A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph. The boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical segmentation of the image, and may be rendered as vector graphics. A persistence lens determines a varilet basis for the luminance image, in which image simplification is a realized by subspace projection. Image scale space, and image fractal analysis, result from applying a scale measure to each basis function.
@cite_61 define a regularized equation whose solution provides a complete global image segmentation. Their approach has been refined and solutions have been explored; for a review see @cite_54 .
@cite_61 @cite_54
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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 have applied this approach to segmenting static images and found results very encouraging. 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. In this paper, the crowd counting and segmentation problem is formulated as a maximum a posterior problem, in which 3D human shape models are designed and matched with image evidence provided by foreground background separation and probability of boundary. The solution is obtained by considering only the human candidates that are possible to be un-occluded in each iteration, and then applying on them a validation and rejection strategy based on minimum description length. The merit of the proposed optimization procedure is that its computational cost is much smaller than that of the global optimization methods while its performance is comparable to them. The approach is shown to be robust with respect to severe partial occlusions. In this paper we introduce a novel higher-order regularization term. The proposed regularizer is a non-local extension of the popular second-order Total Generalized variation, which favors piecewise affine solutions and allows to incorporate soft-segmentation cues into the regularization term. These properties make this regularizer especially appealing for optical flow estimation, where it offers accurately localized motion boundaries and allows to resolve ambiguities in the matching term. We additionally propose a novel matching term which is robust to illumination and scale changes, two major sources of errors in optical flow estimation algorithms. We extensively evaluate the proposed regularizer and data term on two challenging benchmarks, where we are able to obtain state of the art results. Our method is currently ranked first among classical two-frame optical flow methods on the KITTI optical flow benchmark.