Abstract
AbstractWe present a methodology for synthesizing high resolution micrographs from low resolution ones using a parametric texture model and a particle filter. Information contained in high resolution micrographs is relevant to the accurate prediction of microstructural behavior and the nucleation of instabilities. As these micrographs may be tedious and uneconomical to obtain over an extended spatial domain, we propose a statistical approach for interpolating fine details over a whole computational domain starting with a low resolution prior and high resolution micrographs available only at a few spatial locations. As a first step, a small set of high resolution micrographs are decomposed into a set of multi-scale and multi-orientation subbands using a complex wavelet transform. Parameters of a texture model are computed as the joint statistics of the decomposed subbands. The synthesis algorithm then generates random micrographs satisfying the parameters of the texture model by recursively updating the gray level values of the pixels in the input micrograph. A density-based Monte Carlo filter is used at each step of the recursion to update the generated micrograph, using a low resolution micrograph at that location as a measurement. The process is continued until the synthesized micrograph has the same statistics as those from the high resolution micrographs. The proposed method combines a texture synthesis procedure with a particle filter and produces good quality high resolution micrographs.
Highlights
Recent capabilities in the multi-scale modeling and simulation of material behavior have been matched by technologies for sensing and characterizing materials at distinct spatial scales
In the first case (Figures 8, 9 and 10), a parametric texture model with the synthesis procedure described in section “Micrograph synthesis procedure” is used to construct a high resolution micrograph, whereas in the second case (Figures 11, 12 and 13), the parametric texture model along with the density-based Monte Carlo filter described in section “Density-based Monte Carlo filter” is used to estimate a high resolution micrograph
When the particle filter is not used, the synthesis procedure does not make use of the low resolution micrographs available at a given location
Summary
Recent capabilities in the multi-scale modeling and simulation of material behavior have been matched by technologies for sensing and characterizing materials at distinct spatial scales. Three approaches are commonly used, in light of their simplicity, for generating high resolution images from lower resolution ones These are based on nearest neighbor, bilinear and cubic interpolation methods [3]. In PIGE, higher order polynomial bases are used for interpolation In these methods, gradient based enhancement accounts for the position of calibration images relative to the spatial location of the simulated image. Gradient based enhancement accounts for the position of calibration images relative to the spatial location of the simulated image Both WIGE and PIGE methods are shown to be very effective in synthesizing high resolution images from low resolution ones with the aid of few calibrating high resolution images. A particle filter is used to estimate the high resolution micrograph at a location given the low resolution micrograph at that location
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