多邊形內插方法在三維影像的研究與應用｜國立清華大學博碩士論文庫

簡易檢索 / 詳目顯示

回結果列表

研究生：	陳春元
論文名稱：	多邊形內插方法在三維影像的研究與應用 Polygon Interpolation for 3-D Image Reconstruction
指導教授：	莊克士
口試委員:
學位類別：	博士 Doctor
系所名稱：	原子科學院 - 生醫工程與環境科學系 Department of Biomedical Engineering and Environmental Sciences
論文出版年：	2004
畢業學年度：	92
語文別：	英文
論文頁數：	68
中文關鍵詞：	多邊形、內插、重建
相關次數：	點閱：2 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

摘要
物體3-D表面數據的重建對醫學影像應用非常重要。這些3-D表面的數據可以用來協助視覺、外科手術、放射治療計畫以及診斷。對於兩張來自不同醫療設備影像的對位融合，如將核磁共振造影(MRI)及正子放射斷層造影 (PET) 融合，需將影像資料從新數位化。而影像內插技術即為解決上述問題的好方法。以灰階及形狀為基礎的影像內插法已被廣泛討論與應用，且被發現存在一些不足。在本篇論文中，我們提出一個全新的，以多邊形近似圖形的影像內插方法。多邊形近似圖形的目的主要為用最少的多邊形線段而可以掌握圖形的特性。影像的內插或邊界的重建則以此多邊形的頂點或邊為基礎。在第二章中，我們假設物件邊界的內插即相當於內插近似物件的多邊形。如果用以近似物件的多邊形其頂點可被求出，則邊界可由這些頂點以立體線段( Cubic-spline )內插方式得出。再第三張及第四章中，多邊形被用來近似物件的外型，然後進行內插。對於每一個在目標多邊形( target polygon )中的像素( pixel )值係因其對應到多邊形的邊或頂點的相對位置而決定。對於邊界的內插，我們的方法與形狀為基礎的方法比較後被證明較快且較好。除此以外，多邊形方法的影像品質較優良且與傳統的灰階內插法比較時均方差( mean-squared difference )較小。

Abstract

The reconstruction of a 3-D surface is important in many medical applications. These 3-D surface data can be used to reconstruct the object for visualization, surgery, radiation treatment planning and diagnosis. To register images for different modalities, such as MR and positron emission tomography (PET), these data must be re-digitized. The image interpolation is a useful tool to help solve these problems. Gray-level and shape-based image interpolation methods have been discussed and used extensively. However, these methods bring some drawbacks into existence. In this dissertation, we propose a novel image interpolation method that uses polygon approximation to improving those mentioning methods. Aim for polygon approximation is to capture the essence of the object shape with the fewest possible polygonal segments. Image interpolation or contour construction is then performed based on the polygon vertexes or edges. In Chapter 2, we assume that approximates the object shape. If the polygon vertexes are defined, then the contour can be approximated from these vertexes using a cubic spline interpolation. In Chapters 3 and 4, we use a polygon to approximate the object shape and perform the interpolation. For each pixel inside the target polygon, we determine its relative location in the source slices using the vertices or edges of a polygon as the references, respectively. The target slice gray-level is then interpolated from the corresponding source image pixels. For contour interpolation, our method yields a better contour and is computationally more efficient than shape-based interpolation. In addition, the image quality of this interpolation method is better and the mean squared difference is smaller compared with traditional gray-level image interpolation.

