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研究生:黃欣玉
研究生(外文):Hsin-Yu Huang
論文名稱:NURBS應用於損壞影像修復及影像壓縮之研究
論文名稱(外文):On Corrupted Image Restoration and Image Compression Using NURBS
指導教授:鄭銘揚鄭銘揚引用關係黃其泮
指導教授(外文):Ming-Yang ChengChipan Huang
學位類別:碩士
校院名稱:大葉大學
系所名稱:電機工程學系碩士班
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:2003
畢業學年度:91
語文別:英文
論文頁數:62
中文關鍵詞:非均勻有理仿曲線
外文關鍵詞:NURBS
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“Non-Uniform Rational B-Splines”非均勻有理仿曲線一般簡稱為NURBS,由於NURBS具有完整的數學架構,因此被廣為採納而制訂成國際標準,在CAD/CAM及電腦繪圖等領域被廣泛應用。在2-D數位影像中可以視為NURBS的3-D曲面,因此我們將它應用在影像處理上。
絕大多數的B-Spline應用在影像內插,直到1997年T. Watanabe提出以B-Spline的數學架構作為影像壓縮,爾後1999年J. W. Park and S. U. Lee利用B-Spline的內插的特性將它應用在影像修補上。然而Park and Lee’s未能適當的找出節點(knot vector)及控制點(control points)。
為了解決這方面的缺點,我們使用bi-variate NURBS 曲面以解決影像上修補及壓縮的問題。在這我們提出單一隱藏層的類神經架構來決定3-D NURBS曲面所需的的控制點,而實驗證明我們所提出的方法能得到較佳的結果。

Due to their excellent property and their incorporation in international standards, “Non-Uniform Rational B-Splines”, commonly referred to as “NURBS”, is very popular among the CAD/CAM and computer graphics community. On the other hand, a 2D gray scale digital image can be viewed as a 3D surface. From this point of view, NURBS is clearly one of the candidates that are able to represent a set of digital image.
Nevertheless, the applications of B-splines surfaces to the fields of image processing are most restricted to the problems of image interpolations. One of few exceptions was, in 1997, T. Watanabe proposed a novel idea to use B-spline surfaces as an image coding algorithm. Later on, in 1999, J. W. Park and S. U. Lee extended the idea of B-splines surfaces interpolation to deal with the corrupted gray level image restoration problem. While satisfactory results were reported in Park and Lee’s paper, the formulas they adopted to determine the knot vectors and the control points are not appropriate.
To overcome these aforementioned difficulties, this study attempts to use a bi-variate NURBS surface to study the corrupted image restoration problem and the image compression problem, respectively. In the proposed approach, a single-hidden layer neural network (NN) is employed to learn the appropriate control points of NURBS that can generate best 3D NURBS approximation surface to the image data. Experimental results suggested that the proposed approach exhibiting satisfactory performance.

Table
Chinese abstract…………………………………………………v
English abstract…………………………………………………vi
Acknowledgment……………………………………………………vii
Table………………………………………………………………ix
List of figure……………………………………………………xi
List of table……………………………………………………xiv
Symbol………………………………………………………………xv
1 Introduction……………………………………………………1
2 Introduction to B-Spline Curve and Surfaces…………6
2.1 B-Spline Curve……………………………………………7
2.2 Degree of a B-spline curve..…………………………9
2.3 Control Points……………………………………………10
2.4 Knot vector and parameter u…………………………11
2.4.1 Parameterization…………………………………11
2.4.2 Knot Vectors………………………………………16
2.5 B-Spline Basis functions………………………………20
2.6 B-Spline Surface…………………………………………25
2.7 Rational B-Spline Curve and Surface………………26
3 Introduction to B-Spline Curve and Surfaces…………28
3.1 Parameterization, Knot Vector Selection and NURBS
Surface Rendering………………………………………28
3.2 Determination of the Values of Control Points…31
3.3 Experimental Results of Corrupted Image Restoration
Using NURBS………………………………………………34
4 Image Compression Using NURBS……………………………40
4.1 Proposed approach for Image Compression Using
NURBS………………………………………………………40
4.2 Determination of Number of Control Points Needed
for Image Block…………………………………………43
4.3 Experimental Results of Image Compression Using
NURBS………………………………………………………47
5 Conclusions and Future Study………………………………57
Reference…………………………………………………………59

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