Abstract We propose an integer programming method for estimating the instantaneous count of pedestrians crossing a line of interest in a video sequence. Through a line sampling process, the video is ?rst converted into a temporal slice image. Next, the number of people is estimated in a set of overlapping sliding windows on the temporal slice image, using a regression function that maps from local features to a count. Given that count in a sliding window is the sum of the instantaneous counts in the corresponding time interval, an integer programming method is proposed to recover the number of pedestrians crossing the line of inter est in each frame. Integrating over a speci?c time interval yields the cumulative count of pedestrian crossing the line. Compared with current methods for line counting, our proposed approach achieves state-of-the-art performance on several challenging crowd video datasets.