在這篇論文中我們提出了一個新穎的3-D物體重建演算法用於相機前加裝雙稜鏡所拍攝的影像。相機透過雙稜鏡所拍攝的影像分別成像於相片中的左半部及右半部。因此可將一張圖片上的左、右半部視為兩不同視角所取得的影像。此原理為物體通過左右對稱的稜鏡經過兩次折射後分別投影到相機中，本篇論文將根據此現象找出重構演算法。此演算法包括兩部分，第一部分是根據稜鏡所拍攝的影像找出左右半部的對應點。第二部分則是根據前者找到的對應點做3D空間點的重構。
在第一部分找對應點所會遇到的困難是透過稜鏡取得的影像有色散和變形的問題，針對這兩現象我們利用了CCH(Contrast Context Histogram)演算法，準確的找出左、右半部的對應點。第二部分將利用影像平面的逆向投影(back project)向量，模擬通過稜鏡兩次折射，進而推導出空間點。

In this paper, we propose a novel algorithm to reconstruct 3-D models using a double prism placed in front of a camera. The image of the object captured by the camera is divided into left and right halves, which contain two refraction sides of the double prism. These two halves can be considered as a pair of stereo images and are used to reconstruct the 3-D model of the object. As shown in the experiment, through the image of the double prism, we can accurately reconstruct the 3-D model of the captured objects.

[1] R. Hartley, and A. Zisserman, Multiple View Geometry in Computer Vision, Second Ed. Cambridge University Press, 2004.
[2] T. Kreis, “Digital Holography Methods in 3D-TV,” in Proc. of IEEE, 3D-TV Conference, pp. 1-4, 2007.
[3] Y. Nishimoto and Y. Shirai, “A feature-based stereo model using small disparities,” IEEE Computer Vision and Pattern Recognition, pp. 192–196, 1987.
[4] A. Goshtasby, and W. A. Gruver, “Design of a Single-lens Stereo Camera System,” Pattern Recognition, vol. 26, no. 6, pp. 923-936, 1993.
[5] S. A. Nene, and S. K. Nayar, “Stereo with Mirrors,” in Proc. of the International Conference on Computer Vision, pp. 1087-1094, 1998.
[6] Z. Y. Zhang, and H. T. Tsui, “3D Reconstruction from a Single View of an Object and Its Image in a Plane Mirror,” in Proc. of Fourteenth International Conference on Pattern Recognition, vol. 2, pp. 1174-1176, 1998.
[7] J. Gluckman, and S. K. Nayar “Planar Catadioptric Stereo: Geometry and Calibration,” in Proc. of IEEE Computer Vision and Pattern Recognition, vol. 1, pp. 22-28, 1999.
[8] H.-H.P. Wu, “Rectification of Stereoscopic Video for Planar Catadioptric Stereo Systems,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 17, no.6, pp.686-698, 2007.
[9] T.-P. Pachidis and J.-N. Lygouras, “Pseudo-Stereo Vision System: A Detailed Study” Journal of Intelligent and Robotic Systems, vol. 42, pp. 135–167, 2005.
[10] J. Gluckman and S.-K. Nayar, “Rectified Catadioptric Stereo Sensors,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 2, pp. 224-236, 2002.
[11] M. Inaba, T.Hara, and H. Inoue, “A Stereo Viewer Based on a Single Camera with View-Control Mechanisms,” IEE/RSJ International Conference on Intelligent Robots and Systems, 1993.
[12] G. Somanath, M. V. Rohith, and C. Kambhamettu, “Single Camera Stereo System Using Prism and Mirrors,” in Proc. of the 6th International Conference on Advances in Visual Computing, vol. 2, pp. 170-181, 2010.
[13] L. Duvieubourg, S. Ambellouis, and F. Cabestaing, “Single-Camera Stereovision Setup with Orientable Optical Axes.” Computational Imaging and Vision, vol. 32, pp. 173-178, 2006.
[14] T. Lu, and T.-H. Chao, “A Single-camera System Captures High-resolution 3D Images in One Shot,” Electronic Imaging and Signal Processing, pp. 1-3, 2006.
[15] Y. Xiao, and K. B. Lim, “A Prism-based Single-lens Stereovision System: From Trinocular to Multi-ocular,” Image and Vision Computing, vol. 25, no. 11, pp. 1725-1736, 2007.
[16] S. Yi and N. Ahuja, “An Omnidirectional Stereo Vision System Using a Single Camera,” in Proc. of The 18th International Conference on Pattern Recognition, vol. 4, pp. 861 - 865, 2006.
[17] D. Lee, and I. Kweon, “A Novel Stereo Camera System by a Biprism,” IEEE Transactions on Robotics and Automation, vol. 16, no. 5, pp. 528-541, 2000.
[18] Lei Li, Allen Y. Yi , “Design and fabrication of a freeform prism array for 3D microscopy,” Optical Society of America, 2010
[19] C.-Y. Chen, and T.-T. Yang, and W.-S. Sun, “Optics System Design Applying a Micro-prism Array of a Single Lens Stereo Image Pair,” Optical Express, vol. 16, no. 20, pp. 15495-15505, 2008.
[20] Z. Zhang, “A Flexible New Technique for Camera Calibration,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1330-1334, 2000.
[21] Y. Boykov, O. Veksler, and R. Zabih, “Fast Approximate Energy Minimization via Graph Cuts,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 11, pp. 1222-1239, Nov. 2001.
[22] H.H. Baker and T.O. Binford, “Depth from Edge and IntensityBased Stereo,” Proc. Int’l Joint Conf. Artificial Intelligence, vol. 2,pp. 631-636, Aug. 1981.
[23] C. Strecha, R. Fransens, and L. Van Gool, “Combined Depth and Outlier Estimation in Multi-View Stereo,” Proc. IEEE Conf. on Computer Vision and Pattern Recognition, 2006.
[24] D. G. Lowe, “Distinctive Image Features from Scale Invariant Keypoints,” International Journal of Computer Vision, vol. 20, no. 2, pp. 91-110, 2004.
[25] K. Mikolajczyk and C. Schmid, “A Performance Evaluation of Local Descriptors,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 10, pp. 1615-1630, Oct. 2005.
[26] E. Tola, V. Lepetit, and P. Fua, “DAISY: An Efficient Dense Descriptor Applied to Wide-Baseline Stereo,” IEEE Transactions on Pattern Analysis and Machine intelligence, vol. 32, no. 5, pp. 818-830, May 2010.
[27] C.-R. Huang, C.-S. Chen, and P.-C. Chung, “Contrast Context Histogram - An Efficient Discriminating Local Descriptor for Object Recognition and Image Matching,” Pattern Recognition, vol.41, no.10, pp. 3071-3077, 2008.
[28] F. Kahl and R. Hartley, “Multiple-View Geometry under the L∞-Norm,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 30, no. 9, pp. 1603-1617, 2008.
[29] M. S. Lobo, L. Vandenberghe, S. P. Boyd, and H. Lebret, “Applications of Second-Order Cone Programming,” Linear Algebra and Its Applications, vol. 284, pp. 193-228, 1998.
[30] J.F. Sturm, “Using SeDuMi 1.02, a MATLAB Toolbox for Optimization over Symmetric Cones,” Optimization Methods and Software, vols. 11-12, pp. 625-653, 1999.