Extended structure tensors for multiple directionality estimation

References

1. ArseneauS. and CooperstockJ.2006. An improved representation of junctions through asymmetric tensor diffusion. Advances in Visual Computing, 363–372.
   [Google Scholar]
2. BainaR., NguyenS., NobleM., and LambaréG.2003. Optimal antialiasing for raybased depth Kirchhoff migration. 73rd Annual International Meeting, Society of Exploration Geophyicists, 1130–1133.
   [Google Scholar]
3. BeylkinG.1995. On the fast Fourier transform of functions with singularities. Applied and Computational Harmonic Analysis2(4), 363–381.
   [Google Scholar]
4. BeylkinG.1998. On applications of unequally spaced fast Fourier transforms. Lecture notes for Mathematical Geophysics Summer School at Stanford, August 1998, 1–8. Stanford University.
   [Google Scholar]
5. BigunJ. and GranlundG.H.1987. Optimal orientation detection of linear symmetry. First International Conference on Computer Vision, ICCV (London), 433–438.
   [Google Scholar]
6. BilletteF. and LambaréG.1998. Velocity macromodel estimation from seismic reflection data by stereotomography. Geophysical Journal International135, 671–680.
   [Google Scholar]
7. BilletteF., BegatS.L., PodvinP., and LambaréG.2003. Practical aspects and applications of 2D sterotomography. Geophysics68, 1008–1021.
   [Google Scholar]
8. CasasantaL. and FomelS.2011. Velocity‐independent tau‐p moveout in a vertically‐varying VTI medium. Geophysics76, U45–U57.
   [Google Scholar]
9. ChopraS. and MarfurtK.J.2007. Seismic Attributes for Prospect Identification and Reservoir Characterization11, Geophysical Developments Series. SEG.
   [Google Scholar]
10. ClaerboutJ.F.1958. Imaging the Earth's Interior. Blackwell Scientific Publications, Inc.
    [Google Scholar]
11. ClaytonR. and EngquistB.1980. Absorbing boundary conditions for wave‐equation migration. Geophysics45, 895–904.
    [Google Scholar]
12. CoxD., LittleJ., and O'SheaD.2007. Ideals, varieties, and algorithms: (An introduction to computational algebraic geometry and commutative algebra Undergraduate Texts in Mathematics). Springer, New York, third edition.
    [Google Scholar]
13. DuchkovA.A., AnderssonF., and OjalaR.2012. Prestack shot‐gather depth migration by a rigid flow of Gaussian wave packets. Studia Geophysica et Geodaetica56(1), 83–106.
    [Google Scholar]
14. DuttA. and RokhlinV.1993. Fast Fourier transforms for nonequispaced data. SIAM Journal on Scientfic Computing14(6), 1368–1393.
    [Google Scholar]
15. FehmersG.C. and HöckerC.F.W.2003. Fast structural interpretations with structure‐oriented filtering. Geophysics68, 1286–1293.
    [Google Scholar]
16. FomelS.2002. Applications of plane‐wave destruction filters. Geophysics67(6), 1946–1960.
    [Google Scholar]
17. FomelS.2007. Velocity‐independent time‐domain seismic imaging using local event slopes. Geophysics72(3), S139–S147.
    [Google Scholar]
18. FörstnerW.1994. A framework for low level feature extraction. Computer Vision – ECCV'94, 383–394.
    [Google Scholar]
19. FörstnerW. and GülchE.1987. A fast operator for detection and precise location of distinct points, corners and centres of circular features. Proceedings of the ISPRS Intercommission Conference on Fast Processing of Photogrammetric Data, 281–305.
    [Google Scholar]
20. GalićI., WeickertJ., WelkM., BruhnA., BelyaevA., and SeidelH.P.2005. Towards PDE‐based image compression. Variational, Geometric, and Level Set Methods in Computer Vision, 37–48.
    [Google Scholar]
21. GoldinS.V.2003. Geometrical fundamentals of seismic imaging: realization of contact mappings. Siberian Journal of Numerical Mathematics6(4), 323–345.
    [Google Scholar]
22. GoldinS.V.1998. Geometric fundamentals of seismic imaging: A geometric theory of the upper level. In Amplitude‐preserving seismic reflection imaging. Proceedings of the Workshop held in Seeheim, Germany, 45–71. London, Geophysical Press LTD.
    [Google Scholar]
23. GoldinS.V. and VingalovV.M.1986. Use of kinematically equivalent continuations of wave field for isolating interfering waves. Soviet Geology and Geophysics11, 83–95.
