Top

Journal of Scientific Computing

Published in:

01-04-2015

Redistancing Dynamics for Vector-Valued Multilabel Segmentation with Costly Fidelity: Grain Identification in Polycrystal Images

Authors: Matt Elsey, Benedikt Wirth

Published in: Journal of Scientific Computing | Issue 1/2015

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A novel numerical method for multilabel segmentation of vector-valued images is presented. The algorithm seeks minimizers for a generalization of the piecewise-constant Mumford–Shah energy and is particularly appropriate for energies with a fitting (or fidelity) term that is computationally expensive to evaluate. The framework for the algorithm is the standard alternating-minimization scheme in which the update of the partition is alternated with the update of the vector-valued constants associated with each part of the segmentation. The update of the partition is based on the distance function-based diffusion-generated motion algorithms for mean curvature flow. The update of the vector-valued constants is based on an Augmented Lagrangian method. The scheme automatically chooses the appropriate number of segments in the partition. It is initialized with a partition of many more segments than are expected to be necessary. Adjacent segmentations of the partition are merged when energetically advantageous. The utility of the algorithm is demonstrated in the context of atomic-resolution polycrystalline image segmentation.

previous article Topological Derivative for the Inverse Conductivity Problem: A Bayesian Approach

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. Oxford University Press, New York (2000)

Bae, E., Yuan, J., Tai, X.C.: Global minimization for continuous multiphase partitioning problems using a dual approach. Int. J. Comput. Vis. 92(1), 112–129 (2010). doi:10.1007/s11263-010-0406-y CrossRefMathSciNet

Berkels, B., Rätz, A., Rumpf, M., Voigt, A.: Extracting grain boundaries and macroscopic deformations from images on atomic scale. J. Sci. Comput. 35(1), 1–23 (2008). doi:10.1007/s10915-007-9157-5 CrossRefMATHMathSciNet

Boerdgen, M., Berkels, B., Rumpf, M., Cremers, D.: Convex relaxation for grain segmentation at atomic scale. In: Fellner, D. (ed.) VMV 2010—Vision, Modeling and Visualization, pp. 179–186. Eurographics Association (2010)

Bresson, X., Esedoḡlu, S., Vandergheynst, P., Thirau, J.-P., Osher, S.: Fast global minimization of the active contour/snake model. J. Math. Imaging Vis. 28, 151–167 (2007). doi:10.1007/s10851-007-0002-0

Chan, T.F., Esedoglu, S., Nikolova, M.: Finding the global minimum for binary image restoration. In: Proceedings of the International Conference on Image Processing, vol. 1, pp. 121–124 (2005). doi:10.1109/ICIP.2005.1529702

Chan, T.F., Sandberg, B.Y., Vese, L.A.: Active contours without edges for vector-valued images. J. Vis. Commun. Image Represent. 11(2), 130–141 (2000). doi:10.1006/jvci.1999.0442 CrossRef

Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001). doi:10.1109/83.902291 CrossRefMATH

Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. SIAM, Philadelphia (2000)CrossRefMATH

10.

Delong, A., Boykov, Y.: Globally optimal segmentation of multi-region objects. In: Proceedings of the International Conference on Computer Vision, pp. 285–292 (2009)

11.

El-Zehiry, N., Sahoo, P., Xu, S., Elmaghraby, A.: Graph cut optimization for the Mumford-Shah model. In: Proceedings of the International Conference on Visualization, Imaging and Image Processing (IASTED), pp. 182–187 (2007)

12.

El-Zehiry, N.Y., Elmaghraby, A.: A graph cut based active contour for multiphase image segmentation. In: Proceedings of the International Conference on Image Processing (ICIP), pp. 3188–3191 (2008). doi:10.1109/ICIP.2008.4712473

13.

El-Zehiry, N.Y., Grady, L.: Combinatorial optimization of the discretized multiphase Mumford–Shah functional. Int. J. Comput. Vis. 104, 270–285 (2013)CrossRefMATHMathSciNet

14.

Elder, K.R., Grant, M.: Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. Phys. Rev. E 70, 051,605 (2004)CrossRef

15.

Elsey, M., Esedoḡlu, S.: Fast and accurate redistancing by directional optimization. SIAM J. Sci. Comput. 36(1), A219–A231 (2014). doi:10.1137/120889447 CrossRefMATHMathSciNet

16.

