Abstract
Existing approaches to computational anatomy assume that a perfectly conforming diffeomorphism applied to an anatomy of interest captures its morphological characteristics relative to a template. However, biological variability renders this task extremely difficult, if possible at all in many cases. Consequently, the information not reflected by the transformation, is lost permanently from subsequent analysis. We establish that this residual information is highly significant for characterizing subtle morphological variations and is complementary to the transformation. The amount of residual, in turn, depends on transformation parameters, such as its degree of regularization as well as on the template. We, therefore, present a methodology that measures morphological characteristics via a lossless morphological descriptor, based on both the residual and the transformation. Since there are infinitely many [transformation, residual] pairs that reconstruct a given anatomy, which collectively form a nonlinear manifold embedded in a high-dimensional space, we treat them as members of an Anatomical Equivalence Class (AEC). A unique and optimal representation, according to a certain criterion, of each individual anatomy is then selected from the corresponding AEC, by solving an optimization problem. This process effectively determines the optimal template and transformation parameters for each individual anatomy, and removes respective confounding variation in the data. Based on statistical tests on synthetic 2D images and real 3D brain scans with simulated atrophy, we show that this approach provides significant improvement over descriptors based solely on a transformation, in addition to being nearly independent of the choice of the template.
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References
Christensen, G., Rabbit, R., Miller, M.: A deformable neuroanatomy textbook based on viscous fluid mechanics. In: Proc. CISS’93 1993, pp. 211–216 (1993)
Miller, M., Banerjee, A., et al.: Statistical methods in computational anatomy. Statistical Methods in Medical Research 6, 267–299 1, 2 (1997)
Miller, M., Younes, L.: Group actions, homeomorphisms, and matching: a general framework. International Journal of Computer Vision 41(1), 61–84, 1 (2001)
Ashburner, J., Friston, K.: Nonlinear spatial normalization using basis functions. Human Brain Mapping 7(4), 254–266, 1 (1999)
Shen, D., Davatzikos, C.: HAMMER: Hierarchical attribute matching mechanism for elastic registration. IEEE TMI 21(11), 1421–1439 1,3 (2002)
Davatzikos, C., et al.: A computerized approach for morphological analysis of the corpus callosum. Journal of Comp. Assisted Tomography 20(1), 88–97 1, 2 (1996)
Ashburner, J., et al.: Identifying global anatomical differences: deformation-based morphometry. Human Brain Mapping 6(6), 348–357 1, 2 (1998)
Chung, M., Worsley, K., et al.: A unified statistical approach to deformation-based morphometry. NeuroImage 14(3), 595–600 1, 2 (2001)
Ashburner, J., Friston, K.J.: Voxel-based morphometry – the methods. NeuroImage 11(6), 805–821 1, 2 (2000)
Davatzikos, C., Genc, A., Xu, D., Resnick, S.: Voxel-based morphometry using RAVENS maps: methods and validation using simulated longitudinal atrophy. Neuroimage 14, 1361–1369 1,2,5 (2001)
Chetelat, G., et al.: Mapping gray matter loss with voxel-based morphometry in mild cognitive impairment. Neuroreport 13(15), 1939–1943 1, 2 (2002)
Thompson, P., et al.: Growth patterns in the developing human brain detected using continuum-mechanical tensor mapping. Nature 404(6774), 190–193 1,2 (2000)
Leow, A., Klunder, A., et al.: Longitudinal stability of mri for mapping brain change using tensor-based morphometry. Neuroimage 31(2), 627–640 1,2 (2006)
Joshi, S.: Large deformation diffeomorphisms and Gaussian random fields for statistical characterization of brain sub-manifolds. PhD thesis, Washington University, St. Louis 2 (1998)
Makrogiannis, S., et al.: Anatomical equivalence class: A computational anatomy framework using a lossless shape descriptor. IEEE TMI (Accepted) 5
Karaçhali, B., Davatzikos, C.: Simulation of tissue atrophy using a topology preserving transformation model. IEEE TMI 25(5), 649–652 9 (2006)
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Baloch, S., Verma, R., Davatzikos, C. (2007). An Anatomical Equivalence Class Based Joint Transformation-Residual Descriptor for Morphological Analysis. In: Karssemeijer, N., Lelieveldt, B. (eds) Information Processing in Medical Imaging. IPMI 2007. Lecture Notes in Computer Science, vol 4584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73273-0_49
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DOI: https://doi.org/10.1007/978-3-540-73273-0_49
Publisher Name: Springer, Berlin, Heidelberg
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