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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 趙鍵哲(Jen-Jer Jaw) | |
| dc.contributor.author | Cheng-Wei Chao | en |
| dc.contributor.author | 趙晟瑋 | zh_TW |
| dc.date.accessioned | 2022-11-25T05:33:48Z | - |
| dc.date.available | 2023-08-31 | |
| dc.date.copyright | 2021-11-11 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-08-26 | |
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Orthogonal splines based on B-splines - with applications to least squares, smoothing and regularisation problems, Numerical Algorithms, 5(1):25-40. Meijering, E. H. W., 2000. Spline interpolation in medical imaging: Comparison with other convolution-based approaches, Proceedings of 10th European Signal Processing Conference, Tampere, Finland, pp. 1-8. Panda, R. and B. N. Chatterji, 1999. B-spline signal processing using harmonic basis functions, Signal Processing, 72(3):147-166. Pei, S. and J. Horng, 1995. Fitting digital curve using circular arcs, Pattern Recognition, 28(1):107-116. Piegl, L., 1989. Modifying the shape of rational B-splines. Part 1: curves, Computer-Aided Design, 21(8):509-518. Piegl, L. and W. Tiller, 1997a. The NURBS Book. Springer-Verlag, Heidelberg, Baden-Württemberg, pp. 47-116. Piegl, L. and W. Tiller, 1997b. The NURBS Book, Curve and Surface Fitting, Springer-Verlag, Heidelberg, Baden-Württemberg, pp. 361-453. Piegl, L. and W. Tiller, 1997c. The NURBS Book. 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Boundary segmentation by detection of corner, inflection and transition points, Proceedings of Workshop on Visualization and Machine Vision, 13-17. Versprille, K. J., 1975. Computer-Aided Design Applications of the Rational B-Spline Approximation Form, Ph.D. dissertation, Syracuse University, Syracuse, New York. Walz, M., T. Zebrowski, J. Küchenmeister and K. Busch, 2013. B-spline modal method: A polynomial approach compared to the Fourier modal method, Optics Letters, 21(12):14683-14697. Wong, Y. K., J. F. Poliakoff, P. D. Thomas and N. Sherkat, 1996. Automated path segmentation for 2-dimensional vectorised data, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems, 1:406-411. Google，2017。Google 地球版本，Google 地球，URL: https://www.google.com/intl/zh-TW/earth/versions/#earth-pro，Google，山景城，加利福尼亞州(last date accessed: 14 August 2021)。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/81997 | - |