Contents
摘要                                                           I
Abstract                                                        II
Contents     III
List of figures     VI
List of tables     VII
Chapter 1 Introduction                                          1
1.1 Why image interpolation                                  1
1.2 Methods of traditional image interpolation               1
1.2.1 Gray-level image interpolation                            1
1.2.2 Shape-based image interpolation                           2
1.3 Research scope                                           2
1.3.1 Image interpolation using polygon approximation     2
1.3.2 Polygon contour interpolation     2
1.3.3 Vertex-based image interpolation     3
1.3.4 Edge-based image interpolation     3
1.4 Organization     3
     1.4.1 Brief description of the second chapter                    3
     1.4.2 Brief description of the third chapter                      4
     1.4.3 Brief description of the fourth chapter                     4
Chapter 2 Polygon Contour Interpolation                           4
2.1 Introduction                                              6
2.2 Method and materials                                   7
  2.2.1 Polygon approximation                                8
2.2.2 Interpolation of long-axis and vertex parameters           8
2.2.3 Reconstruction of polygon     9
2.2.4 Spline interpolation     9
2.2.5 Branching cases     10
2.3 Gray-level interpolation                                   10
2.4 Experiments and results                                  11
2.5 Discussion                                              12
  2.5.1 Comparison between shape-based and polygon interpolation     12
  2.5.2 Long-axis     13
2.5.3 Number of vertices     13
2.5.4 Computation time     13
2.5.5 Gray-level interpolation     14
2.6 Conclusion     14
Chapter 3 Vertex-based Image Interpolation                      29
3.1 Introduction                                             29
3.2 Methods                                                 30
3.2.1 Shape-based interpolation                          31
3.2.2 Polygon approximation                                32
3.2.3 Interpolation of position                              32
3.2.4 Interpolation of gray-levels                             34
3.3 Experiments and results                             34
  3.3.1 Objects     34
  3.3.2 Mean squared difference     35
     3.3.3 Pixel displacement     35
     3.3.4 Results     35
3.4 Discussion                                 36
3.4.1 Comparison with gray-level interpolation     36
3.4.2 Comparison with shape-based interpolation     36
     3.4.3 Polygon approximation     37
   3.4.4 Weighting parameter     37
   3.4.5 Number of vertices     37
   3.4.6 Mean squared difference     38
 3.4.7 Displacement     39
3.5 Conclusion     39
Chapter 4 Edge-based Image Interpolation       50
4.1 Introduction                                             50
4.2 Method                        51
4.2.1 Shape-based interpolation                        52
4.2.2 Polygon approximation                                52
4.2.3 Interpolation of position                               53
4.2.4 Interpolation of gray-levels     54
4.3 Experiments and Results                                 55
  4.3.1 Objects     55
  4.3.2 Mean squared difference     55
  4.3.3 Results     55
4.4 Discussion                                 55
4.4.1 Effect of vertices number     55
4.4.2 Weighting parameter a and b     56
4.4.3 Comparison with gray-level interpolation     56
4.5 Conclusion     57
Chapter 5 Conclusion                                          63
5.1 Validation of the assumption     63
5.2 Number of vertex     63
5.3 Long axis     63
5.4 Vertex-based vs edge-based     64
5.5 Polygon interpolation vs shape-based interpolation     64
5.6 Polygon interpolation vs direct gray-level interpolation     64
References                                                   69

List of Figures
Figure 2.1 Inflection point and contour segment.     15
Figure 2.2 Polygon approximation of a contour.     15
Figure 2.3 A pixel to be interpolated using the vertex as a reference.     16
Figure 2.4 The intermediate slices produced by shape-based interpolation for object 1.     16
Figure 2.5 The intermediate slices produced by polygon interpolation for object 1 with vertex number equal to 32.      17
Figure 2.6 The intermediate slices produced by shape-based interpolation for object 2.     18
Figure 2.7 The intermediate slices produced by polygon interpolation for object 2 with vertex number equal to 32.     19
Figure 2.8 The intermediate slices produced by shape-based interpolation for object 3.     20
Figure 2.9 The intermediate slices produced by polygon interpolation for object 3 with vertex number equal to 32.     21
Figure 2.10 The intermediate slices produced by polygon interpolation for object 1 with vertex number equal to 4.     22
Figure 2.11 The intermediate slices produced by polygon interpolation for object 1 with vertex number equal to 8.     23
Figure 2.12 The intermediate slices produced by polygon interpolation for object 1 with vertex number equal to 16.    24
Figure 2.13 The intermediate slices produced by polygon interpolation for object 3 with vertex number equal to 4.     25
Figure 2.14 The intermediate slices produced by polygon interpolation for  object 3 with vertex number equal to 8.     26
Figure 2.15 The intermediate slices produced by polygon interpolation for object 3 with vertex number equal to 16.     27
Figure 2.16 Results of linear gray-level interpolation and polygon interpolation.     28
Figure 3.1 Shape-based interpolation.     42
Figure 3.2 The long axis and the construction of the polygon.     42
Figure 3.3 The relation of a pixel and vertex in a parallelogram.     43
Figure 3.4 Result of gray-level interpolation for first data set.     44
Figure 3.5 Resultant images of shape-based gray-level interpolation using various weights for first data set.     45
Figure 3.6 Result of gray-level interpolation for second data set.     46
Figure 3.7 Resultant images of shape-based gray-level interpolation using various vertices numbers for second data set.      47
Figure 3.8 Mean squared difference of the new method for the first
object.     48
Figure 3.9 Mean squared difference of the new method for the second object.     49
Figure 4.1 Shape-based interpolation.     58
Figure 4.2 The corresponding position of a pixel with respect to edge.     58
Figure 4.3 Three situation of the projection of pixel Pk on edge.      59
Figure 4.4 Original images of the first object at slices and result of gray-level interpolation.      59
Figure 4.5 The results of the edge-based interpolation for the first data
set.     60
Figure 4.6 Original images of the second object and result of gray-level interpolation.      61
Figure 4.7 The results of the edge-based and vertex-based interpolation for the second data set.     62
Figure 5.1 The results of vertex-based and edge-based interpolation.     66
Figure 5.2 The original two slices to be interpolated are approximated by polygons using long axis and axis pass through midline.     67
Figure 5.3 The results of edge-based interpolation using long-axis and midline axis polygon.     67
Figure 5.4 The parameters of a point inside a polygon in vertex-based and edge-based model.    68
Figure 5.5 The relative position to an edge in the edge-based and vertex-based model.      68
Figure 5.6 The relative position is determined by the intersection of two lines originating vertically from edges of a common vertex.     68


