Fast Methods for Computing Isosurface Topology with Betti Numbers

Betti numbers can be used as a means for feature detections to aid in the exploration of complex large-scale data sets. We present a fast algorithm for the calculation of Betti numbers for triangulated isosurfaces, along with examples of their use. Once any isosurface is extracted from a data set, calculating Betti numbers only requires time and space proportional to the isosurfaces, not the data set. Because the overhead of obtaining Betti numbers is small, our algorithm can be used with large data