| D. L. Donoho and X. Huo, "Beamlets and multiscale image analysis," in Multiscale and Multiresolution Methods, Lecture Notes in Computational Science and Engineeing. Springer, 2001. |
....images) in the multiscale wedgelet representation. The structure of the model allows efficient algorithms for finding the optimal MWR given an image and a set of complexity and geometry constraints. A major strength of the wedgelet framework (and the closely related beamlet framework in [3]) is that it captures geometrical structure of the image at multiple scales. We can infer the gross geometrical structure of an image using a coarse (parsimonious) wedgelet representation. Refining the wedgelet representation not only yields a more accurate image approximation (in terms of ....
....the wedgelet representation not only yields a more accurate image approximation (in terms of squared error) but results in a better geometrical description as well. Applications of wedgelet decompositions and representations include detecting linear singularities in the presence of noise [3] v 2 j,k S R b Fig. 1. A wedgelet on a dyadic square S j;k is a piecewise constant function over two regions Ra and R b on either side of the line defined by the orientation (v1 ; v2 ) and image coding [4] The contributions of this paper are the efficient discrete multiscale wedgelet ....
D. L. Donoho and X. Huo, "Beamlets and multiscale image analysis," in Multiscale and Multiresolution Methods, Lecture Notes in Computational Science and Engineeing. Springer, 2001.
....coefficients of the images. Wainwright et al. 28] have studied a family of Gaussian mixtures, resulting from different mixing densities, for modeling the observed histograms. Lee et al. 17] have presented a synthesis model for capturing the statistics in the images of leaves. Donoho and Flesia [7] and Donoho and Huo [6] have proposed edge based transforms to account for the patterns in the observed histograms. Using a physical model for image formation, we have proposed a family of two parameter probability densities [11] called Bessel K forms, to model the horizontal and the vertical ....
D.L. Donoho and X. Huo, "Beamlets and Multiscale Image Analysis," http://www-stat.stanford.edu/donoho/Reports, 2001.
.... knowledge, the images are simply treated as matrices of numbers, and one seeks a low dimensional subspace that best represents those numbers (under some chosen criterion) Principal components [9] independent components It0] tt] sparse coding [12] 13] Fisher s discriminant [14] beamlets [15], local linear embedding [16] and their variations, are all examples of this approach. The main advantage here is the computational efficiency and the main drawback is that these representations are knowledge deficient. They do not involve any physical or contextual information about the imaged ....
D. L. Donoho and X. Huo, "Beamlets and multiscale image analysis, " http://www-stat. stanford. edu/ donoho/Reports/, 2001.
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