FAST METHODS FOR COMPUTING ISOSURFACE TOPOLOGY WITH BETTI NUMBERS Shirley F. Konkle University of California, Davis konkle@cs.ucdavis.edu Patrick J. Moran NASA Ames Research Center pmoran@nas.nasa.gov Bernd Hamann University of California, Davis hamann@cs.ucdavis.edu Kenneth I. Joy University of California, Davis joy@cs.ucdavis.edu Keywords: Betti Numbers, Isosurface topology. Abstract Betti numbers can be used as a means for feature detection 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 an 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. 1. INTRODUCTION Topology can be used as a means of automated feature detection. One example is determining whether molecules have bonded, which is done by calculating the isosurface of the electron density for the outer 1