Inference on point processes with unobserved one-dimensional reference structure
Su, J. (Jionglong), Hill, Bryony, Kendall, Wilfrid S. and Thönnes, Elke (2008) Inference on point processes with unobserved one-dimensional reference structure. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
We present a novel approach to examining local anisotropy in planar point processes. Our method is based on a kernel Principal Component Analysis and produces a tensor field that describes local orientation. The approach is illustrated on an example examining pore patterns in ink fingerprints.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Point processes, Fingerprints -- Mathematical models|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||11|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:|| V. Arsigny, P.Fillard, X. Pennec, and N. Ayache. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine, 56:411–421, 2006.  David R. Ashbaugh. Quantitative-Qualitative friction ridge analysis - an introduction to basic and advanced ridgeology. CRC Press, Boca Raton, 1999.  J-M. Azaıs and M. Wschebor. On the distribution of the maximum of a Gaussian field with d parameters. The Annals of Applied Probability, 15:254–278, 2005.  P.G. Batchelor, M. Moakher, D. Atkinson, F. Calamante, and A. Connelly. A rigorous framework for diffusion tensor calculus. Magnetic Resonance in Medicine, 53:221–225, 2005.  Thierry Delmarcelle and Lambertus Hesselink. The topology of symmetric, second-order tensor fields. In IEEE Visualization, pages 140–147, 1994.  A.K. Jain, Y. Chen, and M. Demirkus. Pores and Ridges: High Resolution Fingerprint Using Level 3 Features. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29:15–27, 2007.  R. Mathias and K. Veseli´c. A relative perturbation bound for positive definite matrices. Linear Algebra and its applications, 270:315–321, 1998.  N.R. Parsons, J.Q. Smith, E. Th¨onnes, L.Wang, and Roland Wilson. Rotationally invariant statistics for examining the evidence from the pores in fingerprints. Law, Probability and Risk, 7:1–14, 2008.  A.K. Penttinen and D. Stoyan. Statistical analysis for a class of line segment processes. Forest Science, 38:806–824, 1989.  William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes with Source Code CD-ROM 3rd Edition: The Art of Scientific Computing. Cambridge University Press, Cambridge, 2007.  S.O. Rice. Mathematical analysis of random noise. Bell Systems Technical Journal, 23:292–332, 1944.  S.O. Rice. Mathematical analysis of random noise. Bell Systems Technical Journal, 24:46–156, 1945.  B. Sch¨olkopf, A.J. Smola, and K.R. M¨uller. Kernel principal component analysis. In 7th International Conference on Artificial Neural Networks, ICANN 97, volume 1327 of Springer Lecture Notes in Computer Science, pages 583–588, Berlin, 1997.  D. Stoyan. Describing the anisotropy of marked planar point processes. Statistics, 22:449–462, 1991.  D. Stoyan and V. Benes. Anisotropy analysis for article systems. Journal of Microscopy, 164:159–168, 1991.  D. Stoyan, W.S. Kendall, and J. Mecke. Stochastic Geometry and its applications. Wiley, Chichester, second edition, 1998.  K. Veseli´c and I. Slapniˇcar. Floating-point perturbations of Hermitian matrices. Linear Algebra and its applications, 195:81–116, 1993.  C. Watson. NIST Special Database 30: Dual Resolution Images from Paired Fingerprint Cards. National Institute of Standards and Technology, Gaithersburg, MD.|
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