High resolution micrograph synthesis using a parametric texture model and a particle filter
Tóm tắt
We present a methodology for synthesizing high resolution micrographs from low resolution ones using a parametric texture model and a particle filter. Information contained in high resolution micrographs is relevant to the accurate prediction of microstructural behavior and the nucleation of instabilities. As these micrographs may be tedious and uneconomical to obtain over an extended spatial domain, we propose a statistical approach for interpolating fine details over a whole computational domain starting with a low resolution prior and high resolution micrographs available only at a few spatial locations. As a first step, a small set of high resolution micrographs are decomposed into a set of multi-scale and multi-orientation subbands using a complex wavelet transform. Parameters of a texture model are computed as the joint statistics of the decomposed subbands. The synthesis algorithm then generates random micrographs satisfying the parameters of the texture model by recursively updating the gray level values of the pixels in the input micrograph. A density-based Monte Carlo filter is used at each step of the recursion to update the generated micrograph, using a low resolution micrograph at that location as a measurement. The process is continued until the synthesized micrograph has the same statistics as those from the high resolution micrographs. The proposed method combines a texture synthesis procedure with a particle filter and produces good quality high resolution micrographs.
Tài liệu tham khảo
Ghosh S, Valiveti D, Harris SJ, Boileau J: A domain partitioning based pre-processor for multi-scale modelling of cast aluminium alloys. Model Simul Mater Sci Eng 2006, 14: 1363–1396. 10.1088/0965-0393/14/8/006
Valiveti DM, Ghosh S: Morphology based domain partitioning of multi-phase materials: A preprocessor for multi-scale modelling. Int J Numer Meth Engng 2007, 69: 1717–1754. 10.1002/nme.1834
Lehmann TM, Gönner C, KSpitzer: Survey: Interpolation methods in medical image processing. IEEE Trans Med Imaging 1999, 18: 1049–1075. 10.1109/42.816070
Singh H, Gokhale AM, Mao Y, Spowart JE: Computer simulations of realistic microstructures of discontinuously reinforced aluminum alloy (dra) composites. Acta Materialia 2006, 54: 2131–2143. 10.1016/j.actamat.2005.12.037
Groeber M, Ghosh S, Uchic MD, Dimiduk DM: A framework for automated analysis and simulation of 3d polycrystalline microstructures.: Part 1: Statistical characterization. Acta Materialia 2008a, 56: 1257–1273. 10.1016/j.actamat.2007.11.041
Groeber M, Ghosh S, Uchic MD, Dimiduk DM: A framework for automated analysis and simulation of 3d polycrystalline microstructures. part 2: Synthetic structure generation. Acta Materialia 2008b, 56: 1274–1287. 10.1016/j.actamat.2007.11.040
Rollett AD, Lee SB, Campman R, Rohrer G: Three-dimensional characterization of microstructure by electron back-scatter diffraction. Annu Rev Mater Res 2007, 37: 627–658. 10.1146/annurev.matsci.37.052506.084401
Tewari A, Gokhale AM, Spowart JE, Miracle DB: Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions. Acta Materialia 2004, 52: 307–319. 10.1016/j.actamat.2003.09.016
Geman S, Geman D: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Pat Anal Mach Intell 1984, 6: 721–741.
Geman S, Graffigne C: Markov random field image models and their applications to computer vision. In Proceedings of International Congress of mathematicians. Berkeley, California, USA; 1986. pp 1496–1517 pp 1496–1517
Berthod M, Kato Z, Yu S, Zerubia J: Bayesian image classification using markov random fields. Image Vis Comput 1996, 14: 285–295. 10.1016/0262-8856(95)01072-6
Fan G, Xia XG: Wavelet-based texture analysis and synthesis using hidden markov models. IEEE Trans Circuits Syst I: Fundam Theory Appl 2003, 50: 106–120. 10.1109/TCSI.2002.807520
Choi H, Baraniuk RG: Multiscale image segmentation using wavelet-domain hidden markov models. IEEE Trans Image Process 2001, 10: 1309–1321. 10.1109/83.941855
Kato Z, Pong TC: A markov random field image segmentation model for color textured images. Image Vis Comput 2000, 24: 1103–1114.
