# 臺灣博碩士論文加值系統

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 所謂一張影像的「動態範圍」(Dynamic Range)，即是影像中可擷取的光線範圍，從最暗的陰影到最亮的高亮度區域。在傳統建構高動態範圍影像(High Dynamic Range Image)的方式有許多限制，除了需限制相機在拍攝場景時需固定之外，亦需假設景是固定不動的。本論文能在拍攝不同曝光值影像序列時，可以使用非固定式的相機(或攝影機)，且不需假設場景中的各項物體皆為靜止的情況下，依舊能進行相機反應曲線的校正。在拍攝場景中，使用強建式演算法(Robust Estimator)找到在兩張影像間之共平面的物體，估測出兩張影像之共平面的單應性矩陣，以協助我們找到大範圍對應點。再經由分析對應區塊的亮度資訊後，建立影像序列之間的亮度對應函式，進而可校正出相機反應曲線，而得到一高動態範圍影像。在本論文中探討因估算與應用單應性矩陣（Homography）時所造成的數值誤差和量化誤差。這些誤差在邊緣點(Edge)很容易影響計算BTF的結果，故可先預先排除之。本論文會呈現初步的實驗結果。關鍵字：單應性、高動態範圍影像、亮度轉換函數、數值誤差、量化誤差。
 The dynamic range of an image is the range between the maximum and minimum values of a physical measurement. Its definition depends on what the dynamic range refers to. Although there are lots of papers proposed for the high dynamic range images (HDRI), there are lots of limitations for producing the HDRI traditionally. The commonly-used limitation is to assume that both the camera and the scenes should be stationary.In this thesis, while the camera can be non-stationary, the radiometric response curve can be calibrated using a sequence of images in different exposure values. The robust estimator is used to find the coplanar objects in two images. Based on the found coplanar objects, the homography matrix can be estimated. Lots of corresponding point pairs can be obtained using the estimated homography matrix. The brightness transfer function can be obtained by using the corresponding point pairs within these two corresponding regions. Then, the radiometric response curve can be calibrated by using the brightness transfer function. Finally, the HDRI can be produced.In this thesis, the issue about the numerical error and quantization errors caused by estimating the homograhpy and using the homography will be discussed. Since there are the numerical error and quantization error, the edge points will affect the results for computing BTF. Some prelimiliary experimental results are shown in this thesis.Keyword：Homography, High dynamic range image, Brightness transfer function, Numerical error, Quantization error.
 誌 謝 I摘 要 IIABSTRACT III目 錄 V表 錄 VII圖 錄 VIII一、緒論 - 1 -1.1 研究背景與動機 - 1 -1.2 研究目的 - 2 -1.3 相關研究 - 3 -1.4 論文架構 - 5 -二、基本理論 - 6 -2.1單應性Homography - 6 -2.2影像的幾何轉換 - 8 -2.2.1座標轉換 - 8 -2.2.2像素值的內插 - 9 -三、高動態範圍影像 - 12 -3.1 高動態範圍影像High Dynamic Range Image - 12 -3.2 亮度對應函式 - 14 -(1) Comparagram - 14 -(2)亮度直方圖Brightness histogram - 16 -(3)單應性Homography - 19 -3.3利用多項式擬合BTF - 20 -3.4相機反應曲線Radiometric Response Function - 21 -四、誤差對估算BTF的影響 - 23 -五、實驗結果 - 27 -六、結論與未來工作 - 57 -參考文獻 - 58 -
 [1].Alasdair McAndrew. Introduction to Digital Image Processing with MATLAB, school of computer science and mathematics Victoria University. April 7, 2004.[2].M. J. Black, G. Sapiro, D. H. Marimont, and D. Heeger, “Robust anisotropic diffusion,” IEEE Transactions on Image Processing, 7, 421-432, 1998.[3].D. Barash, “A fundamental relationship between bilateral filtering, adaptive smoothing and nonlinear diffusion equation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24(6), pp. 844-850, 2002.[4].J. Cohen, C. Tchou, T. Hawkins, and P. Debevec, “Real-Time high dynamic range texture mapping,” in Rendering techniques, pp. 313-320, 2001.