Volume thinning for automatic isosurface propagation

Abstract

An isosurface c an be eciently generated by visiting adjacent intersected c ells in order, as if the isosurface were p r opagating itself. We previously proposed an extrema graph method, which generates a graph connecting extremum points. The isosurface p r opagation starts from some of the intersected c ells that are found both by visiting the cells through which arcs of the graph pass and by visiting the cells on the boundary of a volume.In this paper, we propose an ecient method o f searching for cells intersected by an isosurface. This method generates a volumetric skeleton consisting of cells, like an extrema graph, by applying a thinning algorithm used in the image recognition area. Since i t preserves the topological features of the volume and the connectivity of the extremum points, it necessarily intersects every isosurface. The method is more ecient than the extrema graph method, since i t d o es not require that cells on the boundary be visited.

Biomedical Visualization

“…In addition, the marching cubes method proposed a simple and efficient local triangulation scheme that uses a lookup table. Subsequently, researchers created methods for accelerating the search phase for isosurface extraction [21][22][23][24][25] all of which have a complexity of O(n), where n is the number of voxels in the volume. We introduced the span space [26] as a means for mapping the search onto a two-dimensional space and then used it to create a near optimal isosurface extraction (NOISE) algorithm that has a time complexity of O( √ n + k), where k is the size of the isosurface.…”

View dependent isosurface extraction

“…Given an isovalue, one can then descend the hierarchy, pruning empty subtrees based on this minmax scheme. In recent years, many other methods for accelerating the search phase were proposed [3,4,6,7,15,20,19] all of which have a complexity of On, where n is the size of the dataset. In 1996, we introduced the span space [10] as a mean for mapping the search onto a two-dimension space.…”

Interactive point-based isosurface extraction

“…Early work [23,11,27,8,28,14,26,15] on isosurface extraction focused on a complete isosurface computation and exhibits a worst case time complexity of O(n), where n is the size of the data. Cignoni et al [5] presented an optimal isosurface extraction method based on the span space introduced by Livnat et al [22].…”