Recovering shadows is an important step for many vision algorithms. Current approaches that work with time-lapse sequences are limited to simple thresholding heuristics. We show these approaches only work with very careful tuning of parameters, and do not work well for long-term time-lapse sequences taken over the span of many months. We introduce a parameter-free expectation maximization approach which simultaneously estimates shadows, albedo, surface normals, and skylight. This approach is more accurate than previous methods, works over both very short and very long sequences, and is robust to the effects of nonlinear camera response. Finally, we demonstrate that the shadow masks derived through this algorithm substantially improve the performance of sun-based photometric stereo compared to earlier shadow mask estimation.