High resolution texture analysis

• Applicants: Professor Dr. Jürgen Prestin; Professor Dr. Helmut Schaeben
• Subject Area: Mineralogy, Petrology and Geochemistry
• Term: from 2003 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5399900

• Final Report Year: 2008

Final Report Abstract

Das Ergebnis des DFG Projekts "Hochauflösende Texturanalyse" ist nicht weniger als eine umfassende Revision der "Mathematische(n) Methoden der Texturanalyse" (Bunge, 1969) auf der Grundlage, das inverse Problem der Texturanalyse als Inversion der Radon Transformation zu identifizieren. Damit wurde das in der Textur-Gemeinde immer wieder als "einmalig" dargestellte Problem in die (fast) klassische Mathematik der Radon Transformation zurückgeholt.

Publications

• Bernstein, S,, Hielscher, R., Schaeben, H., 2005, The Generalized Spherical Radon Transform, Kernels, Wavelets, and Standard Functions in Texture Analysis: in Simos, T.B., Tsitouras, Ch., (eds.), Proc. International Conference on Numerical Analysis and Applied Mathematics (ICNAAM) 2005, 900-903
  
  
• Bernstein, S-, Schaeben, H., 2005, A one-dimensional Radon transform on SO(3) and its application to texture goniometry: Mathematical Methods in the Applied Sciences 28, 1269-1289
  
  
• Bernstein, S., 2004, The Radon transform in texture analysis; in Simos, T.E., Tsitouras, Ch., (eds.), Proc. International Conference on Numerical Analysis and Applied Mathematics (ICNAAM) 2004, 482-485
  
  
• Bernstein, S., 2007, Wavelets on the Group S0(3) and the sphere S3: AIP Conference Proceedings 936, Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics, Corfu, Greece, 16-20 September 2007, American Institute of Physics, Melville, New York, 713-716
  
  
• Bernstein, S., Hielscher, R., Schaeben, H., 2005, Common basics of mathematical texture analysis: van Houtte, P. and Kestens, L., (eds.), Proceedings ICOTOM14, Leuven, Jul 11-15, 2005, Materials Science Forum 495-497, 277-282
  
  
• Bernstein, S., Hielscher, R., Schaeben, H., 2006, A brief survey of mathematical texture analysis with special emphasis on Radon transforms and their inverses: in Le Hung Son, Tutschke, W., Jain, S., (eds.), Methods of Complex and Clifford Analysis, SAS International Publication, 3-40
  
  
• Boogaart, K.G.v.d., Hielscher, R., Prestin, J,, Schaeben, H., 2007, Kernelbased methods for inversion of the Radon transform on SO(3) and their applications to texture analysis: J. Comput. Appl. Math. 199, 122-140
  
  
• Hielscher, R., 2007, The inversion of the Radon transform on the rotational group and its application to texture analysis: PhD thesis, TU Freiberg, Germany
  
  
• Hielscher, R., Bernstein, S., Schaeben, H., Boogaart, K.G.v.d., Beckmann, J., Prestin, J., 2005, PDF-to-ODF inversion by approximation with spherical radial basis functions: van Houtte, P. and Kestens, L., (eds.), Proceedings ICOTOM14, Leuven, Jul 11-15, 2005, Materials Science Forum 495-497, 313-318
  
  
• Hielscher, R., Potts, D., Prestin, J., Schaeben, H., Schmalz, M., 2008, The Radon Transform on SO(3): A Fourier Slice Theorem and Numerical Inversion: Inverse Problems 24
  
  
• Hielscher, R., Schaeben, H., 2006, A novel method to determine crystallographic preferred orientations from diffraction experiments: Proceedings IAMG'2006, Liege, Sep 3-8, 2006, CD S06-12, lp
  
  
• Hielscher, R., Schaeben, H., 2006, Numerical Inversion of the Crystallographic X-Ray Transform: Proc. Intern. Conf. Tikhonov and Contemporary Mathematics, Moscow, June 19-25, 2006, section 4, 73
  
  
• Hielscher, R., Schaeben, H., 2008, Multi-Scale Texture Modeling: Mathematical Geosciences 40, 63-82
  
  
• Hielscher, R., Schaeben, H., Chateigner, D., 2007, On the entropy to texture index relationship in quantitative texture analysis: J. Appl. Cryst. 40, 371-375
  
  
• Schaeben, H., Bernstein, S., Hielscher, R., Beckmann, J-, Keiner, J., Prestin, J., 2005, High resolution texture analysis with spherical wavelets, Invited Lecture: van Houtte, P. and Kestens, L., feds.), Proceedings ICOTOM14, Leuven, Jul 11-15, 2005, Materials Science Forum 495-497, 245-254
  
  
• Schaeben, H., Bernstein, S., Hielscher, R.f 2005, The spherical Radon Transform and its Inverse to analyse preferred crystallographic Orientation: in Cheng, Q. and Bonham-Carter, G-, Proceedings IAMG'2005, Toronto, August 21-26, 2005, 1159-1164
  
  
• Schaeben, H., Hielscher, R., 2006, Modeling Texture Goniometry with Spherical Radon Transforms and Their Properties with Special Emphasis on Localization: Proc. Intern. Conf. Tikhonov and Contemporary Mathematics, Moscow, June 19-25, 2006, section 5, 56
  
  
• Schaeben, H., Hielscher, R., 2006, Resolving the Inverse Radon Problem on SO(3) - Special Cases: Proceedings IAMG'2006, Liege, Sep 3-8, 2006, CD Sll-30, 4p
  
  
• Schaeben, H., Hielscher, R., Fundenberger, J.-J., Potts, D., Prestin, J., 2007, Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers: J. Appl. Cryst. 40, 570-579
  
  
• Schaeben, H., Hielscher, R., Fundenberger, J.-J., Potts, D., Prestin, J., 2007, Successive computations of an ODF while measuring its corresponding PDFs with respect to progressively locally refined spherical grids: in Zhao, P., Agterberg, F., Chen, Q., (eds.), Proceedings IAMG'2007, Beijing, August 26-31, 2007, 48-50