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Events in surveillance video occur over many time scales, but common approaches to background subtraction and video representation are implicitly based on a single temporal scale. In this work, we derive a set of causal filters which define a temporal scale-space representation for the activity at each pixel. This scale-space can be maintained and continuously updated in real time and, for static cameras viewing dynamic scenes, has several interesting properties. In particular, it directly characterizes interesting temporal features and supports approximate reconstruction of the video history under challenging noise conditions. The temporal scale-space grounds novel approaches to several applications, including a natural visualization tool to summarize recent video behavior in a single image, and a tool to directly report how long the object has been present in a scene without reexamining any video data.