在生命科學或神經科學領域,科學家想要利用大腦研究來解開人類記憶和學習之謎。甚至用來解答帕金森氏症、阿茲海默症等等我們未知的大腦疾病如何形成。但是人類的大腦是由數十億個神經細胞相互連結所形成的超巨大神經網路架構，對我們現在的科技來說太過複雜，所以很難瞭解人的大腦是如何運作的。果蠅大腦在很多控制基因與運作機制跟人類頗為相似。因此，研究果蠅大腦在人類大腦的研究領域扮演極為重要的角色。
我們的影像是由生命科學系利用共軛焦顯微鏡所取得的影像切片。由於每隻果蠅的生長速度所形成的個體差異會令我們無法正確判斷出兩隻不同果蠅大腦影像的真實差異。所以必須將所有果蠅的大腦經過體積影像的對位把所有的影像都對到一個預先建立的標準腦上，藉由這樣才能看出每個果蠅之間的實際差異。
在這篇論文裡，我們設計了一個系統用來做影像對位的部分。我們使用薄板曲線對位的方式來完成此目標，由於薄板曲線對位有一些問題沒有考慮到，所以我們將其延伸成限制邊界的薄板曲線對位和近似的薄板曲線對位來解決這些問題。最後，我們使用方向性的中值濾波器來補因為對位所產生的黑洞。

As a noted topic of life science, brain research is aimed to solve how people learn and memorize. Brain research also helps us discover the cause of brain diseases such as Alzheimer's or Parkinson's disease. However, the brain of human is very complicated. It is connected between billions of neural cells to form a big neural network. For this reason, understanding the neural network of human’s brain is a difficult challenge. In Drosophila brain, it is discovered that several brain controlling genes are very similar to human’s, and so as how they function. Thus, Drosophila brain plays an important role for studying simple neural networks and can help us figure out such main functions as learning and memory.
In order to study the main structures and functions of Drosophilas brain, confocal microscope is used to image fluorescent brain slices. Due to the individual difference between the different Drosophilas, it is hard to know the actual difference between the different Drosophilas. Hence, we have to warp all the Drosophilas brain image to a standard one which we have created.
In our work, we design a system to warp the source image to the target one. We use thin-plate splines to build the deformation field. However, there are some drawbacks of this approach. We extend original thin-plate splines to approximating thin-plate splines and boundary-constrained thin-plate splines to solve these problems. Finally we use directional median filter to interpolate the result image after warping. The result from the system can mostly match to the target image.

[1] Anand A. Joshi, David W. Shattuck, Paul M. Thompson and Richard M. Leahy, “Surface-Constrained Volumetric Brain Registration Using Harmonic Mappings”, IEEE Transactions on Medical Imaging, 26, pp. 1657–1669, 2007

[2] Wells III, W. M., Viola, P. and Kikinis, R. “Multi-modal volume registration by maximization of mutual information.” In Medical Robotics and Computer Assisted Surgery, pp. 55–62.Wiley, New York, 1995

[3] J. Wang, T. Jiang, “Nonrigid registration of brain MRI using NURBS”, ParallelRecognit. Lett. 28 (2) 214–223, 2007

[4] H. Chui and A. Rangarajan. “A new point matching algorithm for non-rigid registration.” CVIU, 89:114–141, 2003

[5] Liu, T., Shen, D., Davatzikos, C. “Deformable registration of cortical structures via hybrid volumetric and surface warping”. Neuroimage 22 (4), 1790–1801, 2004

[6] Shen D, Davatzikos C “HAMMER: hierarchical attribute matching mechanism for elastic registration”. In: Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, pp 29–36. Kauai, Hawaii, December, 2001

[7] 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

[8] J. Duchon, “Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces,” R.A.I.R.O. Analyze Numérique, vol. 10, no. 12, pp. 5–12, 1976.

[9] G. Wahba, “Spline Models for Observational Data. Philadelphia”, PA: Soc. Ind. Appl. Math., 1990.

[10] Herve Lombaert, Farida Cheriet, “Geodesic Thin Plate Splines for Image Segmentation” , International Conference on Pattern Recognition, 2010

[11] 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

[12] Anat Levin, Dani Lischinski and Yair Weiss, “A Closed Form Solution to Natural Image Matting”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 2, 2008

[13] H. Noori and Saeid Saryazdi, “Image Inpainting Using Directional Median Filters”, International Conference on Computational Intelligence and Communication Networks, 2010