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Machine Vision and Applications

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01-08-2013 | Original Paper

Geometric steerable medial maps

Authors: Sergio Vera, Debora Gil, Agnés Borràs, Marius George Linguraru, Miguel Angel González Ballester

Published in: Machine Vision and Applications | Issue 6/2013

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Abstract

To provide more intuitive and easily interpretable representations of complex shapes/organs, medial manifolds should reach a compromise between simplicity in geometry and capability of restoring the anatomy/shape of the organ/volume. Existing morphological methods show excellent results when applied to 2D objects, but their quality drops across dimensions. This paper contributes to the computation of medial manifolds from a theoretical and a practical point of view. First, we introduce a continuous operator for accurate and efficient computation of medial structures of arbitrary dimension. Second, we present a validation protocol for assessing the suitability of medial surfaces for anatomical representation in medical applications. We evaluate quantitatively the performance of our method with respect to existing approaches and show its higher performance for medical imaging applications in terms of medial simplicity and capability of reconstructing the anatomical volume.

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Ahuja, N., Chuang, J.H.: Shape representation using a generalized potential field model. IEEE Trans Pattern Anal. Mach. Intell. 19(2), 169–176 (1997)CrossRef

Amenta, N., Bern, M.: Surface reconstruction by voronoi filtering. Discret. Comput. Geom. 22, 481–504 (1998)MathSciNetCrossRef

Amenta, N., Choi, S., Kolluri, R.: The power crust, unions of balls, and the medial axis transform. Comput. Geom. Theory Appl. 19(2–3), 127–153 (2001)MathSciNetMATHCrossRef

Bertrand, G.: A parallel thinning algorithm for medial surfaces. Pattern Recognit. Lett. 16(9), 979–986 (1995)

Bigun, J., Granlund, G.: Optimal orientation detection of linear symmetry. In: ICCV, pp. 433–438 (1987)

Blum, H.: A Transformation for extracting descriptors of shape. MIT Press, Cambridge (1967)

Bouix, S., Siddiqi, K.: Divergence-based medial surfaces. In: ECCV, pp. 603–618 (2000)

Bouix, S., Siddiqi, K., Tannenbaum, A.: Flux driven automatic centerline extraction. Med. Image Anal. 9(3), 209–221 (2005)CrossRef

Canny, J.: A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986)CrossRef

10.

Chang, M., Leymarie, F., Kimia, B.: 3d shape registration using regularized medial scaffolds. In: Proceedings of the 3D data processing, visualization, and transmission (3DPVT), pp. 987–994. IEEE Computer Society, Washington, DC (2004)

11.

Crouch, J., Pizer, S., Chaney, E., Hu, Y.C., Mageras, G., Zaider, M.: Automated finite-element analysis for deformable registration of prostate images. IEEE Trans. Med. Imaging 26(10), 1379–1390 (2007)CrossRef

12.

Dey, T.K., Zhao, W.: Approximate medial axis as a voronoi subcomplex. In: Proceedings of the seventh ACM symposium on solid modeling and applications. SMA ’02, pp. 356–366. ACM, New york (2002)

13.

Fletcher, P.T., Lu, C., et al.: Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Trans. Med. Imaging 23(8), 995–1005 (2004)CrossRef

14.

Freeman, W., Adelson, E.: of Technology. Media Laboratory. Vision, M.I., Group, M.: The design and use of steerable filters. IEEE Trans. Pattern Ana. Mach. Intell. 13(9), 891–906 (1991)

15.

Garcia-Barnes, J., Gil, D., A. Hernandez, A.: 3d shape registration using regularized medial scaffolds. In: Proceedings of the 3D data processing, visualization, and transmission (3DPVT), pp. 987–994. IEEE Computer Society (2004)

16.

Gil, D., Radeva, P.: Extending anisotropic operators to recover smooth shapes. Comput. Vis. Image Underst. 99(1), 110–125 (2005)CrossRef

17.

