We propose a new video representation in terms of an over-segmentation of dense trajectories covering the whole video. Trajectories are often used to encode long-temporal information in several computer vision applications. Similar to temporal superpixels, a temporal slice of super-trajectories are superpixels, but the later contains more information because it maintains the long dense pixel-wise tracking information as well. The main challenge in using trajectories for any application, is the accumulation of tracking error in the trajectory construction. For our problem, this results in disconnected superpixels. We exploit constraints for edges in addition to trajectory based color and position similarity. Analogous to superpixels as a preprocessing tool for images, the proposed representation has its applications for videos, especially in trajectory based video analysis.
We show that the complexity of the recently introduced medoid-shift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in over-fragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under- and over-fragmentation. Like medoid shift, quick shift operates in non-Euclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories. We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging. A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.  Abstract Superpixels group perceptually similar pixels to create visually meaningful entities while heavily reducing the number of primitives for subsequent processing steps. As of these properties, superpixel algorithms have received much attention since their naming in 2003 (Ren and Malik, 2003). By today, publicly available superpixel algorithms have turned into standard tools in low-level vision. As such, and due to their quick adoption in a wide range of applications, appropriate benchmarks are crucial for algorithm selection and comparison. Until now, the rapidly growing number of algorithms as well as varying experimental setups hindered the development of a unifying benchmark. We present a comprehensive evaluation of 28 state-of-the-art superpixel algorithms utilizing a benchmark focussing on fair comparison and designed to provide new insights relevant for applications. To this end, we explicitly discuss parameter optimization and the importance of strictly enforcing connectivity. Furthermore, by extending well-known metrics, we are able to summarize algorithm performance independent of the number of generated superpixels, thereby overcoming a major limitation of available benchmarks. Furthermore, we discuss runtime, robustness against noise, blur and affine transformations, implementation details as well as aspects of visual quality. Finally, we present an overall ranking of superpixel algorithms which redefines the state-of-the-art and enables researchers to easily select appropriate algorithms and the corresponding implementations which themselves are made publicly available as part of our benchmark at http: www.davidstutz.de projects superpixel-benchmark . 