From the latest models of galaxy formation and evolution, it is becoming clear that there is a more fundamental distinction in the galaxy population than the usual classification: elliptical vs. spiral galaxies. The striking difference between elliptical and spiral galaxies is a result of variation in the relative visual prominence of the spheroid and disk components. However, measuring the properties of the single components within a galaxy is considerably more difficult than measuring its overall properties. Galaxies are complex structures and, beyond the general distinction between spheroids and disks, they display a range of higher level features; in addition to spiral arms, these include bars, rings, etc. These complexities make it difficult for computational methods to extract meaningful information. We plan to tackle this problem through the combination of statistical techniques and utilizing the full set of multi-color information available for each galaxy. To control the computational intensity of the task, we will develop efficient algorithms and tools to optimally search the high-dimensional parameter space, distributed on parallel machines. Only using a combination of all these components can we hope to develop a robust and timely solution to this problem. It is central to our goals that we produce reliable tools that we can put to practical scientific use. The tools we develop will be also provided for use by the astronomical and computer science communities.