Abstract
Here we introduce a novel multi-scale heat kernel based regional shape statistical approach that may improve statistical power on the structural analysis. The mechanism of this analysis is driven by the graph spectrum and the heat kernel theory, to capture the volumetric geometry information in the constructed tetrahedral mesh. In order to capture profound volumetric changes, we first use the volumetric Laplace-Beltrami operator to determine the point pair correspondence between two boundary surfaces by computing the streamline in the tetrahedral mesh. Secondly, we propose a multi-scale volumetric morphology signature to describe the transition probability by random walk between the point pairs, which reflects the inherent geometric characteristics. Thirdly, a point distribution model is applied to reduce the dimensionality of the volumetric morphology signatures and generate the internal structure features. The multi-scale and physics based internal structure features may bring stronger statistical power than other traditional methods for volumetric morphology analysis. To validate our method, we apply support vector machine to classify synthetic data and brain MR images. In our experiments, the proposed work outperformed FreeSurfer thickness features in Alzheimer’s disease patient and normal control subject classification analysis.
Chapter PDF
Similar content being viewed by others
Keywords
References
Jones, S.E., Buchbinder, B.R., Aharon, I.: Three-dimensional mapping of cortical thickness using Laplace’s equation. Hum. Brain Mapp. 11(1), 12–32 (2000)
Fischl, B., Dale, A.M.: Measuring the thickness of the human cerebral cortex from magnetic resonance images. Proc. Natl. Acad. Sci. U.S.A. 97(20), 11050–11055 (2000)
Raviv, D., Bronstein, M.M., Bronstein, A.M., Kimmel, R.: Volumetric heat kernel signatures. In: Proc. Intl. Workshop on 3D Object Retrieval (3DOR), pp. 39–44. ACM Multimedia (2010)
Castellani, U., Mirtuono, P., Murino, V., Bellani, M., Rambaldelli, G., Tansella, M., Brambilla, P.: A new shape diffusion descriptor for brain classification. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011, Part II. LNCS, vol. 6892, pp. 426–433. Springer, Heidelberg (2011)
Wang, G., Zhang, X., Su, Q., Shi, J., Caselli, R.J., Wang, Y.: A novel cortical thickness estimation method based on volumetric Laplace-Beltrami operator and heat kernel. Med. Image Anal. 22(1), 1–20 (2015)
Coifman, R.R., Lafon, S., Lee, A.B., Maggioni, M., Nadler, B., Warner, F., Zucker, S.W.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods. Proc. Natl. Acad. Sci. U.S.A. 102(21), 7432–7437 (2005)
Chung, M.K., Dalton, K.M., Shen, L., Evans, A.C., Davidson, R.J.: Weighted Fourier representation and its application to quantifying the amount of gray matter. IEEE Transactions on Medical Imaging 26, 566–581 (2007)
Shen, L., Ford, J., Makedon, F., Saykin, A.: A surface-based approach for classification of 3D neuroanatomic structures. Intelligent Data Analysis 8, 519–542 (2004)
Mueller, S.G., Weiner, M.W., Thal, L.J., Petersen, R.C., Jack, C., Jagust, W., Trojanowski, J.Q., Toga, A.W., Beckett, L.: The Alzheimer’s disease neuroimaging initiative. Neuroimaging Clin. N. Am. 15(4), 869–877 (2005)
Fischl, B., Sereno, M.I., Dale, A.M.: Cortical surface-based analysis. II: Inflation, flattening, and a surface-based coordinate system. Neuroimage 9(2), 195–207 (1999)
Lederman, C., Joshi, A., Dinov, I., Vese, L., Toga, A., Van Horn, J.D.: The generation of tetrahedral mesh models for neuroanatomical MRI. Neuroimage 55(1), 153–164 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Wang, G., Wang, Y. (2015). Multi-scale Heat Kernel Based Volumetric Morphology Signature. In: Navab, N., Hornegger, J., Wells, W., Frangi, A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015. MICCAI 2015. Lecture Notes in Computer Science(), vol 9351. Springer, Cham. https://doi.org/10.1007/978-3-319-24574-4_90
Download citation
DOI: https://doi.org/10.1007/978-3-319-24574-4_90
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24573-7
Online ISBN: 978-3-319-24574-4
eBook Packages: Computer ScienceComputer Science (R0)