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Visual repetition is ubiquitous in our world. It appears in human activity (sports, cooking), animal behavior (a bee's waggle dance), natural phenomena (leaves in the wind) and in urban environments (flashing lights). Estimating visual repetition from realistic video is challenging as periodic motion is rarely perfectly static and stationary. To better deal with realistic video, we elevate the static and stationary assumptions often made by existing work. Our spatiotemporal filtering approach, established on the theory of periodic motion, effectively handles a wide variety of appearances and requires no learning. Starting from motion in 3D we derive three periodic motion types by decomposition of the motion field into its fundamental components. In addition, three temporal motion continuities emerge from the field's temporal dynamics. For the 2D perception of 3D motion we consider the viewpoint relative to the motion; what follows are 18 cases of recurrent motion perception. To estimate repetition under all circumstances, our theory implies constructing a mixture of differential motion maps: F , ∇ F , ∇ · F and ∇ × F . We temporally convolve the motion maps with wavelet filters to estimate repetitive dynamics. Our method is able to spatially segment repetitive motion directly from the temporal filter responses densely computed over the motion maps. For experimental verification of our claims, we use our novel dataset for repetition estimation, better-reflecting reality with non-static and non-stationary repetitive motion. On the task of repetition counting, we obtain favorable results compared to a deep learning alternative. [ABSTRACT FROM AUTHOR]

The aim of this paper is fine-grained categorization without human interaction. Different from prior work, which relies on detectors for specific object parts, we propose to localize distinctive details by roughly aligning the objects using just the overall shape. Then, one may proceed to the classification by examining the corresponding regions of the alignments. More specifically, the alignments are used to transfer part annotations from training images to unseen images (supervised alignment), or to blindly yet consistently segment the object in a number of regions (unsupervised alignment). We further argue that for the distinction of sub-classes, distribution-based features like color Fisher vectors are better suited for describing localized appearance of fine-grained categories than popular matching oriented shape-sensitive features, like HOG. They allow capturing the subtle local differences between subclasses, while at the same time being robust to misalignments between distinctive details. We evaluate the local alignments on the CUB-2011 and on the Stanford Dogs datasets, composed of 200 and 120, visually very hard to distinguish bird and dog species. In our experiments we study and show the benefit of the color Fisher vector parameterization, the influence of the alignment partitioning, and the significance of object segmentation on fine-grained categorization. We, furthermore, show that by using object detectors as voters to generate object confidence saliency maps, we arrive at fully unsupervised, yet highly accurate fine-grained categorization. The proposed local alignments set a new state-of-the-art on both the fine-grained birds and dogs datasets, even without any human intervention. What is more, the local alignments reveal what appearance details are most decisive per fine-grained object category. [ABSTRACT FROM AUTHOR]