摘要
在影像追尋還原物體在空間中位置或速度的研究方面上，可預期的是增加攝影機數目可以減小影像追尋還原物體運動的誤差，事實上在實際應用也的確如此。但至今為止，並未有明確的數學理論方面研究，來証明增加攝影機數目可以減小影像追尋還原物體運動的誤差。本文於是提出採用數學上統計機率的概念，以最小平方法計算，由已知光流反推空間中的平移速度向量為基礎，並以高斯分佈的光流誤差量進行理論誤差分析及模擬，以期提供一個有效的數學理論模式供實際應用上的參考。


關鍵字：影像追尋、最小平方法、高斯分佈、誤差分析。

Abstract
In the researches of image tracking to restore an object’s position or velocity in the space, it is expectable that increasing numbers of camera can reduce the error. In fact, this phenomenon happens in practical applications. But so far, the physical theory behind this effect has not been fully known. Therefore, based on this motivation, this thesis tends to lay the physical foundation of specific machine vision problem using the statistical probability concept. Extensive error analysis and computer simulation for motion vector of translation movement solved by the least squares technique are conducted by incorporating Gaussian noised into optical flow components. It is expected to provide an effective theoretical model for further developments.


Keywords：Image tracking, The least squares method, Gauss distribution, Error
analysis.

目錄
目錄……………………………………………………………………………..ⅰ
圖索引………………………………………………………………………….ⅲ
表索引………………………………………………………………………….ⅳ
摘要…………………………………………………………………………….ⅴ
Abstract………………………………………………………………………...ⅵ
第一章 緒論....................................................1
1.1 動機與目的…………………………………………………………...1
1.2 文獻回顧………………………………………………………….......1
1.3 論文架構……………………………………………………………...6
第二章 光流系統………………………………………………………………7
　　2.1 光流及影像流之定義…………………………………………….......7
　　2.2 光流之演算…………………………………………………………...8
第三章 攝影機架構之數學推導及誤差模擬分析………………………..…11
　　3.1 攝影機架構之數學推導………………………………………….....11
　　　3.1.1 双眼架構………...……………………………………………...12
3.1.2 一維三眼等距並排架構..............................................................14
3.1.3 一維四眼等距並排架構………………………………………..15
3.1.4 一維五眼等距並排架構………………………………………..16
3.1.5 二維三眼正三角排列架構……………………………………..18
3.1.6 二維四眼菱形排列架構………………………………………..19
　　3.2 誤差分析…………………………………………………………….21
　　3.3 模擬結果…………………………………………………………….25
第四章 攝影機架構擴展及分析……………………………………………..29
　　4.1 攝影機架構擴展…………………………………………………….29
　　　4.1.1 一維N眼等距並排架構……………………………………….29
　　　4.1.2 二維N*N眼等距矩陣架構…………………………………....30
　　4.2 誤差模擬比較……………………………………………………….34
　　4.3 各軸運動方向之誤差比較………………………………………….36
第五章 結論與未來展望…………………………………………………......39
參考文獻……………………………………………………………………....40














圖索引
圖2.1(a) 影像流幾何圖示..................................................................................7
圖2.1(b) 影像流一般表示法..............................................................................7
圖3.1 影像投影幾何關係圖.............................................................................11
圖3.2 双眼架構.................................................................................................13
圖3.3 一維三眼等距並排架構.........................................................................14
圖3.4 一維四眼等距並排架構.........................................................................15
圖3.5 一維五眼等距並排架構.........................................................................17
圖3.6 二維平面三眼正三角排列架構.............................................................18
圖3.7 二維平面四眼菱形排列架構.................................................................20
圖3.8 二眼及一維三眼等距並排架構誤差示意圖.........................................23
圖4.1 一維N眼等距並排架構........................................................................29
圖4.2 二維N*N眼等距矩陣架構示意圖(N奇數)........................................31
圖4.3 二維N*N眼等距矩陣架構示意圖(N偶數)........................................33
圖4.4 一維N眼等距並排架構之誤差標準差..………………….…………..35
圖4.5 二維N*N眼等距矩陣架構之誤差標準差..……………………….....36





表索引
表3.1 誤差變異數之係數表……………………………………………….....24
表3.2 誤差模擬比較表………………………………………………….…....27
表4.1 X軸方向誤差標準差..……………………….......................................37
表4.2 Y軸方向誤差標準差..……………………….......................................37
表4.3 Z軸方向誤差標準差..……………………….......................................38

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