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In this paper, we propose a novel motion representation and apply it to abnormality detection and behavior recognition. At first, pointwise correspondences for the foreground in two consecutive video frames are established by performing a salient-region-based pointwise matching algorithm. Then, based on the established pointwise correspondences, a pointwise motion image (PMI) for each frame is built up to represent the motion status of the foreground. The PMI is more suitable for video analysis as it encapsulates a variety of motion information such as pointwise motion speed, pointwise motion orientation, pointwise motion duration, as well as the global shape of the foreground. In addition, it represents all of these pieces of information by a color image in the HSV space, by which many popular techniques in the image processing field can be straightforwardly adopted. By combining the PMI and AdaBoost, a method for abnormality detection and behavior recognition is proposed. The proposed method is shown to possess a high discriminative ability and is capable of dealing with local motion, global motion, and similar motions with different speeds. Experiments including a comparison with two existing methods demonstrate the effectiveness of the proposed representation in abnormality detection and behavior recognition.