Dass SC, Nair VN: Edge detection, spatial smoothing, and image reconstruction with partially observed multivariate data. J Am Stat Assoc 2003, 98: 77–89. 10.1198/01621450338861911
Niezgoda SR, Yabansu YC, Kalidindi SR: Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Materialia 2011, 59: 6387–6400. 10.1016/j.actamat.2011.06.051
Fleuret F, Geman D: Coarse-to-fine face detection. Int J Comput Vision 2001, 41: 85–107. 10.1023/A:1011113216584
Pan R, Reeves SJ: Efficient huber-markov edge-preserving image restoration. IEEE Trans Image Process 2006, 15: 3728–3735.
Zhu SC, Mumford D: Prior learning and gibbs reaction-diffusion. IEEE Trans Pattern Anal Mach Intell 1997, 19: 1236–1250. 10.1109/34.632983
Schultz R, Stevenson RL: A bayesian approach to image expansion for improved definition. IEEE Trans Image Process 1994, 3: 233–242. 10.1109/83.287017
Zhang X, Lam KM, Shen L: Image magnification based on adaptive mrf model parameter estimation. In Proceedings of 2005 International Symposium on Intelligent Signal Proceeding and Communication Systems. Hong Kong; 2005. pp 653–656 pp 653–656
Zhu S, Wu YN, Mumford D: Filters, random fields and maximum entropy (FRAME):towards the unified theory for texture modeling. Int J Comput Vis 1998,27(2):107–126. 10.1023/A:1007925832420
Wu YN, Zhu SC, Liu X: Equivalence of julesz ensembles and FRAME models. Int J Comput Vis 2000, 38: 247–265. 10.1023/A:1008199424771
Portilla J, Simoncelli E: A parametric texture model based on joint statistics of complex wavelet coefficients. Int J Comput Vis 2000,40(1):49–70. 10.1023/A:1026553619983
Simoncelli EP: Freeman W (1995) The steerable pyramid: A flexible architecture for multi-scale derivative computation. In In Second Int’l Conf. on Image Proc.,. Washington, DC: IEEE Sig. Proc. Society; vol III, pp 444–447 vol III, pp 444–447
Simoncelli EP, Freeman W, Adelson E, Heeger D: Shiftable multi-scale transforms. IEEE Trans Inf Theory 2000,38(2):587–607.
Tipireddy R, Nasrellah HA, Manohar CS: A kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data. Probabilistic Eng Mech 2009, 24: 60–74. 10.1016/j.probengmech.2008.01.001
Doucet A, Godsill S, Andrieu C: On sequential monte carlo sampling methods for bayesian filtering. Stat Comput 2000, 10: 197–208. 10.1023/A:1008935410038
Ghosh SJ, Manohar CS, Roy D: A sequential importance sampling filter with a new proposal distribution for state and parameter estimation of nonlinear dynamical systems. Proc R Soc A 2008, 464: 25–47. 10.1098/rspa.2007.0075
Gordon NJ, Salmond DJ, Smith AFM: Novel approach to nonlinear/non-gaussian bayesian state estimation. IEEE Trans Radar Signal Proc 1993, 140: 107–113. 10.1049/ip-f-2.1993.0015
Manohar CS, Roy D: Monte carlo filters for identification of nonlinear structural dynamical systems. Sadhana 2006,31(4):399–427. 10.1007/BF02716784
Tanizaki H: Nonlinear filters: estimation and applications,. Berlin, Germany: Springer; 1996.
Julesz B: Visual pattern discrimination. IRE Trans Info Theory IT-8 1962, 84–92.
Simoncelli EP 2009.https://doi.org/www.cns.nyu.edu/~eero/steerpyr/ matlabpyrtools code.