Optimal Subdivision and Complexity of Discrete Surfaces in the Dividing-Cubes algorithm (original) (raw)
This report presents a particular implementation, and experiments on the Dividing -Cubes algorithm whose the aim is to extract and display an iso-surface from a three-dimensional (3D) medical image. The regular subdivision of the voxels allows the projection of a subdivided voxel, on the raster image, to be at most equal to the size of a pixel. We optimize the subdivision parameters to get a compromise between a good representation of the image and a minimization of the memory space. Then, we exhibit a complexity model for discrete surfaces obtained by regular subdivisions of cells. We use it for estimating the number of points that will be generated by the Dividing-Cubes algorithm to represent the surface of 3D medical objects. Under the assumption that surfaces have uniform orientations in the space, and can be locally be assimilated to planes, we show that the average number of points is a quadratic function of the subdivision factors. We give analytical expressions of the coe cients in the quadratic form. Some results obtained on a medical image and on an arti cial one illustrate the validity of our formulations.
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