| dc.description.abstract | 為了降低資料量並避免資料損失，B-spline作為電腦工程領域數學擬合中最為常用的函數之一，除了廣泛應用於傳統的電腦工程領域的訊號重建外，更常見於其他領域，如影像處理；因其除了能利用相對較少的資料量呈現幾何圖形並保有一定的精度，其所使用之參數(如節點向量、階數、基底函數和NURBS權重、控制點與曲線資料觀測值權重)亦提供擬合對象適切的運作彈性。 然而，過往針對B-spline成果調整的研究皆專注於如何修改其參數以主觀地調整擬合成果；僅有些許研究著墨於如何於擬合前即由客觀的隨機誤差預先設定數學擬合模式的參數以控制擬合成果。此外，針對具不同複雜度之幾何資料，例如湖泊、海岸與河川濱線等空間資訊，則此時僅能選定單一階數的B-spline便無法有效地因應不同複雜度的幾何特徵，易形成擬合不足或過度擬合。 本研究導入可調變階數的B-spline函數：CD-spline，並以Gauss-Markov Model with Constraint平差模式進行擬合以確保成果能忠實反映點位的隨機誤差。資料處理對象為三座臺灣湖泊之二維濱線，並考量資料獲取之隨機誤差樣態。透過建立一個包括測試樣本的建立、曲線資料觀測、分段、驗證和檢核點位的揀選、曲線函數參數的設定、曲線資料觀測值權重值的設定與成果檢核等步驟之工作流程，與比較和分析B-spline與CD-spline的實驗，擬合成果顯示透過本研究所提出之CD-spline工作流程除了確實能產製具有較高擬合忠實度且相對精準的成果外，更能有效地表達不同複雜度的幾何特徵，並透過設定合適的階數值避免過度擬合誤差產生。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-25T05:33:48Z (GMT). No. of bitstreams: 1 U0001-2108202118394700.pdf: 12976645 bytes, checksum: d33349c74de400c60977bd8fb75cd255 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | "口試委員審定書 I 誌謝 II 中文摘要 III 英文摘要 IV 目錄 V 圖目錄 VIII 表目錄 XIII 第一章 緒論 1 1.1 研究背景與動機 1 1.2 研究方法與流程 2 1.3 論文架構(章節大綱) 3 第二章 文獻回顧 4 2.1 常用之內插方法與擬合函數比較與分析 4 2.2 B-SPLINE基本介紹 8 2.2.1 B-SPLINE定義(PIEGL AND TILLER, 1997A) 8 2.2.2 B-SPLINE之調整彈性 9 2.2.3 B-SPLINE之實務應用 10 2.3 CD-SPLINE基本介紹 15 2.3.1 CD-SPLINE定義 15 2.3.2 CD-SPLINE之實務應用 16 2.4 總結 18 第三章 研究方法 19 3.1 B-SPLINE與CD-SPLINE參數設定 20 3.1.1 B-SPLINE參數設定 21 3.1.2 CD-SPLINE參數設定 22 3.2 控制點解算與理論精度推導 34 3.2.1 控制點解算 34 3.2.2 理論精度推導 40 3.3 成果檢核與比較分析 43 3.3.1 理論精度檢核 43 3.3.2 實際精度檢核 43 3.3.3 精度水準檢定 44 3.3.4 幾何外觀檢核 44 3.3.5 計算成本評估 45 第四章 實驗及成果分析 46 4.1 實驗資料建置 47 4.1.1 衛星影像取得 47 4.1.2 濱線偵測 48 4.1.3 濱線點位讀取 50 4.2 資料處理 52 4.2.1 降低取樣頻率處理與點位揀選 52 4.2.2 曲線資料觀測點位隨機誤差的模擬 58 4.3 擬合成果參數設定與實驗項目和目的 63 4.4 實驗一：CD-SPLINE之有效性分析 65 4.5 實驗二：加權模式之有效性分析 96 4.6 實驗三：雙方向階數向量之有效性分析 122 第五章 結論與建議 149 5.1 結論 149 5.2 建議 151 參考文獻 152 附錄一、中英文名詞對照及備註表 156 附錄二、B-SPLINE與CD-SPLINE名詞解釋表 158 附錄三、曲線資料觀測點位於進行CD-SPLINE擬合時之節點值與控制點係數範例 159" | |
| dc.language.iso | zh-TW | |
| dc.subject | 基底函數 | zh_TW |
| dc.subject | 可調變階數 | zh_TW |
| dc.subject | 濱線 | zh_TW |
| dc.subject | 邊緣線 | zh_TW |
| dc.subject | Gauss-Markov模式 | zh_TW |
| dc.subject | Gauss-Markov model | en |
| dc.subject | B-spline | en |
| dc.subject | CD-spline | en |
| dc.subject | shoreline | en |
| dc.subject | edge | en |
| dc.title | 以加權最小二乘法之CD-spline進行二維湖泊濱線擬合 | zh_TW |
| dc.title | On Weighted Least-squares CD-spline for Fitting the Two-dimensional Lake Shorelines | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡展榮(Hsin-Tsai Liu),邱式鴻(Chih-Yang Tseng),莊子毅 | |
| dc.subject.keyword | 基底函數,可調變階數,濱線,邊緣線,Gauss-Markov模式, | zh_TW |
| dc.subject.keyword | B-spline,CD-spline,shoreline,edge,Gauss-Markov model, | en |
| dc.relation.page | 160 | |
| dc.identifier.doi | 10.6342/NTU202102573 | |
| dc.rights.note | 同意授權(限校園內公開) | |
| dc.date.accepted | 2021-08-27 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
| dc.date.embargo-lift | 2023-08-31 | - |
| 顯示於系所單位： | 土木工程學系 | |
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