30th July 2002

Matrix Cubic Splines for Progressive 3D Imaging

posted in 2D, 3D, Interpolación a trozos, Investigación, JCR, Polinomios matriciales, Publicaciones, Reconstrucción de imagen, Splines cúbicos matriciales, Transmisión progresiva |

Published paper “Matrix Cubic Splines for Progressive 3D Imaging” (E. Defez, J. Villanueva Oller, R.J. Villanueva), in the Journal of Mathematical Imaging and Vision, nº 17, ISSN 0924-9907, pp. 41-53 (year 2002). Ed. Springer.

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 rendering 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.

Keywords: progressive 3D rendering, progressive transmission of images, matrix cubic splines, matrix polynomial reconstructions.