We develop a new algorithm for isosurface extraction and view-dependent filtering from large time-varying fields, by using a novel Persistent Time-Octree (PTOT) indexing structure. Previously, the Persistent Octree (POT) was proposed to perform isosurface extraction and view-dependent filtering, which combines the advantages of the interval tree (for optimal searches of active cells) and of the Branch-On-Need Octree (BONO, for view-dependent filtering), but it only works for steady-state (i.e., single time step) data. For time-varying fields, a 4D version of POT, 4D-POT, was proposed for 4D isocontour slicing, where slicing on the time domain gives all active cells in the queried time step and isovalue. However, such slicing is not output sensitive and thus the searching is sub-optimal. Moreover, it was not known how to support view-dependent filtering in addition to time-domain slicing. In this paper, we develop a novel Persistent Time-Octree (PTOT) indexing structure, which has the a...