1 March 2008 Calibrating image roughness by estimating Lipschitz exponents, with applications to image restoration
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Optical Engineering, 47(3), 037012 (2008). doi:10.1117/1.2899144
Abstract
Most images f(x,y) are not smoothly differentiable functions of x and y, but display edges, localized singularities, and other significant fine-scale roughness, or texture. Correct characterization and calibration of image roughness is vital in many image processing tasks. The L1 Lipschitz exponent α, where 0<1α≤1, measures fine-scale image roughness provided the image is relatively noise free. A recently developed mathematical technique for estimating α is described. The method is based on successively blurring the image by convolution with increasingly narrower Gaussians, using commonly available fast Fourier transform algorithms. Instructive examples are used to illustrate the quantitative changes in α that occur when an image is either degraded or restored. Of particular interest are the documented changes in α that accompany APEX blind deconvolution of real images from the Hubble space telescope, from magnetic resonance imaging and positron emission tomography brain scans, and from state-of-the-art nanoscale scanning electron microscopy. Additional applications include monitoring of image sharpness and imaging performance in imaging systems, evaluation of image reconstruction software quality, detection of abnormal fine structure in biomedical images, and monitoring of surface finish in industrial applications.
Alfred S. Carasso, András E. Vladár, "Calibrating image roughness by estimating Lipschitz exponents, with applications to image restoration," Optical Engineering 47(3), 037012 (1 March 2008). https://doi.org/10.1117/1.2899144
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