一直以來，人類腦部的研究一直是個熱門的研究領域，科學家試圖找出人腦中神經網路與腦部疾病的關係。果蠅非常廣泛的被用於腦部研究領域中，因為幾個非常好的特性像是與人類一樣具有學習與記憶的能力、易於繁殖而且相對於人腦較為簡單的結構。
在研究果蠅腦部機制的過程中，常常需要比較不同果蠅個體間腦部結構或神經網路的差異。然而，不同個體間的變異容易造成分析的困難以及誤差，所以在觀察不同果蠅腦部實驗時，會先將欲比較的腦部資料做三維的對位處理。對位處理的過程包含將整個果蠅腦的三維資料依照指定的特徵點做移動、縮放以及變形處理，使其在對位過後特徵點能夠落在同一空間座標上。傳統的三維腦部對位演算法大多是考慮特徵點的資訊，進而對整個三維腦部資料做變形，造成果蠅腦殼的形狀被嚴重的扭曲。如果為了避免腦部外殼形狀的嚴重變形以及提升對位後的精準度，則必須將三維腦部資料中每一張掃描的圖的外殼形狀圈出並作為特徵點一併加入對位演算法中以確保腦部形狀的完整。但是這麼做會增加所需要的特徵點擷取及配對工作以及大大的提升三維對位演算法所需的時間。所以，在這篇論文中我們提供了一個適用於果蠅腦部表面模型的對位方法，可以依照表面模型提供的資訊將其中一個果蠅腦表面變形到與另一果蠅腦近乎一模一樣。在經過我們方法的腦部表面對位完成以後，就可以在盡量保留腦殼表面資訊的前提下，只進行腦內對位的處裡，將可以大大的降低三維腦部對位所需要的處理量以及降低腦殼嚴重變形的程度。此外，因為腦殼表面已對齊良好，所以也會增加對位後的精確度。在我們的演算法中，給定兩個果蠅腦部以及使用者欲對齊的表面區域資訊以後，其中一腦部模型將會變形至與目標腦相同之形狀，而且確保指定區域的良好對齊，過程中不用額外的人為調控參數以及修正，處理完畢以後會得到兩個形狀近似且特徵點對齊之果蠅腦部模型。

Research on structures and functions in human brains has long been popular. Scientists are trying to find out connections between neural networks in brains and the related diseases such as Alzheimer's or Parkinson's disease. Drosophila, also called fruit fly informally, is widely used in brain research due to some appealing properties such as its similarities in some brain functions like memorizing and learning things, simplicity compared to human brains and easily culturing characteristic. When analyzing brains from different flies, one should first align the significant organs or neurons inside the brains in order to eliminate variations between different flies, making the analysis easier and more robust. Thus, a volumetric registration process is required to match two volume data of brains. When volumetric registration is applied, we need to specify features, those points should be aligned after the procedure, and deform the brain volume into the target one according to these pre-specified features. In practice, large numbers of feature points are necessitated to obtain a precise registration result. However, great number of features involved implying more time is needed for the registration process, especially for 3D volume data. Notice that there is a great amount of features allocated on the boundary of brain slices, that is, the surface of the volume data. We develop a surface registration framework for drosophila brains which can first align the surfaces of brains, thus reducing the number of features required for the following volumetric registration process. Moreover, combined with our surface registration approach, performance of volumetric registration can be greatly improved since traditional volumetric registration process does not take surfaces into account.

[1] M. Alexa, “Recent Advances in Mesh Morphing”, Computer Graphics Forum 2002, vol. 21, issue 2, page 173-198

[2] P.J. Besl, “A Method for Registration of 3-D Shapes”, IEEE Transactions on Pattern analysis and Machine Intelligence, vol. 14, no. 2, 1992

[3] A.A. Joshi, D.W. Shattuck, P.M. Thompson, and R.M. Leahy, “Cortical surface parameterization by p-harmonic energy minimization”, IEEE Biomedical Imaging: Nano to Macro, 2004

[4] K. Rohr, H.S. Stiehl, R. Sprengel, T.M. Buzug, J. Weese, and M.H. Kuhn, “Landmark-based elastic registration using approximating thin-plate splines”, IEEE Transactions on Medical Imaging, vol. 20, no. 6, page 526-534, 2001

