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研究生:莊耀棟
研究生(外文):Yao-Tung Chuang
論文名稱:以信賴區域演算法減緩三維物面之全域貼合誤差
論文名稱(外文):Relaxation of Global Registration Error of 3D Models with the Trust-Region Algorithm
指導教授:石勝文石勝文引用關係
指導教授(外文):Sheng-Wen Shih
學位類別:碩士
校院名稱:國立暨南國際大學
系所名稱:資訊工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:83
中文關鍵詞:全域貼合多張貼合三維資料貼合逆向工程信賴區域
外文關鍵詞:global registrationmultiview registration3-D registrationreverse engineeringtrust-region
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  • 被引用被引用:0
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  • 下載下載:31
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由實體表面所取得之三維點資料來建構三維模型是逆向工程的基礎技術,為了取得完整的物面資料, 通常必須由不同的視角對物體掃描取點。在不同視角取得的三維點資料必須要經過貼合運算, 以估算座標轉換矩陣。然而在貼合時會因錯誤的對應關係和資料的量測雜訊等,而讓貼合的結果產生誤差。當兩兩貼合時, 誤差也許不是很明顯, 但是當全域貼合時, 累積後的誤差將有可能會造成全域貼合後的模型有嚴重的變型或裂痕, 因此全域貼合便成為逆向工程中的關鍵技術。全域貼合時要處理的資料量大,且相關的變數多,若處理不當則無法縮減誤差。比較可行的方式是利用羅德里格斯公式(Rodrigues’ Formula) 的近似式來代替非線性項以簡化問題, 但是在累積誤差大到無法使用此一近似式時, 將會導致錯誤的計算結果。在本論文中, 我們使用信賴區域演算法(Trust-Region Algorithm ) 自動調整信賴區域半徑值, 以兼顧近似式的計算效率以及累積誤差大時的精確度。實驗結果顯示在本研究中所使用的信賴區域演算法, 不只可以解決迴圈累積誤差太大的問題, 對於一般迴圈累積誤差不大的三維點資料之貼合效率也非常高。
Three-dimensional data acquisition techniques form the basis of reverse engineering. In order to obtain the complete information of an object surface, it is usually required to scan the object from different angles of views. Therefore, the data sets have to be registered to compute the coordinate transformation matrices among them. However, the registration results may contain estimation errors owing to the incorrect correspondences and measurement noise. The effect of registration error may be not obvious in pair-wise registration, but the accumulated registration error often results in serious flaws in global registration. Therefore, global registration is one of the key issues in reverse engineering. Because the amount of data and variables that have to be dealt with in global registration can be very large, reducing the global registration error is a difficult task. A feasible approach is to linearize Rodrigues’ formula for rotation matrices so that the constrained large scale nonlinear optimization problem can be simplified to be tractable. However, when the accumulation error is too large to be linearized, the linearization solutions will fail. In this thesis, we propose a trust-region algorithm that can automatically adjust the trust radius of linearization zone so that we can take advantages of both the efficiency of linearization and the accuracy of nonlinear constraints. Experiments showed that the proposed method is efficient and accurate.
1 簡介 1
1.1 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究成果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 章節架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 三維資料貼合文獻探討 6
2.1 兩兩貼合演算法. . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 點對點貼合. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 點對面貼合. . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 多張貼合演算法. . . . . . . . . . . . . . . . . . . . . . 11
2.3 分配誤差多張貼合演算法. . . . . . . . . . . . . 15
3 線性化條件之多張貼合 20
3.1 貼合圖型表示法. . . . . . . . . . . . . . . . . . . . . . 20
3.2 兩兩貼合的貼合誤差. . . . . . . . . . . . . . . . . .21
3.3 定義多張貼合誤差隱藏的問題. . . . . . . . . 23
3.3.1 兩兩貼合目標方程式. . . . . . . . . . . . . . . . 23
3.3.2 多張貼合的限制條件. . . . . . . . . . . . . . . . 23
3.3.3 多張貼合的目標方程式. . . . . . . . . . . . . . 24
3.4 使用誤差貼合參數(DRP) 於多張貼合. . . 26
3.4.1 兩兩貼合近似目標方程式. . . . . . . . . . . .26
3.4.2 將非線性限制條件線性化. . . . . . . . . . . .27
3.4.3 使用線性化條件之最佳化問題. . . . . . . 31
4 信賴區域演算法之多張貼合 34
4.1 使用信賴區域演算法之最佳化問題. . . . 34
4.2 信賴區域演算法. . . . . . . . . . . . . . . . . . . . . .36
4.2.1 Karush Kuhn Tucker 最佳化條件 . . . . .42
4.3 使用信賴區域演算法之詳細流程. . . . . . .44
5 實驗結果 48
5.1 樣本貼合結果. . . . . . . . . . . . . . . . . . . . . . . .48
5.1.1 Dino 資料樣本 . . . . . . . . . . . . . . . . . . . . . 49
5.1.2 OSUBunny 資料樣本 . . . . . . . . . . . . . . . .56
5.1.3 Disk 資料樣本 . . . . . . . . . . . . . . . . . . . . . 63
5.1.4 Venus 資料樣本. . . . . . . . . . . . . . . . . . . . 67
5.1.5 RedDino 資料樣本. . . . . . . . . . . . . . . . . . 74
6 結論及未來展望 82
6.1 研究結論. . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . 83
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