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Morphological Pyramids in Multiresolution MIP Rendering of Large Volume Data: Survey and New Results

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Abstract

We survey and extend nonlinear signal decompositions based on morphological pyramids, and their application to multiresolution maximum intensity projection (MIP) volume rendering with progressive refinement and perfect reconstruction. The structure of the resulting multiresolution rendering algorithm is very similar to wavelet splatting. Several existing classes of pyramids are discussed, and their limitations indicated. To enhance the approximation quality of visualizations from reduced data (higher levels of the pyramid), two approaches are explored. First, a new class of morphological pyramids, involving connectivity enhancing operators, is considered. In the pyramidal analysis phase, a conditional dilation operator is used, with a given number n of iterations. The corresponding pyramids for n = 0 and n = 1 are known as the adjunction pyramid and Sun-Maragos pyramid, respectively. We show that the approximation quality when rendering from higher levels of the pyramid does increase as a function of the number of iterations n of the conditional dilation operator, but the improvement for n > 1 is limited. The second new approach, called streaming MIP-splatting, again starts from the adjunction pyramid. The new element is that detail coefficients of all levels are considered simultaneously and are resorted with respect to decreasing magnitude of a suitable error measure. All resorted coefficients are projected successively, until a desired accuracy of the resulting MIP image is obtained. We show that this method outperforms the previous methods based on morphological pyramids, both with respect to image quality with a fixed amount of detail data, and in terms of flexibility of controlling approximation error or computation time.

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Authors and Affiliations

  1. Institute for Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700, AV Groningen, The Netherlands

    Jos B. T. M. Roerdink

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  1. Jos B. T. M. Roerdink
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Correspondence to Jos B. T. M. Roerdink.

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Jos B.T.M. Roerdink received his M.Sc. (1979) in theoretical physics from the University of Nijmegen, the Netherlands. Following his Ph.D. (1983) from the University of Utrecht and a two-year position (1983–1985) as a Postdoctoral Fellow at the University of California, San Diego, both in the area of stochastic processes, he joined the Centre for Mathematics and Computer Science in Amsterdam. There he worked from 1986–1992 on image processing and tomographic reconstruction. He was appointed associate professor (1992) and full professor (2003), respectively, at the Institute for Mathematics and Computing Science of the University of Groningen, where he currently holds a chair in Scientific Visualization and Computer Graphics. His current research interests include morphological image processing, biomedical visualization, neuroimaging and bioinformatics.

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Roerdink, J.B.T.M. Morphological Pyramids in Multiresolution MIP Rendering of Large Volume Data: Survey and New Results. J Math Imaging Vis 22, 143–157 (2005). https://doi.org/10.1007/s10851-005-4887-1

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