Gray, A.: Tubes. Birkhäuser (2004)

18.

Haralick, R.: Ridges and valleys on digital images. Comput. Vis. Gr. Image Process. 22(10), 28–38 (1983)CrossRef

19.

Heimann, T., van Ginneken, B., Styner, M.A., Arzhaeva, Y., Aurich, V.: Comparison and evaluation of methods for liver segmentation from CT datasets. IEEE Trans. Med. Imaging 28(8), 1251–1265 (2009)CrossRef

20.

Ju, T., Baker, M.L., Chiu, W.: Computing a family of skeletons of volumetric models for shape description. In: Geometric Modeling and Processing, pp. 235–247 (2007)

21.

Keim, D., Panse, C., North, S.: Medial-axis-based cartograms. IEEE Comput. Gr. Appl. 25, 60–68 (2005)CrossRef

22.

Lee, T.C., Kashyap, R.L., Chu, C.N.: Building skeleton models via 3-D medial surface axis thinning algorithms. Gr. Model Imaging Process. 56(6), 462–478 (1994)CrossRef

23.

Lindeberg, T.: Feature detection with automatic scale selection. Int. J. Comput. Vis. 30(2), 79–116 (1998)CrossRef

24.

Linguraru, L., Pura, J., Chowdhury, A., Summers, R.: Multi-organ segmentation from multi-phase abdominal CT via 4D graphs using enhancement, shape and location optimization. In: Med Image Comput Comput Assist Interv., LNCS, vol. 13(Pt 3), pp. 89–96. Springer, Berlin (2010)

25.

Liu, X., Linguraru, M., Yao, J., Summers, R.: Organ pose distribution model and an MAP framework for automated abdominal multi-organ localization, pp. 393–402. Springer, Berlin, (2010)

26.

Lopez, A., Lumbreras, F., Serrat, J., Villanueva, J.: Evaluation of methods for ridge and valley detection. IEEE Trans. Pattern Anal. Mach. Intell. 21(4), 327–335 (1999)CrossRef

27.

Palagyi, K., Kuba, A.: A parallel 3d 12-subiteration thinning algorithm. Gr. Models Image Process. 61(4), 199–221 (1999)CrossRef

28.

Pizer, S., Fletcher, P., et al.: Deformable M-Reps for 3D medical image segmentation. Int. J. Comput. Vis. 55(2), 85–106 (2003)CrossRef

29.

Pizer, S., Fletcher, P., et al.: A method and software for segmentation of anatomic object ensembles by deformable M-Reps. Med. Phys. 32(5), 1335–1345 (2005)CrossRef

30.

Pudney, C.: Distance-ordered homotopic thinning: a skeletonization algorithm for 3D digital images. Comput. Vis. Image Underst. 72(2), 404–413 (1998)CrossRef

31.

Sheehy, D., Armstrong, C., Robinson, D.: Shape description by medial surface construction. IEEE Trans. Vis. Comput. Gr. 2(1), 62–72 (1996)CrossRef

32.

Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.: Hamilton-Jacobi skeletons. Int. J. Comput. Vis. 48(3), 215–231 (2002)MATHCrossRef

33.

Stough, J., Broadhurst, R., Pizer, S., Chaney, E.: Regional appearance in deformable model segmentation, vol. 4584, pp. 532–543 (2007)

34.

Styner, M., Gerig, G., Lieberman, J., Jones, D., Weinberger, D.: Statistical shape analysis of neuroanatomical structures based on medial models. Med. Image Anal. 7(3), 207–220 (2003)

35.

Styner, M., Lieberman, J.A., Pantazis, D., Gerig, G.: Boundary and medial shape analysis of the hippocampus in schizophrenia. Med. Image Anal. 8(3), 197–203 (2004)

36.

