Uncertainty Estimation by Convolution Using Spatial Statistics

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Bernabeu Martínez, Eusebio
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IEEE Institute of Electrical and Electronics Engineers
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Kriging has proven to be a useful tool in image processing since it behaves, under regular sampling, as a convolution. Convolution kernels obtained with kriging allow noise filtering and include the effects of the random fluctuations of the experimental data and the resolution of the measuring devices. The uncertainty at each location of the image can also be determined using kriging. However, this procedure is slow since, currently, only matrix methods are available. In this work, we compare the way kriging performs the uncertainty estimation with the standard statistical technique for magnitudes without spatial dependence. As a result, we propose a much faster technique, based on the variogram, to determine the uncertainty using a convolutional procedure. We check the validity of this approach by applying it to one-dimensional images obtained in diffractometry and two-dimensional images obtained by shadow moire.
© IEEE. The work of L. M. Sánchez-Brea was supported by the Ministerio de Educación y Ciencia of Spain, within the ”Ramón y Cajal” program. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Til Aach. The authors thank Dr. J. Zoido, Dr. J. A. Quiroga, Dr. J. Alda, and Dr. A. Luis for their help and fruitful discussions.
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