Topological Zone Organization of Scalar Volume Data

  • Authors:

  • Jim Cox;D. B. Karron;Nazma Ferdous

  • Affiliations:

  • Brooklyn College, The City University of New York Graduate Center and Computer Aided Surgery Inc. cox@sci.brooklyn.cuny.edu;Computer Aided Surgery, Inc. and City College of the City University of New York. karron@casi.net;The Space Telescope Science Institute. nfrahman@stsci.edu

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2003

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Abstract

We present a new method for preprocessing and organizing discrete scalar volume data of any dimension on external storage. We describe our implementation of a visual navigation system using our method. The techniques have important applications for out-of-core visualization of volume data sets and image understanding. The applications include extracting isosurfaces in a manner that helps reduce both I/O and disk seek time, a priori topologically correct isosurface simplification (prior to extraction), and producing a visual atlas of all topologically distinct objects in the data set. The preprocessing algorithm computes regions of space that we call topological zone components, so that any isosurface component (contour) is completely contained in a zone component and all contours contained in a zone component are topologically equivalent. The algorithm also constructs a criticality tree that is related to the recently studied contour tree. However, unlike the contour tree, the zones and the criticality tree hierarchically organize the data set. We demonstrate that the techniques work on both irregularly and regularly gridded data, and can be extended to data sets with nonunique values, by the mathematical analysis we call Digital Morse Theory (DMT), so that perturbation of the data set is not required. We present the results of our initial experiments with three dimensional volume data (CT) and describe future extensions of our DMT organizing technology.