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| 研究生： |
吳紀煌 Ji-Huang Wu |
|---|---|
| 論文名稱： |
部分重疊曲面之快速全域配準 Fast Global Registration of Partially Overlapping Surfaces |
| 指導教授： |
鄭經斅
Ching-Hsiao Cheng |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2025 |
| 畢業學年度： | 113 |
| 語文別： | 英文 |
| 論文頁數： | 42 |
| 中文關鍵詞： | 快速全域配準 、部分重疊 、FPFH 、RANSAC 、Levenberg-Marquardt |
| 外文關鍵詞： | fast global registration, partial overlap, FPFH, RANSAC, Levenberg-Marquardt |
| 相關次數： | 點閱：38 下載：0 |
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本論文提出一套高效的三維點雲快速全域配準框架，專為處理僅具部分重疊或不完全對應的資料情境。為了克服傳統 Iterative Closest Point（ICP）演算法在初始姿態誤差大或重疊區域較小時容易陷入局部極小值的問題，本研究採用一套實用的多階段流程。首先，透過多尺度的 Fast Point Feature Histogram（FPFH）與 KD-tree 搜尋建立初步對應集合 K₁，接著進行互相一致性檢查以篩選為 K₂。再者，利用 300 次迭代的 RANSAC 估計初始剛體轉換，最後透過改良的 Levenberg–Marquardt 非線性優化進行精化。在此過程中，引入 Geman–McClure 強健核函數與自適應阻尼參數更新策略，有效抑制離群值影響並提升收斂穩定性。
本研究在多組公開點雲資料集上驗證所提方法，並與兩種基準流程進行比較，分別為：FPFH + K₁ + K₂ + RANSAC（迭代 10000 次）以及 FPFH + K₁ + K₂ + ICP。實驗結果顯示，在相同運算時間下，所提流程在姿態估計準確度、收斂速度與穩健性方面皆優於基準方法，並能有效處理部分重疊與較大初始誤差的情形，展現其在文化資產保存、3D 掃描及其他電腦視覺高精度配準任務中的應用潛力。
This thesis presents an efficient framework for fast global registration of 3D point clouds with limited overlap or partial correspondences. To overcome the limitations of the Iterative Closest Point (ICP) algorithm—such as local minima and failure under large pose errors—a practical multi-stage pipeline is proposed. It begins with multi-radius Fast Point Feature Histograms (FPFH) and KD-tree search for correspondence (K1), refined by mutual consistency checking (K2). An initial transformation is estimated using 300 iterations of RANSAC, followed by robust nonlinear refinement via an improved Levenberg–Marquardt method with the Geman–McClure kernel and adaptive damping, effectively suppressing outliers and ensuring stable convergence.
The proposed method is validated on multiple public point cloud datasets and compared against two baselines: (1) FPFH + K1 + K2 + RANSAC with 10,000 iterations, and (2) FPFH + K1 + K2 + ICP. Experimental results demonstrate that, under comparable runtime constraints, the proposed pipeline achieves superior pose estimation accuracy, faster convergence, and greater robustness—particularly in scenarios with partial overlap and large initial misalignment. These findings highlight its potential for applications in cultural heritage preservation, 3D scanning, and other high-precision registration tasks in computer vision.
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