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High Dimensional Geometry of Sliding Window Embeddings of Periodic Videos
We explore the high dimensional geometry of sliding windows of periodic videos. Under a reasonable model for periodic videos, we show that the sliding window is necessary to disambiguate all states within a period, and we show that a video embedding with a sliding window of an appropriate dimension lies on a topological loop along a hypertorus. This hypertorus has an independent ellipse for each harmonic of the motion. Natural motions with sharp transitions from foreground to background havefatcat:675a2uxtsvgohbrmncx6qeyg2m