臺灣博碩士論文加值系統

我們提出一個非剛性形體間之對齊與對應的方法。許多基於形變的方法改進迭代最近點法，並且將形體之對齊與對應的問題轉化為最佳化問題。然而，基於迭代最近點法的非線性能量系統必須在每次迭代時改變對應的最近點，並且移除當中被認為是不好的對應。此項行為造成最佳化的過程中改變了能量系統，因此最佳化處理時無法直截了當地求解。相反地，我們使用基於核關聯的方法來表示非線性能量系統，此法間接地給了動點一個方向，並且保證最佳化過程中擁有固定的數學表示式。我們的演算法不將每個形變物表上的取樣點對應到目標表物表上的另一個取樣點，而是將其對應到目標物表上的一個合理位置，因此獲得更合意的對齊與對應結果。此外，我們的演算法因擁有固定的數學表示式而能更有效率地求出最佳解。

We present an algorithm for shape registration of non-rigid partial scans. Many deformation-based methods adapt their algorithm based on iterative closest point (ICP) and formulate the registration as an optimization problem. However, non-linear energy systems based on ICP should change the set of closest points iteratively and remove some of them for filtering out bad correspondence. This behavior changes the formulation during energy minimization and the optimization process can not be solved straightforwardly. On the contrary, we formulate the energy system using kernel correlation (KC), which implicitly gives a direction for a moving point and guarantees a fixed formulation during optimization. Our algorithm gains a more preferable result since each point on the source surface is not fitted to a point but a reasonable 3D position on the target surface, and can be more efficient due to the fixed formulation of energy equations.

1 Introduction 1
2 Related Work 4
2.1 Rigid Registration . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Non-Rigid Registration for Range Images . . . . . . . . . . . . 5
2.2.1 Template-Based Registration . . . . . . . . . . . . . . . 6
2.2.2 Registration Without Using A Template . . . . . . . . 7
2.2.3 Non-Rigid Registration by Deformation . . . . . . . . . 8
2.2.4 Non-Rigid ICP-Based Energy System . . . . . . . . . . 11
2.3 A Correlation-Based Approach for Point Set Registration . . . 12
3 Non-Rigid Registration using Kernel Correlation . . .. . .. . .13
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Deformation Model . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Kernel Correlation as a Fitting Function .. . . . . . . . . . . 20
3.4 Solving the Optimization Process . . . . . . . . . . . . . . . 26
3.5 The Trusted Set of Fitting Function . . . . . . . . . . . . . . 29
4 Experimental Results 33
4.1 Implementations and Parameters . . . . . . . . . . . . . . . . 33
4.2 Registration Errors and Time Statistics . . . . . . . . . . . . 41
5 Conclusions 45
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 Future Works . . . . . . .. . . . . . . . . . . . . . . . . . . 47
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . .49

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