A new method that enables randomized Hough transform (RHT)-based recovery of ellipsoid parameters from a collection of 3D points is presented. The approach is attractive since it can alleviate the traditional Hough transform's disadvantages of large computation time and memory usage - in particular for the ellipsoid detection's high-dimensional parameter space. The new method uses two RHT-based stages, first exploiting shape to enable recovery of position and then exploiting eigen analysis to recover the remaining parameters (of shape and orientation). Experimental results on synthetic and real data are also presented