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This paper addresses the problem of detecting coherent motions in crowd scenes and presents its two applications in crowd scene understanding: semantic region detection and recurrent activity mining. It processes input motion fields (e.g., optical flow fields) and produces a coherent motion field named thermal energy field. The thermal energy field is able to capture both motion correlation among particles and the motion trends of individual particles, which are helpful to discover coherency among them. We further introduce a two-step clustering process to construct stable semantic regions from the extracted time-varying coherent motions. These semantic regions can be used to recognize pre-defined activities in crowd scenes. Finally, we introduce a cluster-and-merge process, which automatically discovers recurrent activities in crowd scenes by clustering and merging the extracted coherent motions. Experiments …