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Estimation of the standard deviation in three-dimensional microscopy by spatial statistics

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Publication Date
2005-05
Authors
Bernabeu Martínez, Eusebio
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Blackwell Publishing Ltd.
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Abstract
Usually, the calibration process for three-dimensional microscopy involves the use of a reference flat surface. The random fluctuations of the topographic image for this reference surface are used for determining the uncertainty of the microscope. When the sample material or the measuring conditions of the microscope are modified (such as the objective used in a confocal microscope, or the tip in an atomic force microscope), the measuring conditions vary and thus a new calibration is required. In this work, a technique based on spatial statistics methods (more specifically, the variogram function) is proposed to determine accurately the standard deviation for three-dimensional microscopy that does not require a reference flat surface and therefore eliminates the need for a previous calibration process of this parameter.
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© 2005 The Royal Microscopical Society. The authors thank Javier Alda for his fruitful discussions and interest in this research. This work has been supported by the Secretaría de Estado de Política Científica y Tecnológica (Spain), project DPI2001-1238. Dr. Sánchez-Brea is currently contracted within the frame of the ‘Ramón y Cajal’ research program of the Ministerio de Educación y Ciencia of Spain.
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1. Bevington, P. (1969) Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New York. 2. Christiensen, R. (1985) Linear Models for Multivariate, Time Series, and Spatial Data. Springer-Verlag, Berlin. 3. Conan, V., Gesbert, S., Howard, C.V., Jeulin, D., Meyer, F. & Renard, D. (1992) Geostatistical and morphological methods applied to 3- dimensional microscopy. J. Microsc. 166, 169–184. 4. Cressie, N.A. (1991) Statistics for Spatial Data. J. Wiley & Sons, New York. 5. ISO (1995) Guide to the Expression of the Uncertainty in Measurement. International Standardization Organization, Geneva. 6. Pratt, W.K. (1978) Digital Image Processing. J. Wiley & Sons, New York. 7. Sánchez-Brea, L.M. & Bernabeu, E. (2002) On the standard deviation in CCD cameras: a variogram-based technique for non-uniform images. J. Electron. Imag. 11, 121–126.
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