    [Google Scholar]
24. GoldinS.V., EpinatjevaA.M., GoloshubinG.M., and VingalovV.M.1989. Migration of refracted wave fields. In Proceedings of the 34th International Geophysical Meeting, Budapest, 251–255.
    [Google Scholar]
25. HaleD.2011. Structure‐oriented bilateral filtering of seismic images SEG. Annual Meeting Expanded Abstracts 30, 3596–3600.
    [Google Scholar]
26. HarrisC. and StephensM.1988. A combined corner and edge detector. Alvey vision conference, Vol. 15, page 50. Manchester, UK.
    [Google Scholar]
27. HitchcockF.L.1927. Multiple invariants and generalized rank of a p‐way matrix or tensor. Jematical Mathematical Physics7(1), 39–79.
    [Google Scholar]
28. HuaB. and McMechanG.A.2003. Parsimonious 2D prestack Kirchhoff depth migration. Geophysics68, 1043–1051.
    [Google Scholar]
29. JónssonG.F. and VavasisS.A.2005. Accurate solution of polynomial equations using Macaulay resultant matrices. Mathematics of Computation74(249), 221–262.
    [Google Scholar]
30. KnutssonH., WestinC.F., and AnderssonM.2011. Representing local structure using tensors II. Image Analysis, 545–556.
    [Google Scholar]
31. KötheU.2003. Edge and junction detection with an improved structure tensor. Pattern Recognition, 25–32.
    [Google Scholar]
32. LambaréG., AleriniM., BainaR., and PodvinP.2004. Stereotomography: a semiautomatic approach for velocity macromodel estimation. Geophysical Prospecting52, 671–681.
    [Google Scholar]
33. LuoS. and HaleD.2011. Non‐vertical deformations for seismic image flattening. Annual Meeting Expanded Abstracts 30, 970–974.
    [Google Scholar]
34. ÖzarslanE. and MareciT.H.2003. Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging. Magnetic Resonance in Medicine50(5), 955–965.
    [Google Scholar]
35. RiabinkinL.A.1957. Fundamentals of resolving power of controlled directional reception (CDR) of seismic waves. Slant‐stack processing, 1991: Society of Exploration Geophysicists (Translated and paraphrased from Prikladnaya Geofizika, 16, 3‐36), 36–60.
    [Google Scholar]
36. RieberF.1936. A new reflection system with controlled directional sensitivity. Geophysics1, 97–106.
    [Google Scholar]
37. SchleicherJ., CostaJ.C., SantosL.T., NovaisA., and TygelM.2009. On the estimation of local slopes. Geophysics74(4), P25–P33.
    [Google Scholar]
38. SchonewilleM.A. and DuijndamA.J.W.2001. Parabolic Radon transform, sampling and efficiency. Geophysics66(2), 667–678.
    [Google Scholar]
39. SchultzT., WeickertJ., and SeidelH.P.2009. A higher‐order structure tensor. Visualization and Processing of Tensor Fields, 263–279.
    [Google Scholar]
40. SherwoodJ.W.C., SherwoodK., TiemanH., and SchleicherK.2009. 3D beam prestack depth migration with examples from around the world. The Leading Edge28(9), 1120–1127.
    [Google Scholar]
41. StoltR.H.1978. Migration by Fourier transform. Geophysics43, 23–48.
    [Google Scholar]
42. SwordC.H.1987. Tomographic determination of interval velocities from reflection seismic data: The method of controlled directional reception. PhD thesis, Stanford University.
    [Google Scholar]
43. SymesW.W.1994. The plane wave detection problem. Inverse Problems10, 1361–1391.
    [Google Scholar]
44. TschumperléD. and DericheR.2001. Diffusion tensor regularization with constraints preservation. Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on, 1, I–948. IEEE.
    [Google Scholar]
45. TschumperleD. and DericheR.2005. Vector‐valued image regularization with PDEs: A common framework for different applications. Pattern Analysis and Machine Intelligence, IEEE Transactions27(4), 506–517.
    [Google Scholar]
46. WeickertJ.1998. Anisotropic diffusion in image processing, Vol. 1. Teubner Stuttgart.
    [Google Scholar]
47. YoonK. and MarfurtK.J.2006. Reverse‐time migration using the Poynting vectors. Exploration Geophysics37, 102–107.
    [Google Scholar]
48. ZhangL., ZhangL., and ZhangD.2010. A multi‐scale bilateral structure tensor based corner detector. Computer Vision–ACCV 2009, 618–627.
    [Google Scholar]