Abstract
We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both necessary and natural to employ spheres as their natural domains. We develop an automatic and efficient algorithm, which transforms a brain surface to a single spherical spline whose maximal error deviation from the original data is less than the user-specified tolerance. Compared to the discrete mesh-based representation, our spherical spline offers a concise (low storage requirement) digital form with high continuity (C n − − 1 continuity for a degree n spherical spline). Furthermore, this representation enables the accurate evaluation of differential properties, such as curvature, principal direction, and geodesic, without the need for any numerical approximations. Thus, certain shape analysis procedures, such as segmentation, gyri and sulci tracing, and 3D shape matching, can be carried out both robustly and accurately. We conduct several experiments in order to demonstrate the efficacy of our approach for the quantitative measurement and analysis of brain surfaces.
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References
Avants, B.B., Gee, J.C.: The shape operator for differential analysis of images. In: IPMI, pp. 101–113 (2003)
Cachia, A., Mangin, J.-F., Rivière, D., Boddaert, N., Andrade, A., Kherif, F., Sonigo, P., Papadopoulos-Orfanos, D., Zilbovicius, M., Poline, J.-B., Bloch, I., Brunelle, F., Régis, J.: A mean curvature based primal sketch to study the cortical folding process from antenatal to adult brain. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 897–904. Springer, Heidelberg (2001)
Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yau, S.T.: Genus zero surface conformal mapping and its application to brain surface mapping. In: IPMI, pp. 172–184 (2003)
Gu, X., Vemuri, B.C.: Matching 3d shapes using 2d conformal representations. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 771–780. Springer, Heidelberg (2004)
Tao, X., Han, X., Rettmann, M.E., Prince, J.L., Davatzikos, C.: Statistical study on cortical sulci of human brains. In: IPMI, pp. 475–487 (2001)
Tao, X., Prince, J.L., Davatzikos, C.: An automated method for finding curves of sulcal fundi on human cortical surfaces. In: ISBI, pp. 1271–1274 (2004)
Thompson, P.M., Toga, A.W.: A surface-based technique for warping 3-dimensional images of the brain. IEEE Trans. Medical Images 15, 402–417 (1996)
Thompson, P.M., Mega, M.S., Vidal, C., Rapoport, J.L., Toga, A.W.: Detecting disease-specific patterns of brain structure using cortical pattern matching and a population-based probabilistic brain atlas. In: IPMI, pp. 488–501 (2001)
Pfeifle, R., Seidel, H.P.: Spherical triangular b-splines with application to data fitting. Comput. Graph. Forum 14, 89–96 (1995)
He, Y., Gu, X., Qin, H.: Fairing triangular B-splines of arbitrary topology. In: Proceedings of Pacific Graphics 2005 (2005) (to appear)
Seidel, H.P.: Polar forms and triangular B-spline surfaces. In: Du, D.Z., Hwang, F. (eds.) Euclidean Geometry and Computers, 2nd edn., pp. 235–286. World Scientific Publishing Co., Singapore (1994)
Gormaz, R.: B-spline knot-line elimination and Bézier continuity conditions. In: Curves and surfaces in geometric design, pp. 209–216. A.K. Peters, Wellesley (1994)
Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: VisMath 2002 (2002)
Taubin, G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. In: ICCV, pp. 902–907 (1995)
Goldfeather, J., Interrante, V.: A novel cubic-order algorithm for approximating principal direction vectors. ACM Trans. Graph. 23, 45–63 (2004)
Rusinkiewicz, S.: Estimating curvatures and their derivatives on triangle meshes. In: 3DPVT, pp. 486–493 (2004)
Surazhsky, T., Magid, E., Soldea, O., Elber, G., Rivlin, E.: A comparison of gaussian and mean curvatures estimation methods on triangular meshes. In: ICRA, pp. 1021–1026 (2003)
Theisel, H., Rössl, C., Zayer, R., Seidel, H.P.: Normal based estimation of the curvature tensor for triangular meshes. In: Pacific Conference on Computer Graphics and Applications, pp. 288–297 (2004)
Belyaev, A.G., Pasko, A.A., Kunii, T.L.: Ridges and ravines on implicit surfaces. In: Computer Graphics International, pp. 530–535 (1998)
Ohtake, Y., Belyaev, A.G., Seidel, H.P.: Ridge-valley lines on meshes via implicit surface fitting. ACM Trans. Graph. 23, 609–612 (2004)
Thompson, P.M., Toga, A.W.: A framework for computational anatomy. Computing and Visualization in Science 5, 1–12 (2002)
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He, Y., Li, X., Gu, X., Qin, H. (2005). Brain Image Analysis Using Spherical Splines. 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_41
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DOI: https://doi.org/10.1007/11585978_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30287-2
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