman, G.T.: Geometry of Digital Spaces. Birkhuser, Boston (1998)
Köthe, U., Stelldinger, P.: Shape Preserving Digitization of Ideal and Blurred Binary Shapes. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 82–91. Springer, Heidelberg (2003)
Latecki, L.J., Conrad, C., Gross, A.: Preserving Topology by a Digitization Process. Journal of Mathematical Imaging and Vision 8, 131–159 (1998)
Latecki, L.J.: Discrete Representation of Spatial Objects in Computer Vision. Kluwer, Dordrecht (1998)
Lorensen, W.E., Cline, H.E.: Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics 21(4) (1987)
Pavlidis, T.: Algorithms for Graphics and Image Processing. Computer Science Press, Rockville (1982)
Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)
Stelldinger, P., Köthe, U.: Shape Preservation During Digitization: Tight Bounds Based on the Morphing Distance. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 108–115. Springer, Heidelberg (2003)
Wang, Y., Bhattacharya, P.: Digital Connectivity and Extended Well-Composed Sets for Gray Images. Computer Vision and Image Understanding 3, 330–345 (1997)
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Stelldinger, P. (2004). Shape Preserving Sampling and Reconstruction of Grayscale Images. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_38
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DOI: https://doi.org/10.1007/978-3-540-30503-3_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23942-0
Online ISBN: 978-3-540-30503-3
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