臺灣博碩士論文加值系統

本文提出應用數位影像相關法建立一套平面位移量測系統。由於本文的目的是計算大變形所以先定義大變形的應變 40% 針對待測物。擷取影像進行相關性分析、區域連通演算法以及形狀函數分析，再經由位移方程式及亮度轉換模型配合牛頓法理論進行此位移方程式之優化，透過迭代運算求得物體表面變形後位移之次像素精度後，最終得到物體表面位移場及應變場變化。然而如果使用牛頓迭代的話就必須給定初始值，而這些初始值的來源則必須先利用連通區域標記法將每一個連通的區域標註記號，然後再利用這些編號的特性找出影像內每一個網格點，有了變形前後的網格點後就能很快地找到這些位移的初始值。實驗部分則是先將製作好的圖案印在要實驗的物體上，再利用數位攝影機拍攝物體在受力前後的影像，並透過數位影像相關性理論以及形狀函數所撰寫的數位影像分析程式，並直接推算物體表面位移場的變化。最後結論則是分析計算得到的位移場以及探討該如何改進缺點。

The present study has developed a plane displacement measurement system based on a digital image correlation method. For these purposes,the strain of large deformation was defined as 40%. A series of analyses
was performed on the images before and after deformation, including correlational analysis, connected component labeling, and shape interpolation function analysis. Furthermore, optimizations were made employing displacement equations and brightness of transformation
models, in conjunction with Newton’s method. Iterative methods were used to find the underwent displacement of an object after deformation,finally determining the surface displacement field and the strain field.
However, the use of Newton’s method iteration methods requires inputting an initial value. These values must first be derived by marking each connected area with connected component labeling, then constructing a grid with this data and corresponding the before-after
images based on this grid. The methods of this study were to print prepared images onto the object being tested, then to record digital images of the object before and after deformation. Analysis was conducted with software based on digital image correlation theory and shape function, to determine the displacement field of the object’s surface,concluding with a discussion of the displacement field derived from analysis, and possible improvements to be made for future investigations.

摘要............................................................................................................. i
Abstract ...................................................................................................... ii
目錄........................................................................................................... iii
表目錄....................................................................................................... vi
圖目錄...................................................................................................... vii
第一章、緒論.............................................................................................1
1.1 前言 ................................................................................................1
1.2 研究背景與動機............................................................................2
1.3 文獻回顧........................................................................................2
1.4 論文架構........................................................................................4
第二章、研究理論 ....................................................................................6
2.1 數位影像處理(Digital Image Processing) ....................................6
2.2 相關係數(Correlation Coefficient)................................................9
2.3 數位影像相關性(Digital Image Correlation) ............................. 11
2.4 圖像連通區域標記法(Connected Component Labeling)...........12
2.5 次像素原理和位移......................................................................15
2.6 影像內插......................................................................................15
2.6.1 最鄰近點內插(Nearest Neighbor Interpolation) ..............16
2.6.2 雙線性內插(Bilinear Interpolation) ..................................17
2.6.3 雙立方內插(Bi-cubic Interpolation) .................................18
2.6.4 Catmull-Rom 樣條內插(Catmull-Rom Spline Interpolation)
.....................................................................................................20
2.6.5 雙立方樣條內插(Bi-cubic Spline Interpolation) ..............22
2.7 建立影像網格..............................................................................23
2.7.1 網格疏密的影響 ................................................................24
2.7.2 位移函數的形式 ................................................................24
2.7.3 四邊形 4 節點形狀函數....................................................25
2.7.4 四邊形 8 節點形狀函數....................................................29
2.8 牛頓法(Newton’s Method) ..........................................................35
第三章、實驗方法與演算法設計 ..........................................................38
3.1 實驗步驟......................................................................................40
3.2 演算法流程圖..............................................................................41
3.2 影像亮度轉換模型......................................................................42
3.4 位移方程式..................................................................................47
3.5 子區次像素位移及位移梯度 .....................................................48
第四章、模擬與實驗結果 ......................................................................52
4.1 模擬測試......................................................................................52
4.2 實驗結果......................................................................................70
第五章、結論及未來展望 ......................................................................79
5.1 結論 ..............................................................................................79
5.2 未來展望......................................................................................80

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