List of Tables

Table 3.1 Average displacement of pixels between target and source slices for the first data set.      41

Table 3.2 Average displacement of the new method for the second data set.      41

                                

References
Beier T and Neely S 1992 Feature-based image metamorphosis Comput. Graph. 26 35-42

Bloch P and Udupa J K 1983 Application of computerized tomography to radiation and surgical planning Proc. IEEE. 71 351-72

Chen S Y, Lin W C, Liang C C and Chen C T 1990 Improvement on dynamic elastic interpolation technique for reconstructing 3-D objects from serial cross-sections IEEE Trans. Med. Img. 9 71-83

Chuang K S 1993 A refined gray-level gradient for three-dimensional surface display Phys. Med. Biol. 38(4) 557-562

Chuang K S, Chen C Y, Yuan L J and Yeh C K 1999 Shape-based gray-level images interpolation Phys. Med. Biol. 44 1565-77

Christiansen H N and Sederberg T W 1978 Conversion of complex contour line description into polygon element mossaics Computer. Graphics 12 187-92

Cong G and Parvin B 1999 An algebraic solution to surface recovery from cross-sectional contours Graph. Models Image Process 61 222-243

Denham L R 1984 Seismic interpretation Proc. IEEE. 72 1255-65

Dhawan A P and Arata L 1991 Knowledge-based 3D analysis from 2D medical images IEEE Eng. Med. Biol. 10 30-37

Fuchs H, Kedem Z M, and Uselton S P 1977 Optimal surface reconstruction from planar contours Comm. ACM. 20 693-702

Gonzalez R C and Woods R E 1992 Digital Image Processing. (Reading, MA: Addison-Wesley)

Grevera G J and Udupa J K 1996 Shape-based interpolation of multidimensional gray-level images IEEE Trans. Med. Img. 15 881-892

Grevera G J and Udupa J K 1998 An objective comparison of 3-D image interpolation methods IEEE Trans. Med. Img. 17 642-52

Herman G T, Zheng J S, and Bucholtz C A 1992 Shape-based interpolation IEEE Comp. Graph. & Appl. 12 69-79

Higgins W E, Morice C and Ritman E L 1993 Shape-based interpolation of tree-like structures in three-dimensional images IEEE Trans. Med. Img. 12 439-450

Hohne K H and Berstein R 1986 Shading 3D images from CT using gray-level gradients IEEE Trans. Med. Img. 5 45-47

Johnson E M and Capowski J J 1983 A system for the three-dimensional reconstruction for biological structures Comput. Biomed. Res. 16 79-87

Levin D 1986 Multidimensional reconstruction by set-valued approximation IMA J. Numerical Analysis 6 173-184

Liang C C, Chen C T and Lin W C 1991 Intensity interpolation for branching in reconstructing three-dimensional objects from serial cross sections Proc. SPIE. 1445 456-67

Lin W C, Liang C C and Chen C T 1988 Dynamic elastic interpolation for 3-D medical image reconstruction from serial cross sections IEEE Trans. Med. Img. 7 225-32

Press W H, Flannery B P, Teukolsky S A and Vetterling W T 1990 Numerical Recipes in C. Cambridge: Cambridge University 96-97

Raya S and Udupa JK 1990 Shape-based interpolation of multidimensional objects IEEE Trans. Med. Img. 9 33-42

Renner W D, Pugh N O, Ross D B, Berg R E, and Hall D C 1987 An algorithm for planning stereotactic brain implants Int. J. Radiation Oncology Biol. Phys. 13 631-637

Udupa J K and Herman G T 1991 3D Imaging in Medicine. ( Boca Raton, FL: CRC)

全文公開日期本全文未授權公開 (校內網路)
全文公開日期本全文未授權公開 (校外網路)

簡易檢索 / 詳目顯示

相關論文