臺灣博碩士論文加值系統

摘 要
數位影像中如何進行影像特徵擷取，並經由獲得之特徵，進行影像外形量測或邊界表示是一項很重要之課題。目前有關此類之檢測，Ker[1]提出尋找分斷點之方式，將求得之斷點去除，將數位邊界以直線或曲線來表示，在辨認會更實際且更有意義，其主要目的是在所要求之精度下，用最少之線段或曲線來表示邊界形狀的本質。當物體進入一視覺檢測系統時，整個物體必須先轉換成數位化影像，在二值化轉換的過程中將會產生數位化誤差(Digital error)或雜訊(White noise)，Ker之曲率(Curvature)法則，不但無理論做為基礎，當遇到數位化誤差存在時，容易產生不正確的量測結果，且當受檢測之物體在數位化轉換的過程中產生雜訊或分斷點(Break point)所形成之夾角為鈍角時，其斷點位置就無法適當取得，本研究之目的主要為提出K曲率改良式法則，以改進現行K曲率法在檢測分斷點時之缺失，，以便能有效率的檢測出二維物體影像之分斷點。
首先，本研究針對所應用的二維物體外形，依其構成之方式，定義簡單型、複雜型及混合型三種物體基本形態，接著針對K值計算定義K-曲率做為計算之基礎，並發展出K值之上、下限值，以迅速完成程式之執行速度，而後經由所計算之K值，計算物體邊界上每點之曲率值，根據計算所得之各點曲率值，依所求得之臨界值(Threshold value)判斷物體分斷點之位置。
本研究之實驗中，分別以簡單型、複雜型及混合型等各種不同之物體進行試驗，以求得各影像之K值及分斷點數，接著將測試之各影像旋轉，以驗証所提出的K曲率改良式法則，及進行物體分斷斷點檢測之可靠度檢測，本研究所提之K-曲率演算法則，實驗結果較Ker之演算法則為佳。
最後，本研究期能運用所提出的K-曲率改良法則在對影像進行斷點檢
i
測時，能有效判斷出數位化誤差之情形、以及提高傳統之K-曲率法則在鈍角及雜訊下之斷點檢測的成功率，其研究結果期能發展一套二維影像之斷點檢測法則，藉以提高二維影像斷點檢測之效率及量測之精確度。

Abstract
Boundary representation has been an important issue in a computer vision system. Many algorithms have been developed for boundary representation. Break point or dominant point detection is important in object recognition by means of curvature. Curvature is defined as the change rate of slope, and has been widely used in different applications, such as shape representation, feature extraction, corner detection, dominant point detection, break point detection, object recognition and so forth. Also, a great variety of methods about curvature estimation that have developed to locate break points with local extreme curvature on the curve.
In this Paper, a formal theoretical base for break point detection by K-curvature threshold is first reviewed. Then, we proposed the roles of the lower and upper bounds of K value are derived to limit the range of K-curvature for a given object. Within the upper and lower bounds, an optimal K-value is suggested. Then, Three different objects are defined. Three rules are found and the threshold value determination method is also proposed. Finally, as a contribution in this study, a modified K-curvature threshold method is proposed, and the overall theorems are verified by a designed experiment.
Experimental results indicate that the proposed modify method performs much well than Ker’s methods in a wide angle exists in the object. Our study the success rate of detecting the break points is low when a linear and circular joint and wide angle exists in the object.
Keyword： K-Curvature, Break Point, Threshold Value.

目錄
中文摘要………………………………………………………………………...i
英文摘要………………………………………………………….. ………….iii
誌謝………………. …………………………………………………………iv
目錄………………. …………………………………………………………v
表目錄……………………………………………………………………….vii
圖目錄…………………………………………………………………………viii
第一章 緒論……………………………………………………………………1
1.1研究動機與背景…………………………………………………………1
1.2研究目的…………………………………………………………………3
1.3研究方法與步驟…………………………………………………………4
1.4研究範圍…………………………………………………………6
第二章 文獻探討………………………………………………………………7
2.1邊緣偵測…………………………………………………………………7
2.2邊角偵測…………………………………………………………………8
2.2.1以邊界為基礎的邊角檢測法則……………………………………8
2.2.2灰階為基礎的邊角檢測法則……………………………………8
2.3 Ker之斷點檢測法則…………………………………………………10
2.3.1 K值計算……………………………………………………11
2.3.2臨界值T之計算…………………………………………………11
2.4 研究問題…………………………………………………………11
第三章 研究方法與步驟……………………………………………………13
3.1現行K曲率法則……………………………………………………13
3.1.1曲率之基本定義……………………………………………13
3.1.2 K曲率法則之基本定義……………………………………13
3.2物體外形基本型式……………………………………………………15
3.2.1物體外形基本定義…………………………………………15
3.2.2簡單型物體………………………………………………17
3.2.3複雜型物體………………………………………………18
3.2.4混合型物體………………………………………………19
3.3斷點之分類與偵測誤差………………………………………………19
3.3.1數位化後產生偵測誤差的種類………………………………19
3.3.2數位化後產生邊角偵測誤差之討論……………………………21
3.3.3錯誤偵測之修正…………………………………………………22
3.4K曲率改良式法則…………………………………………………22
3.4.1K值計算……………………………………………………23
3.4.1.1下限值……………………………………………………23
3.4.1.2上限值……………………………………………………24
3.4.1.4最佳K值……………………………………………………24
3.4.2臨界值計算之修正…………………………………………………26
第四章 實例驗證……………………………………………………………28
4.1演算法說明………………………………………………………30
4.2 實驗結果……………………………………………………………32
4.2.1簡單型物體實例…………………………………………………32
4.2.1.1執行結果…………………………………………………32
4.2.1.2分析與討論…………………………………………………34
4.2.2物體旋轉實例………………………………………………………34
4.2.2.1執行結果…………………………………………………37
4.2.2.2分析與討論…………………………………………………37
4.2.3複雜型混合型物體實例…………………………………………37
4.2.3.1執行結果…………………………………………………38
4.2.3.2分析與討論…………………………………………………39
4. 3綜合討論……………………..…………………………………………40
第五章 結論與建議…………………………………………………………41
5.1結論……………………………………………………………………41
5.2未來研究方向…………………………………………………………43
參考文獻……………………………………………………………………….44
附件、 程式……………………………………………………………48
表目錄
表一、 成功偵測物體斷點之最佳K值……………………….………………34
表二、三角型物體旋轉各種角度後成功偵測斷點之最佳K值……………37
表三、複雜型及混合型影像成功偵測斷點之最佳K值……………………39
圖目錄
圖1-1研究步驟………………………………………………………………5
圖3-1 簡單型物體…………………………………………………………17
圖3-2複雜型物體…………………………………………………………18
圖3-3混合型物體……………………………………………………………19
圖3-4三種不同數位化角……………………………………………………20
圖3-5邊角檢測錯誤之三種型式……………………………………………21
圖3-6 最大接合點檢測錯誤之修正圖…………………………………25
圖3-7 臨界值分析…………………………………………………………26
圖 4-1 程式執行流程圖………………………………………………………29
圖 4-2 受檢物體影像…………………………………………………………32
圖 4-3 曲率分佈圖……………………………………………………………33
圖 4-4 各種三角形物體之旋轉影像…………………………………………35
圖 4-5 各種旋轉物體之曲率分佈圖…………………………………………36
圖 4-6 複雜型及混合型之影像………………………………………………38
圖 4-7 複雜型及混合型影像之曲率分佈圖…………………………………39

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38. 吳成柯,戴善榮,程湘君,雲立實, 數位影像處理, 儒林圖書公司