[5].P. Choudhury and J. Tumblin, “The Trilateral Filter for High Contrast Images and Meshes,” in Eurographics Symposium on Rendering, pp. 1-11. 2003[6].Paul E. Debevec and J. Malik. “Recovering High Dynamic Range Radiance Maps from Photographs,” In SIGGRAPH 97, pages 369-378, August 1997.[7].J. M. DiCarlo and B. A. Wandell, “Rendering high dynamic range images,” SPIE: Image Sensors, vol. 3965, pp. 392-401, 2000.[8].M. Grossberg and S. Nayar,”What can be Known about the Radiometric Response Function from Images? , ” Proc. ECCV’02. vol. 4, pp. 189-205, 2002.[9].R. Hartley, and A. Zisserman, Multiple view geometry in computer vision, Cambridge University Press: Cambridge, UK.[10].S.J. Kim, M. Pollefeys. “Radiometric Self-Alignment of Image Sequences,” Computer Vision and Pattern Recognition (CVPR), 2004.[11].G. W. Larson, “Overcoming Gamut and Dynamic Range limitations in Digital Images,” IS&T/SID Sixth Color Imaging Conference: Color Science, Systems and Applications; pp. 214-219, November 1998.[12].G. W. Larson, “The LogLuv Encoding for Full Gamut, High Dynamic Range Images,” Journal of Graphics Tools, 3(1):15-31, 1998.[13].S. Mann. “Comparametric equations with practical applications in quant graphic image processing,” IEEE Trans. Image Proc., 9(8):1389–1406, August 2000.[14].S. K. Nayar and T. Mitsunaga, “High dynamic range imaging: spatially varying pixel exposures,” in Proc. Computer Vision and Pattern Recognition (CVPR), pp. 473-479, 2000.[15].S.N.Pattanaik, J. A. Ferwerda, M. D. Fairchild, D.P. Greenberg. “A Multiscale Model of Adaptation and Spatial Vision for Realistic Image Display,” ACM SIGGRAPH pages 287--298, 1998.[16].E. Reinhard, M. Stark, P. Shirley and J. Ferwada, “Photographic tone reproduction for digital images,” ACM Transactions on Graphics, special issue on Proc. Of ACM SIGGRAPH 2002, San Antonio, Texas, vol. 21(3), pp. 267-276, 2002.[17].Tumblin and G. Turk, “LCIS: A boundary hierarchy for detail-preserving contrast reduction,” in Proc. SIGGRAPH 99, ACM SIGGRAPH, Los Angeles, California, Computer Graphics Proceedings, Annual Conference Series, pp. 83-90, 1999.[18].C.-Y. Tang. C.-Y. Tang, H.-L. Chou, Y.-L. Wu and Y.-H. Ding, Fast and Robust Algorithm Using Coplanar Constraints to Estimate Fundamental Matrices,”2006 IEEE International Conference on Systems, Man, and Cybernetics, Taiwan.[19].J. Tumblin, J. Hodgins, and b. Guenter. “Two methods for display of high contrast images,” ACM Transactions on Graphics, 18(1), January 1999.[20].J. Tumblin, and H. Rushmeier, “Tone reproduction for realistic images,” IEEE Computer Graphics and Applications, vol. 13(6), pp. 42-48, 1993.[21].G. Ward Larson, H. Rushmeier, and C. Piatko. “A visibility matching tone reproduction operator for high dynamic range scenes,” IEEE Transactions on Visualization and Computer Graphics, 3(4):291-306, October-December 1997.
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 1 使用單應性做基於影像的繪圖 2 高動態範圍影像合成之研究 3 基於區塊的亮度特性及熵值合併多張不同曝光值影像之高動態範圍影像生成法 4 克服手振因素之清晰高動態範圍影像合成 5 高動態範圍影像以對數為基礎之適應性色調再生演算法 6 基於Homography的自動車定位研究 7 用於多曝光值高動態範圍影像合成法中具移動物件校正與殘影移除之演算法 8 延伸曝光曲線線性特性之調適性高動態範圍影像融合演算法 9 立體顯影之高動態範圍影像合成 10 高動態範圍影像轉換模式之比較研究 11 高動態範圍影像風格化演算法之研究 12 應用模擬退火法於限制性經費之車輛途程問題 13 使用曝光量測完成高動態範圍影像 14 可回復式灰階及高動態範圍影像資訊隱藏演算法之研究 15 應用支援向量機與基因演算法改進產品測試品質-以工業電腦產業為例

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