Sun, H., Avants, B., Frangi, A., Sukno, F., Gee, J., Yushkevich, P.: Cardiac medial modeling and time-course heart wall thickness analysis. In: MICCAI, vol. 5242, pp. 766–773 (2008)

37.

Sun, H., Frangi, A.F., Wang, H., et al.: Automatic cardiac mri segmentation using a biventricular deformable medial model. In: MICCAI, vol. 6361, pp. 468–475. Springer, Berlin (2010)

38.

Svensson, S., Nyström, I., di Baja, G.S.: Curve skeletonization of surface-like objects in 3d images guided by voxel classification. Pattern Recognit. Lett. 23(12), 1419–1426 (2002)

39.

Terriberry, T., Gerig, G.: A continuous 3-d medial shape model with branching. In: International workshop on mathematical foundations of computational anatomy MFCA-2006, in conjunction with MICCAI (2006)

40.

Udrea, R.M., Vizireanu, N.: Iterative generalization of morphological skeleton. J. Electron. Imaging 16(1), 010,501–010,501-3 (2007)

41.

Vera, S., Gil, D., Borràs, A., Sánchez, X., Pérez, F., Linguraru, M.G., Ballester, M.A.G.: Computation and evaluation of medial surfaces for shape representation of abdominal organs. In: LNCS. Springer, Berlin (2010)

42.

Vera, S., Gonzalez, M.A., Gil, D.: A medial map capturing the essential geometry of organs. In: IEEE Proceedings of ISBI (2012)

43.

Vera, S., González, M.A., Linguraru, M.G., Gil, D.: Optimal medial surface generation for anatomical volume representations. In: Abdominal imaging. Computational and clinical applications. Lecture notes in computer science, vol. 7601, pp. 265–273 (2012)

44.

Vizireanu, D.N.: Generalizations of binary morphological shape decomposition. J. Electron. Imaging 16(1), 013,002 (2007)

45.

Vizireanu, D.N.: Morphological shape decomposition interframe interpolation method. J. Electron. Imaging 17(1), 013,007–013,007–5 (2008)

46.

Vizireanu, N., Halunga, S., Marghescu, G.: Morphological skeleton decomposition interframe interpolation method. J. Electron. Imaging 19(2), 023,018–023,018–3 (2010)

47.

Vizireanu, N., Udrea, R.M.: Visual-oriented morphological foreground content grayscale frames interpolation method. J. Electron. Imaging 18(2), 020,502 (2009)

48.

Wade, L., Parent, R.: Automated generation of control skeletons for use in animation. Vis. Comput. 18, 97–110 (2002)MATHCrossRef

49.

Wilcoxon, F.: Individual comparisons by ranking methods. Biometr. Bull. 1(6), 80–83 (1945)CrossRef

50.

Yao, J., Summers, R.: Statistical location model for abdominal organ localization. In: MICCAI, LNCS, vol. 12(Pt 2), pp. 9–17. Springer, Berlin (2009)

51.

Yushkevich, P.: Continuous medial representation of brain structures using the biharmonic PDE. NeuroImage 45(1), 99–110 (2009)MathSciNetCrossRef

52.

Yushkevich, P., Zhang, H., Gee, J.: Continuous medial representation for anatomical structures. IEEE Trans. Med. Imaging 25(12), 1547–1564 (2006)CrossRef

53.

Yushkevich, P., Zhang, H., Simon, T., Gee, J.: Structure-specific statistical mapping of white matter tracts. NeuroImage 41(2), 448–461 (2008)CrossRef

Title: Geometric steerable medial maps
Authors: Sergio Vera
Debora Gil
Agnés Borràs
Marius George Linguraru
Miguel Angel González Ballester
Publication date: 01-08-2013
Publisher: Springer Berlin Heidelberg
Published in: Machine Vision and Applications / Issue 6/2013
Print ISSN: 0932-8092
Electronic ISSN: 1432-1769
DOI: https://doi.org/10.1007/s00138-013-0490-4

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