Abstract
Shapes of biological objects, such as anatomical parts, have been studied intensely in recent years. An emerging need is to model and analyze changes in shapes of biological objects during, for example, growths of organisms. A recent paper by Grenander et al. [5] introduced a mathematical model, called GRID, for decomposing growth induced diffeomorphism into smaller, local deformations. The basic idea is to place focal points of local growth, called seeds, according to a spatial process on a time-varying coordinate system, and to deform a small neighborhood around them using radial deformation functions (RDFs). In order to estimate these variables – seed placements and RDFS – we first estimate optimal deformation from magnetic resonance image data, and then utilize an iterative solution to reach maximum-likelihood estimates. We demonstrate this approach using MRI images of human brain growth.
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References
Bookstein, F.L.: Size and shape spaces for landmark data in two dimensions. Statistical Science 1, 181–242 (1986)
Christensen, G.E., Rabbitt, R.D., Miller, M.I.: A deformable neuroanatomy textbook based on viscous fluid mechanics. In: Prince, J., Runolfsson, T. (eds.) Proceedings of the Twenty-Seventh Annual Conference on Information Sciences and Systems, Baltimore, Maryland, March 24-26, pp. 211–216. Department of Electrical Engineering, The Johns Hopkins University (1993)
Grenander, U., Miller, M.I.: Representations of knowledge in complex systems. Journal of the Royal Statistical Society 56(3) (1994)
Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics LVI(4), 617–694 (1998)
Grenander, U., Srivastava, A., Saini, S.: A pattern-theoretic characterization of biological growth. IEEE Transactions on Medical Imaging, in review (2005)
Khaneja, N., Miller, M.I., Grenander, U.: Dynamic programming generation of curves on brain surfaces. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(11), 1260–1264 (1998)
Kim, B., Boes, J.L., Frey, K.A., Meyer, C.R.: Mutual information for automated unwarping of rat brain autoradiographs. Neuroimage 5(1), 31–40 (1997)
Miller, M.I., Younes, L.: Group actions, homeomorphisms, and matching: A general framework. International Journal of Computer Vision 41(1/2), 61–84 (2002)
Miller, M.I., Christensen, G.E., Amit, Y., Grenander, U.: Mathematical textbook of deformable neuroanatomies. Proceedings of the National Academy of Science 90(24) (December 1993)
Sherratt, J.A., Chaplain, M.A.: A new mathematical models for avascular tumour growth. Journal of Mathematical Biology 43(4), 291–312 (2001)
Thompson, P.M., Toga, A.W.: A framework for computational anatomy. Computing and Visualization in Science 5, 13–34 (2002)
Trouve, A.: Diffemorphisms groups and pattern matching in image analysis. International Journal of Computer Vision 28(3), 213–221 (1998)
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Srivastava, A., Saini, S., Ding, Z., Grenander, U. (2005). Maximum-Likelihood Estimation of Biological Growth Variables. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2005. Lecture Notes in Computer Science, vol 3757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11585978_8
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DOI: https://doi.org/10.1007/11585978_8
Publisher Name: Springer, Berlin, Heidelberg
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