Two-dimensional generalisations of dynamic programming for image analysis
Dynamic programming (DP) is a fast, elegant method for solving many one-dimensional optimisation problems but, unfortunately, most problems in image analysis, such as restoration and warping, are two-dimensional. We consider three generalisations of DP. The first is iterated dynamic programming (IDP...
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| Veröffentlicht in: | Statistics and computing Jg. 19; H. 1; S. 49 - 56 |
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| Abstract | Dynamic programming (DP) is a fast, elegant method for solving many one-dimensional optimisation problems but, unfortunately, most problems in image analysis, such as restoration and warping, are two-dimensional. We consider three generalisations of DP. The first is iterated dynamic programming (IDP), where DP is used to recursively solve each of a sequence of one-dimensional problems in turn, to find a local optimum. A second algorithm is an empirical, stochastic optimiser, which is implemented by adding progressively less noise to IDP. The final approach replaces DP by a more computationally intensive Forward-Backward Gibbs Sampler, and uses a simulated annealing cooling schedule. Results are compared with existing pixel-by-pixel methods of iterated conditional modes (ICM) and simulated annealing in two applications: to restore a synthetic aperture radar (SAR) image, and to warp a pulsed-field electrophoresis gel into alignment with a reference image. We find that IDP and its stochastic variant outperform the remaining algorithms. |
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| AbstractList | Dynamic programming (DP) is a fast, elegant method for solving many one-dimensional optimisation problems but, unfortunately, most problems in image analysis, such as restoration and warping, are two-dimensional. We consider three generalisations of DP. The first is iterated dynamic programming (IDP), where DP is used to recursively solve each of a sequence of one-dimensional problems in turn, to find a local optimum. A second algorithm is an empirical, stochastic optimiser, which is implemented by adding progressively less noise to IDP. The final approach replaces DP by a more computationally intensive Forward-Backward Gibbs Sampler, and uses a simulated annealing cooling schedule. Results are compared with existing pixel-by-pixel methods of iterated conditional modes (ICM) and simulated annealing in two applications: to restore a synthetic aperture radar (SAR) image, and to warp a pulsed-field electrophoresis gel into alignment with a reference image. We find that IDP and its stochastic variant outperform the remaining algorithms. |
| Author | Glasbey, C. A. |
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| Keywords | Pulsed-field gel electrophoresis Image warping Simulated annealing Image restoration Markov random field Forward-backward Gibbs sampler Synthetic aperture radar |
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| References_xml | – reference: Gustafsson, J.: Unwarping and analysing electrophoresis gels. PhD thesis, Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden (2005) – reference: GemanS.GemanD.Stochastic relaxation, Gibbs distributions and the Bayesian restoration of imagesIEEE Trans. Pattern Anal. Mach. Intell.198467217350573.6203010.1109/TPAMI.1984.4767596 – reference: KünschH.R.Robust priors for smoothing and image restorationAnn. Inst. Stat. Math.1994461190805.6203310.1007/BF00773588 – reference: FrielN.RueH.Recursive computing and simulation-free inference for general factorizable modelsBiometrika2007946616721135.6207810.1093/biomet/asm0522410015 – reference: KirkpatrickS.GelattC.D.VecchiM.P.Optimization by simulated annealingScience198322067168010.1126/science.220.4598.671702485 – reference: MacDonaldI.L.ZucchiniW.Hidden Markov and Other Models for Discrete-Valued Time Series1997LondonChapman and Hall0868.60036 – reference: GreigD.M.PorteousB.T.SeheultA.H.Exact maximum a posteriori estimation for binary imagesJ. R. Stat. Soc. Ser. B198951271279 – reference: ScottS.L.Bayesian methods for Hidden Markov Models: recursive computing in the 21st centuryJ. Am. Stat. Assoc.2002973373511073.6550310.1198/016214502753479464 – reference: BoykovY.VekslerO.ZabihR.Fast approximate energy minimization via graph cutsIEEE Trans. Pattern Anal. Mach. Intell.2001231222123910.1109/34.969114 – reference: OliverC.J.Information from SAR imagesJ. Phys. D Appl. Phys.1991241493151410.1088/0022-3727/24/9/001 – reference: NavajasE.A.GlasbeyC.A.McLeanK.A.FisherA.V.CharterisA.J.L.LambeN.R.BungerL.SimmG.In vivo measurements of muscle volume by automatic image analysis of spiral computed tomography scansAnim. Sci.20068254555310.1079/ASC200662 – reference: EddyS.R.RawlingsC.ClarkD.AltmanR.HunterL.LengauerT.WodakS.Multiple alignment using hidden Markov modelsProceedings of the Third International Conference on Intelligent Systems for Molecular Biology1995Menlo ParkAAAI Press114120 – reference: BellmanR.Dynamic Programming1957PrincetonPrinceton University Press – reference: BesagJ.KooperbergC.On conditional and intrinsic autoregressionsBiometrika1995827337460899.621231380811 – reference: GlasbeyC.A.HorganG.W.Image Analysis for the Biological Sciences1995ChichesterWiley0876.92001 – reference: SzeliskiR.ZabihR.ScharsteinD.VekslerO.KolmogorovV.AgarwalaA.TappenM.RotherC.A comparative study of energy minimization methods for Markov random fieldsComputer Vision—ECCV, Part 22006BerlinSpringer1629 – reference: Leung, C., Appleton, B., Sun, C.: Fast stereo matching by Iterated Dynamic Programming and quadtree subregioning. In: Hoppe, A., Barman, S., Ellis, T. (eds.) British Machine Vision Conference, vol. 1, pp. 97–106 (2004) – reference: GlasbeyC.A.ValiL.GustafssonJ.S.A statistical model for unwarping of 1-D electrophoresis gelsElectrophoresis2005264237424210.1002/elps.200500365 – reference: GlasbeyC.A.YoungM.J.Maximum a posteriori estimation of image boundaries by dynamic programmingAppl. Stat.2002512092211111.623041900166 – reference: StorvikG.DahlG.Lagrangian-based methods for finding MAP solutions for MRF modelsIEEE Trans. Image Process.2000946947910.1109/83.826783 – reference: BesagJ.On the statistical analysis of dirty pictures (with discussion)J. R. Stat. Soc. Ser. B1986482593020609.62150876840 – reference: NotredameC.Recent progress in multiple sequence alignment: a surveyPharmacogenomics2002313114410.1517/14622416.3.1.131 – reference: GlasbeyC.A.JonesR.Fast computation of moving average and related filters in octagonal windowsPattern Recogn. Lett.19971855556510.1016/S0167-8655(97)00045-7 – reference: RobertsG.O.SahuS.K.Updating schemes, correlation structure, blocking and parameterization for the Gibbs samplerJ. R. Stat. Soc. Ser. B1997592913170886.6208310.1111/1467-9868.000701440584 – volume-title: Hidden Markov and Other Models for Discrete-Valued Time Series year: 1997 ident: 9068_CR17 – volume: 18 start-page: 555 year: 1997 ident: 9068_CR9 publication-title: Pattern Recogn. Lett. doi: 10.1016/S0167-8655(97)00045-7 – volume: 51 start-page: 271 year: 1989 ident: 9068_CR12 publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.2517-6161.1989.tb01764.x – volume: 24 start-page: 1493 year: 1991 ident: 9068_CR20 publication-title: J. Phys. D Appl. Phys. doi: 10.1088/0022-3727/24/9/001 – volume: 46 start-page: 1 year: 1994 ident: 9068_CR15 publication-title: Ann. Inst. Stat. 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Stat. Soc. Ser. B doi: 10.1111/j.2517-6161.1986.tb01412.x – volume: 9 start-page: 469 year: 2000 ident: 9068_CR23 publication-title: IEEE Trans. Image Process. doi: 10.1109/83.826783 – volume: 59 start-page: 291 year: 1997 ident: 9068_CR21 publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/1467-9868.00070 – volume: 51 start-page: 209 year: 2002 ident: 9068_CR11 publication-title: Appl. Stat. – start-page: 114 volume-title: Proceedings of the Third International Conference on Intelligent Systems for Molecular Biology year: 1995 ident: 9068_CR5 – volume: 82 start-page: 545 year: 2006 ident: 9068_CR18 publication-title: Anim. Sci. doi: 10.1079/ASC200662 – volume: 26 start-page: 4237 year: 2005 ident: 9068_CR10 publication-title: Electrophoresis doi: 10.1002/elps.200500365 – volume: 97 start-page: 337 year: 2002 ident: 9068_CR22 publication-title: J. Am. Stat. Assoc. doi: 10.1198/016214502753479464 – volume: 220 start-page: 671 year: 1983 ident: 9068_CR14 publication-title: Science doi: 10.1126/science.220.4598.671 – ident: 9068_CR16 doi: 10.5244/C.18.12 |
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| SubjectTerms | Algorithms Artificial Intelligence Computation Dynamic programming Mathematics and Statistics Probability and Statistics in Computer Science Simulated annealing Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs Stochasticity Synthetic aperture radar Two dimensional |
| Title | Two-dimensional generalisations of dynamic programming for image analysis |
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