Matrix Cubic Splines for Progressive 3D Imaging

Authors:
E. Defez;J. Villanueva-Oller;R. J. Villanueva;A. Law
Affiliations:
Universidad Politécnica de Valencia, Valencia, Spain;Universidad Politécnica de Valencia, Valencia, Spain;Universidad Politécnica de Valencia, Valencia, Spain rjvillan@mat.upv.es;University of Waterloo, Waterloo, Ontario, Canada
Venue:
Journal of Mathematical Imaging and Vision
Year:
2002

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Abstract

Mathematical theory of matrix cubic splines is introduced, then adapted for progressive rendering of images. 2D subsets of a 3D digital object are transmitted progressively under some ordering scheme, and subsequent reconstructions using the matrix cubic spline algorithm provide an evolving 3D rendering. The process can be an effective tool for browsing three dimensional objects, and effectiveness is illustrated with a test data set consisting of 93 CT slices of a human head. The procedure has been implemented on a single processor PC system, to provide a platform for full 3D experimentation; performance is discussed. A web address for the complete, documented Mathematica code is given.