Elsey, M., Esedoḡlu, S., Smereka, P.: Diffusion generated motion for grain growth in two and three dimensions. J. Comput. Phys. 228(21), 8015–8033 (2009). doi:10.1016/j.jcp.2009.07.020 CrossRefMATHMathSciNet

17.

Elsey, M., Esedoḡlu, S., Smereka, P.: Simulations of anisotropic grain growth: efficient algorithms and misorientation distributions. Acta Mater. 61, 2033–2043 (2013)CrossRef

18.

Elsey, M., Wirth, B.: Fast automated detection of crystal distortion and crystal defects in polycrystal images. SIAM Multiscale Model. Simul. 12(1), 1–24 (2014)CrossRefMathSciNet

19.

Esedoḡlu, S., Otto, F.: Threshold dynamics for networks with arbitrary surface tensions. Commun. Pure Appl. Math. (2014). doi:10.1002/cpa.21527

20.

Esedoḡlu, S., Ruuth, S., Tsai, R.: Diffusion generated motion using signed distance functions. J. Comput. Phys. 229(4), 1017–1042 (2010)CrossRefMathSciNet

21.

Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009). doi:10.1137/080725891 CrossRefMATHMathSciNet

22.

Jeon, M., Alexander, M., Pedrycz, W., Pizzi, N.: Unsupervised hierarchical image segmentation with level set and additive operator splitting. Pattern Recognit. Lett. 26, 1461–1469 (2005). doi:10.1016/j.patrec.2004.11.023 CrossRef

23.

Merriman, B., Bence, J., Osher, S.: Diffusion generated motion by mean curvature. In: Taylor, J.E. (ed.) Computational Crystal Growers Workshop, pp. 73–83. American Mathematical Society, Providence (1992)

24.

Merriman, B., Bence, J.K., Osher, S.: Motion of multiple junctions: a level set approach. J. Comput. Phys. 112(2), 334–363 (1994)CrossRefMathSciNet

25.

Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989). doi:10.1002/cpa.3160420503 CrossRefMATHMathSciNet

26.

Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer Series in Operations Research and Financial Engineering. Springer, New York (2006)MATH

27.

Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation-based image restoration. Multiscale Model. Simul. 4(2), 460–489 (2005)CrossRefMATHMathSciNet

28.

Patala, S., Mason, J.K., Schuh, C.A.: Improved representations of misorientation information for grain boundary science and engineering. Prog. Mater. Sci. 57, 1383–1425 (2012)CrossRef

29.

Potts, R.B.: Some generalized order-disorder transformations. Proc. Camb. Philos. Soc. 48, 106–109 (1952)CrossRefMATHMathSciNet

30.

Read, W.T., Shockley, W.: Dislocation models of crystal grain boundaries. Phys. Rev. 78(3), 275–289 (1950)CrossRefMATH

31.

Ring, W., Wirth, B.: Optimization methods on Riemannian manifolds and their application to shape space. SIAM J. Optim. 22(2), 596–627 (2012)CrossRefMATHMathSciNet

32.

Ruuth, S.J.: A diffusion-generated approach to multiphase motion. J. Comput. Phys. 145, 166–192 (1998)CrossRefMATHMathSciNet

33.

Ruuth, S.J.: Efficient algorithms for diffusion-generated motion by mean curvature. J. Comput. Phys. 144, 603–625 (1998)CrossRefMATHMathSciNet

34.

Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591–1595 (1996)CrossRefMATHMathSciNet

35.

Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Autom. Control 40(9), 1528–1538 (1995)CrossRefMATHMathSciNet

36.

Vese, L.A., Chan, T.F.: A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 50(3), 271–293 (2002). doi:10.1023/A:1020874308076 CrossRefMATH

Title: Redistancing Dynamics for Vector-Valued Multilabel Segmentation with Costly Fidelity: Grain Identification in Polycrystal Images
Authors: Matt Elsey
Benedikt Wirth
Publication date: 01-04-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2015
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9892-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 1/2015

A Matched Alternating Direction Implicit (ADI) Method for Solving the Heat Equation with Interfaces

Topological Derivative for the Inverse Conductivity Problem: A Bayesian Approach

Image Decomposition using a Local Gradient Constraint

Discretely Exact Derivatives for Hyperbolic PDE-Constrained Optimization Problems Discretized by the Discontinuous Galerkin Method

Fast Methods for Computing Centroidal Voronoi Tessellations

On the Spectrum Computation of Non-oscillatory and Highly Oscillatory Kernel with Weak Singularity

Premium Partner