Elf is a runtime for an energy-constrained camera to continuously summarize video scenes as approximate object counts. Elf's novelty centers on planning the camera's count actions under energy constraint. (1) Elf explores the rich action space spanned by the number of sample image frames and the choice of per-frame object counters; it unifies errors from both sources into one single bounded error. (2) To decide count actions at run time, Elf employs a learning-based planner, jointly optimizing for past and future videos without delaying result materialization. Tested with more than 1,000 hours of videos and under realistic energy constraints, Elf continuously generates object counts within only 11% of the true counts on average. Alongside the counts, Elf presents narrow errors shown to be bounded and up to 3.4x smaller than competitive baselines. At a higher level, Elf makes a case for advancing the geographic frontier of video analytics.