We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated by considering data terms at a continuum of scales from the scale space computed from the Heat Equation within regions, and integrating these terms over all time. We show that the energy may be approximately optimized without solving for the entire scale space, but rather solving time-independent linear equations at the native scale of the image, making the method computationally feasible. We provide a multi-region scheme, and apply our method to motion segmentation. Experiments on a benchmark dataset shows that our method is less sensitive to clutter or other undesirable fine-scale structure, and leads to better performance in motion segmentation.
pyramid in segmenation: @cite_4 - pyramid to reduce cost smooth across boundaries, but alginment; we provide a general energy; @cite_46 - multigrid blur across boundaries
@cite_46 @cite_4
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Multi-resolution image features may be approximated via extrapolation from nearby scales, rather than being computed explicitly. This fundamental insight allows us to design object detection algorithms that are as accurate, and considerably faster, than the state-of-the-art. The computational bottleneck of many modern detectors is the computation of features at every scale of a finely-sampled image pyramid. Our key insight is that one may compute finely sampled feature pyramids at a fraction of the cost, without sacrificing performance: for a broad family of features we find that features computed at octave-spaced scale intervals are sufficient to approximate features on a finely-sampled pyramid. Extrapolation is inexpensive as compared to direct feature computation. As a result, our approximation yields considerable speedups with negligible loss in detection accuracy. We modify three diverse visual recognition systems to use fast feature pyramids and show results on both pedestrian detection (measured on the Caltech, INRIA, TUD-Brussels and ETH data sets) and general object detection (measured on the PASCAL VOC). The approach is general and is widely applicable to vision algorithms requiring fine-grained multi-scale analysis. Our approximation is valid for images with broad spectra (most natural images) and fails for images with narrow band-pass spectra (e.g., periodic textures). Feature pyramids are a basic component in recognition systems for detecting objects at different scales. But pyramid representations have been avoided in recent object detectors that are based on deep convolutional networks, partially because they are slow to compute and memory intensive. In this paper, we exploit the inherent multi-scale, pyramidal hierarchy of deep convolutional networks to construct feature pyramids with marginal extra cost. A top-down architecture with lateral connections is developed for building high-level semantic feature maps at all scales. This architecture, called a Feature Pyramid Network (FPN), shows significant improvement as a generic feature extractor in several applications. Using a basic Faster R-CNN system, our method achieves state-of-the-art single-model results on the COCO detection benchmark without bells and whistles, surpassing all existing single-model entries including those from the COCO 2016 challenge winners. In addition, our method can run at 5 FPS on a GPU and thus is a practical and accurate solution to multi-scale object detection. Code will be made publicly available. We learn to compute optical flow by combining a classical spatial-pyramid formulation with deep learning. This estimates large motions in a coarse-to-fine approach by warping one image of a pair at each pyramid level by the current flow estimate and computing an update to the flow. Instead of the standard minimization of an objective function at each pyramid level, we train one deep network per level to compute the flow update. Unlike the recent FlowNet approach, the networks do not need to deal with large motions; these are dealt with by the pyramid. This has several advantages. First, our Spatial Pyramid Network (SPyNet) is much simpler and 96 smaller than FlowNet in terms of model parameters. This makes it more efficient and appropriate for embedded applications. Second, since the flow at each pyramid level is small (< 1 pixel), a convolutional approach applied to pairs of warped images is appropriate. Third, unlike FlowNet, the learned convolution filters appear similar to classical spatio-temporal filters, giving insight into the method and how to improve it. Our results are more accurate than FlowNet on most standard benchmarks, suggesting a new direction of combining classical flow methods with deep learning. Based on multifractal analysis in wavelet pyramids of texture images, a new texture descriptor is proposed in this paper that implicitly combines information from both spatial and frequency domains. Beyond the traditional wavelet transform, a multi-oriented wavelet leader pyramid is used in our approach that robustly encodes the multi-scale information of texture edgels. Moreover, the resulting texture model shows empirically a strong power law relationship for nature textures, which can be characterized well by multifractal analysis. Combined with a statistics on affine invariant local patches, our proposed texture descriptor is robust to scale and rotation changes, more general geometrical transforms and illumination variations. In addition, the proposed texture descriptor is computationally efficient since it does not require many expensive processing steps, e.g., texton generation and cross-bin comparisons, which are often used by existing methods. As an application, the proposed descriptor is applied to texture classification and the experimental results on several public texture datasets verified the accuracy and efficiency of our descriptor.