Abstract
This paper proposes a novel formulation to model and analyze the statistical characteristics of some types of segmentation problems that are based on combining label maps / templates / atlases. Such segmentation-by-example approaches are quite powerful on their own for several clinical applications and they provide prior information, through spatial context, when combined with intensity-based segmentation methods. The proposed formulation models a class of multiatlas segmentation problems as nonparametric regression problems in the high-dimensional space of images. The paper presents a systematic analysis of the nonparametric estimation’s convergence behavior (i.e. characterizing segmentation error as a function of the size of the multiatlas database) and shows that it has a specific analytic form involving several parameters that are fundamental to the specific segmentation problem (i.e. chosen anatomical structure, imaging modality, registration method, label-fusion algorithm, etc.). We describe how to estimate these parameters and show that several brain anatomical structures exhibit the trends determined analytically. The proposed framework also provides per-voxel confidence measures for the segmentation. We show that the segmentation error for large database sizes can be predicted using small-sized databases. Thus, small databases can be exploited to predict the database sizes required (“how many templates”) to achieve “good” segmentations having errors lower than a specified tolerance. Such cost-benefit analysis is crucial for designing and deploying multiatlas segmentation systems.
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References
Aljabar, P., Heckemann, R., Hammers, A., Hajnal, J., Rueckert, D.: Multi-atlas based segmentation of brain images: Atlas selection and its effect on accuracy. NeuroImage 46(3), 726–738 (2009)
Artaechevarria, X., Munoz-Barrutia, A., Ortiz-de-Solorzano, C.: Combination strategies in multi-atlas image segmentation: application to brain MR data. IEEE Trans. Med. Imaging 28(8), 1266–1277 (2009)
Carter, K., Raich, R., Hero, A.: On local intrinsic dimension estimation and its applications. IEEE Trans. Signal Proc. 58(2), 650–663 (2010)
Commonwick, O., Warfield, S.: Estimation of inferential uncertainty in assessing expert segmentation performance from STAPLE. IEEE Trans. Med. Imag. 29(3), 771–780 (2010)
Depa, M., Sabuncu, M.R., Holmvang, G., Nezafat, R., Schmidt, E.J., Golland, P.: Robust atlas-based segmentation of highly variable anatomy: Left atrium segmentation. In: MICCAI Workshop Stat. Atlases Comp. Models Heart, pp. 1–8 (2010)
Felsberg, M., Kalkan, S., Krueger, N.: Continuous dimensionality characterization of image structures. Image and Vision Computing 27(6), 628–636 (2009)
Ha, L., Kruger, J., Fletcher, T., Joshi, S., Silva, C.: Fast parallel unbiased diffeomorphic atlas construction on multi-graphics processing units. In: Euro. Symp. Parallel Graph. Vis., pp. 65–72 (2009)
Hardle, W.: Applied Nonparametric Regression. Cambridge Univ. Press (1990)
Hein, M., Audibert, J.Y.: Intrinsic dimensionality estimation of submanifolds. In: Rd. In: Int. Conf. Mach. Learn., pp. 289–296 (2005)
Isgum, I., Staring, M., Rutten, A., Prokop, M., Viergever, M., Ginneken, B.: Multi-atlas-based segmentation with local decision fusion - application to cardiac and aortic segmentation in CT scans. IEEE Trans. Med. Imag. 28(7), 1000–1010 (2009)
Lotjonen, J., Wolz, R., Koikkalainen, J., Thurfjell, L., Waldemar, G., Soininen, H., Rueckert, D.: ADNI: Fast and robust multi-atlas segmentation of brain magnetic resonance images. NeuroImage 49(3), 2352–2365 (2010)
Mack, Y.P.: Local properties of k-NN regression estimates. SIAM J. Alg. Disc. Meth. 2(3), 311–323 (1981)
Sabuncu, M., Yeo, B., van Leemput, K., Fischl, B., Golland, P.: A generative model for image segmentation based on label fusion. IEEE Trans. Med. Imaging 29(10), 1714–1729 (2010)
Takezawa, K.: Introduction to Nonparametric Regression. Wiley (2005)
Wang, H., Suh, J.W., Das, S., Pluta, J., Altinay, M., Yushkevich, P.: Regression-based label fusion for multi-atlas segmentation. IEEE Conf. Comp. Vis. Pattern Recog. 1, 1113–1120 (2011)
Wang, H., Suh, J.W., Pluta, J., Altinay, M., Yushkevich, P.: Optimal weights for multi-atlas label fusion. In: Int. Conf. Info. Proc. Med. Imag., pp. 73–84 (2011)
Warfield, S., Zou, K., Wells, W.: Validation of image segmentation by estimating rater bias and variance. Phil. Trans. Roy. Soc. 366(1874), 2361–2375 (2008)
Zhu, P., Awate, S.P., Gerber, S., Whitaker, R.: Fast Shape-Based Nearest-Neighbor Search for Brain MRIs Using Hierarchical Feature Matching. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 484–491. Springer, Heidelberg (2011)
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Awate, S.P., Zhu, P., Whitaker, R.T. (2012). How Many Templates Does It Take for a Good Segmentation?: Error Analysis in Multiatlas Segmentation as a Function of Database Size. In: Yap, PT., Liu, T., Shen, D., Westin, CF., Shen, L. (eds) Multimodal Brain Image Analysis. MBIA 2012. Lecture Notes in Computer Science, vol 7509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33530-3_9
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DOI: https://doi.org/10.1007/978-3-642-33530-3_9
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