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Multigrid Convergence Based Evaluation of Surface Approximations

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Book cover Performance Characterization in Computer Vision

Part of the book series: Computational Imaging and Vision ((CIVI,volume 17))

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Abstract

This chapter reports on multigrid convergence based evaluation of surface approximations, and this approach is suggested to be one option for modelbased evaluations of computer vision algorithms in general. This criterion is in common use in numerical mathematics. In general, algorithms may be judged according to criteria, such as methodological complexity of underlying theory, expected time for implementation, or run-time behaviour and storage requirements of the implemented algorithm. Accuracy is an important criterion as well, and this can be modeled as convergence towards the true value for grid based calculations.

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References

  • Artzy, E., Frieder, G. and Herman, G.T. (1981) The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm, CGIP, 15: 1 - 24.

    Google Scholar 

  • Cheng, S.L. (1997) Estimation of volume and surface area from isosurface, Postgraduate project in computer science, 415. 780 FC, CITR Tamaki, University of Auckland.

    Google Scholar 

  • Ciampalini, A., Cignoni, P., Montani, C. and Scopigno, R. (1997) ultiresolution decimation based on global error, The Visual Computer, 13: 228 - 246.

    Google Scholar 

  • Cignoni, P., Puppo, E. and Scopigno, R. (1997) Representation and Visualization of Terrain Surfaces at Variable Resolution, The Visual Computer, 13: 199 - 217.

    Article  Google Scholar 

  • Garland, M. and Heckbert, P.S. (1995) Fast polygonal approximations of terrains and height fields, Carnegie Mellon University, School of Computer Science, TR CMU-CS95-181.

    Google Scholar 

  • Hausdorff, F. (1927) Mengenlehre, Walter de Gruyter and Co., Berlin, page 100.

    MATH  Google Scholar 

  • Heiden, W., Goetze, T. and Brickmann, J (1991) Marching cube Algorithmen zur schnellen Generierung von Isoflächen auf der Basis dreidimensionaler Datenfelder, Visualisierung von Volumendaten, Springer, Berlin, 112 - 117.

    Google Scholar 

  • Klette, R. (1985) The m-dimensional grid point space, CVGIP, 30: 1 - 12.

    MATH  Google Scholar 

  • Klette, R. (1998) Approximation and representation of 3D objects, Advances in Digital and Computational Geometry, Klette, R., Rosenfeld, A. and Sloboda, F. (eds.), Springer, Singapore, 161 - 194.

    Google Scholar 

  • Lorensen, W.E. and Cline, H.E. (1987) Marching cubes: a high resolution 3D surface construction algorithm, Computer Graphics, 21: 163 - 169.

    Article  Google Scholar 

  • Mangoldt, H.v. and Knopp, K. (1965) Einfiihrung in die höhere Mathematik, III. Band, 12. Auflage, Leipzig, S. Hirzel Verlag.

    Google Scholar 

  • Roberts, J.C. (1993) An overview of rendering from volume data including surface and volume rendering, TR, University of Kent at Canterbury.

    Google Scholar 

  • Scherer, W. (1922) Ein Satz über Gitter und Volumen, Mathematische Annalen, 86: 99 - 107.

    Article  MathSciNet  Google Scholar 

  • Sloboda, F. (1997) On Approximation of Jordan Surfaces; a Topological Approach, Int. Memo, CITR group, Tamaki, The University of Auckland.

    Google Scholar 

  • Sloboda, F., Zatko, B.B. and Klette, R. (1998) On the topology of grid continua, Proc. Vision Geometry VII, SPIE Volume 3454, San Diego, 20-22 July, 52 - 63.

    Google Scholar 

  • Wilhelms, J. and Gelder, A.V. (1994) Topological considerations in isosurface generation, Baskin Center for Computer Engineering and Information Sciences, University of California, Santa Cruz, UCSC-CRL-94-31.

    Google Scholar 

  • Wyvill, G., McPheeters, C. and Wyvill, B. (1986) Data structures for soft objects, The Visual Computer, 2: 227 - 234.

    Article  Google Scholar 

  • Zhou, S.-Z. and Klette, R. (1997) Multiresolution surface reconstruction: edge collapsing + simplification envelopes, Keynote paper, DICTA/IVCNZ97 conference, Albany/Auckland, December, Massey University, Dep. of Production Technology, 397 - 402.

    Google Scholar 

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© 2000 Springer Science+Business Media Dordrecht

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Klette, R., Wu, F., Zhou, SZ. (2000). Multigrid Convergence Based Evaluation of Surface Approximations. In: Klette, R., Stiehl, H.S., Viergever, M.A., Vincken, K.L. (eds) Performance Characterization in Computer Vision. Computational Imaging and Vision, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9538-4_19

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  • DOI: https://doi.org/10.1007/978-94-015-9538-4_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5487-6

  • Online ISBN: 978-94-015-9538-4

  • eBook Packages: Springer Book Archive

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