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.
Using an energy that incorporates a discrete number of scales @cite_24 (middle) in this example captures the desired segmentation, however it does not exhibit coarse-to-fine behavior.
@cite_24
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We propose to tackle the optical flow problem by a combination of two recent advances in the computation of dense correspondences, namely the incorporation of image segmentation and robust global optimization via graph-cuts. In the first step, each segment (extracted by colour segmentation) is assigned to an affine motion model from a set of sparse correspondences. Using a layered model, we then identify those motion models that represent the dominant image motion. This layer extraction task is accomplished by optimizing a simple energy function that operates in the domain of segments via graph-cuts. We then estimate the spatial extent that is covered by each layer and identify occlusions. Since treatment of occlusions is hardly possible when using entire segments as matching primitives, we propose to use the pixel level in addition. We therefore define an energy function that measures the quality of an assignment of segments and pixels to layers. This energy function is then extended to work on multiple input frames and minimized via graph-cuts. In the experimental results, we show that our method produces good-quality results, especially in regions of low texture and close to motion boundaries, which are challenging tasks in optical flow computation. Inspired by the success of MRF models for solving object segmentation problems, we formulate the binarization problem in this framework. We represent the pixels in a document image as random variables in an MRF, and introduce a new energy (or cost) function on these variables. Each variable takes a foreground or background label, and the quality of the binarization (or labelling) is determined by the value of the energy function. We minimize the energy function, i.e. find the optimal binarization, using an iterative graph cut scheme. Our model is robust to variations in foreground and background colours as we use a Gaussian Mixture Model in the energy function. In addition, our algorithm is efficient to compute, and adapts to a variety of document images. We show results on word images from the challenging ICDAR 2003 dataset, and compare our performance with previously reported methods. Our approach shows significant improvement in pixel level accuracy as well as OCR accuracy. We present a novel off-line algorithm for target segmentation and tracking in video. In our approach, video data is represented by a multi-label Markov Random Field model, and segmentation is accomplished by finding the minimum energy label assignment. We propose a novel energy formulation which incorporates both segmentation and motion estimation in a single framework. Our energy functions enforce motion coherence both within and across frames. We utilize state-of-the-art methods to efficiently optimize over a large number of discrete labels. In addition, we introduce a new ground-truth dataset, called Georgia Tech Segmentation and Tracking Dataset (GT-SegTrack), for the evaluation of segmentation accuracy in video tracking. We compare our method with several recent on-line tracking algorithms and provide quantitative and qualitative performance comparisons. Most segmentation algorithms are composed of several procedures: split and merge, small region elimination, boundary smoothing,..., each depending on several parameters. The introduction of an energy to minimize leads to a drastic reduction of these parameters. The authors prove that the most simple segmentation tool, the “region merging” algorithm, made according to the simplest energy, is enough to compute a local energy minimum belonging to a compact class and to achieve the job of most of the tools mentioned above. The authors explain why “merging” in a variational framework leads to a fast multiscale, multichannel algorithm, with a pyramidal structure. The obtained algorithm is @math , where n is the number of pixels of the picture. This fast algorithm is applied to make grey level and texture segmentation and experimental results are shown.