[5] F.L. Bookstein, “Principle Warps: Thin-plate splines and the decomposition of deformations”, IEEE Transactions on Pattern analysis and Machine Intelligence, vol. 11, no. 6, 1989

[6] B. Fischl, M.I. Sereno, R.B.H Tootell, and A.M. Dale, “High-resolution intersubject averaging and a coordinate system for the cortical surface”, Human Brain Mapping 8, page 272-284, 1999

[7] A. Joshi, R. Leahy, A. Toga, and D. Shattuck, “A framework for brain registration via simultaneous surface and volume flow”, Information Processing in Medical Imaging, vol.5636, page 576-588, 2009

[8] A. Klein, S.S. Ghosh, B. Avants, B.T.T Yeo, B. Fischl, B. Ardekani, J.C. Gee, J.J. Mann, and R.V. Parsey, “Evaluation of volume-based and surface-based brain image registration methods” NeuroImage, vol, 51, page 214-220, 2010

[9] A. Joshi, D. Shattuck, P. Thompson, and R. Leahy, “Brain image registration using cortically constrained harmonic mappings”, Information Processing in Medical Imaging, vol. 4584, page 359-371, 2007

[10] A.A. Joshi, D.W. Shattuck, P.M. Thompson, and R.M. Leahy, “Surface-constrained volumetric brain registration using harmonic mappings”, IEEE Transaction on Medical Imaging, vol. 26, no. 12, 2007

[11] N. Lepore, A.A. Joshi, R.M. Leahy, C.Brun, Y.Y. Chou, X. Pennec, A.D. Lee, M. Barysheva, G.I. de Zubicaray, M.J. Wright, K.L. McMahon, A.W. Toga, P.M. Thompson, “A new combined surface and volume registration”, SPIE Medical Imaging, 2010

[12] K. S. Arun, T.S. Huang, and S.D. Blostein, “Least-Squares Fitting of Two 3-D Point Sets”, IEEE Transactions on Pattern Analysis and Machine Intelegence, vol. PAMI-9, no. 5, 1987

[13] D. Rueckert, L. I. Sonoda, C. Hayes, D. L. G. Hill, M. O. Leach, “Nonrigid Registration Using Free-Form Deformations: Application to Breast MR Images”, IEEE Transaction on Medical Imaging, vol. 18, no. 8, 1999

[14] R.F. Tobler, S. Maierhofer, “A mesh data structure for rendering and subdivision”, In Proceedings of WSCG (International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision), page 157–162, 2006

[15] G. E. Christensen, S. C. Joshi, and M. I. Miller, “Volumetric transformation of brain anatomy,” IEEE Transactions on Medical Imaging., vol. 16, no. 6, page 864–877, 1997

[16] P. M. Thompson and A. W. Toga, “A surface-based technique for warping 3-dimensional brain,” IEEE Transactions on Medical Imaging., vol. 15, no. 4, page 1–16, 1996.

[17] A. W. F. LEE, W. Sweldens, P. Schroder, L. Cowsar , and D. Dobkin, “MAPS: Multiresolution Adaptive Parameterization of Surfaces”, Proceedings of SIGGRAPH, page. 95–104, 1998

[18] J. Warren, H. Weimer, “Subdivision Methods for Geometric Design”, Academic Press,2002

[19] E. J. Stollnitz, T. D. Derose, D. H. Salesin, “Wavelets for Computer Graphics”, Morgan Kaufmann Publishers, 1996

[20] Loop, “Smooth subdivision surfaces based on triangles”, Master’s thesis, Department of Mathematics, University of Utah, 1987

[21] A. Zaharescu, E. Boyer, Kiran. Varanasi and R. Horaud, P. Team, “Surface Feature Detection and Description with Applications to Mesh Matching”, Computer Vision and Pattern Recognition, 2009.

[22] R. Gal and D. Cohen-Or, “Salient Geometric Features for Partial Shape Matching and Similarity”, ACM Transactions on Graphics (TOG), 2006

[23] P. Cignoni, C. Rocchini and R. Scopigno, “Metro: measuring error on simplified surfaces”, Computer Graphics Forum, 1998