平面物體偵測與追蹤是擴增實境(Augmented Reality)系統中重要的基礎技術。本論文提出一高效且強健的多模板追蹤方法，其包含多個隨機蕨平面偵測器及平面追蹤器，進行平行化運算來達成多平面物體的偵測與追蹤應用。在隨機蕨平面偵測器的設計上，因所訓練出來的隨機蕨分類器佔用相當龐大的記憶體用量，大大限制了系統可偵測的平面物體數量。為了克服此問題，本論文透過最佳化半樸素貝葉斯分類器的參數設定方式，大幅降低每個平面偵測器所需要的記憶體用量，進而實現記憶體高效的多平面偵測系統。在平面追蹤演算法設計上，本論文亦提出一高效監督式下降預測(Efficient Supervised Descent Prediction)方法，其透過監督式下降法(Supervised Descent Method)及高效二階最小化(Efficient Second-order Minimization, ESM)，事先對每個平面物體學習一個多層次線性預測器。在線上追蹤時，則使用預測方式進行強健且精確的平面追蹤效果，讓原本需要計算大量海森矩陣的ESM方法加速至即時追蹤的效果，使得平面追蹤可以兼顧強健性及實時性。實驗結果顯示本論文所提出的方法與現有的平面追蹤方法比較上，不但擁有較高的追蹤成功率及較小的追蹤誤差之外，在影像有強烈雜訊影響下，仍然保有強健的追蹤效果。此外，本論文所提出的方法處理一個平面物體所需的時間僅需3.54ms，因此可達到即時多平面物體的追蹤效果，進而強化擴增實境系統的實用性。

Planar object detection and tracking are important foundational techniques in augmented reality systems. In this thesis, an efficient and robust multi-template tracking method that includes multiple random-ferns planar detectors and real-time planar trackers is proposed for parallelization of multi-template detection and tracking. In the design of the random-ferns planar detector, the trained random-ferns classifier usually occupies a large amount of memory, which greatly limits the number of planar objects detectable by the system. To overcome this problem, this thesis optimizes the parameter settings of a semi-naïve Bayesian classifier to greatly reduce memory usage required by each planar detector, which helps to realize a memory-efficient multi-planar detection system. In the design of the planar tracking algorithm, this thesis proposes an efficient supervised descent prediction method, which learns a multi-layered linear predictor for each planar object in advance based on supervised descent method and efficient second-order minimization (ESM). In the online tracking stage, the proposed supervised descent prediction approach is used for robust and accurate planar tracking, which accelerates the ESM method that originally requires large computational costs on Hessian matrix calculation to achieve fast tracking performance, making planar tracking both robust and real-time. Experimental results show that compared with two existing planar tracking methods, the proposed method not only has a higher tracking success rate and smaller tracking error, but also provides a strong tracking robustness against the influence of high-variance noise in the image. In addition, the proposed method takes only 3.54ms to track a planar object, so simultaneously real-time tracking of multiple planar objects can be achieved, thereby enhancing the practicability of augmented reality system.

中文摘要	I
英文摘要	III
誌謝	IV
目錄	V
圖目錄	VIII
表目錄	X
第一章 序論	1
1.1	研究背景	1
1.2	研究動機與目的	9
1.3	論文架構	10
第二章 相關背景知識	11
2.1  影像規整(Image Warping)	11
2.1.1  單對應規整矩陣定義	12
2.1.2  SL(3)單對應規整矩陣定義	13
2.2 平面物體追蹤演算法	14
2.2.1  超平面模板追蹤	14
2.2.1.1  超平面模板預測器離線學習	14
2.2.1.2 多層超平面預測器	16
2.2.2  Efficient Second-order Minimization (ESM)	19
2.2.2.1牛頓法	19
2.2.2.2 追蹤問題定義	20
2.2.2.3 最佳化追蹤成本函數	20
第三章 平面偵測演算法	22
3.1  隨機蕨(Random Ferns)	23
3.1.1 樸素貝葉斯Naive Bayes	23
3.1.2 蕨的分類器	23
3.1.3 隨機蕨的訓練	26
3.1.4 降低記憶體儲存量	27
第四章 平面追蹤演算法	28
4.1 監督式下降預測	28
4.1.1 監督式下降預測公式	29
4.2  Efficient Supervised Descent Prediction (ESDP)	30
4.2.1 ESDP離線預測器訓練	31
4.2.2 線上追蹤	32
4.3  多平面物體追蹤	35
第五章 實驗結果	38
5.1  軟硬體介紹	38
5.2  實驗參數設定	39
5.3  單平面實驗數據分析	40
5.3.1 偵測數據分析	41
5.3.2 追蹤數據分析	43
5.3.3 追蹤影片分析	50
5.4  多平面實驗數據分析	55
第六章 結論與未來展望	62
參考文獻	64

圖目錄
圖1.1、AR技術的設計層	3
圖2.1、影像規整示意圖	12
圖2.2、學習多層次超平面追蹤預測器	18
圖3.1、偵測流程圖	22
圖3.2、隨機蕨的二元特徵示意圖	24
圖3.3、二元特徵值的儲存方法	25
圖3.4、蕨的特徵分布	26
圖3.5、類別的特徵分布	26
圖4.1、ESDP平面追蹤流程圖	28
圖4.2、ESDP預測器學習方塊圖	33
圖4.3、多平面系統方塊圖(以四個平面為例子)	36
圖4.4、多平面系統架構圖	37
圖5.1、羅技C920攝影機	38
圖5.2、參考影像	39
圖5.3、偵測成功率及精準度結果圖	42
圖5.4、實驗程式流程圖	44
圖5.5、Data1精準度以及追蹤成功率	46
圖5.6、Data1額外雜訊平均值減去無雜訊平均值的變化值	47
圖5.7、Data2精準度以及追蹤成功率	48
圖5.8、Data2額外雜訊平均值減去無雜訊平均值的變化值	49
圖5.9、追蹤效果比較	52
圖5.10、追蹤效果比較圖	52
圖5.11、連續移動變化大時結果圖	53
圖5.12、連續移動變化大時結果圖	54
圖5.13、Data3追蹤精準度及追蹤成功率分析圖	56
圖5.14、Data3姿態估測實驗結果：(a)為模擬產生的理想姿態，(b)為提出方法的估測姿態	57
圖5.15、Data3姿態誤差圖	58
圖5.16、多平面成功追蹤結果	58
圖5.17、追蹤結果圖	60
圖5.18、實際追蹤結果圖	61

表目錄
表2.1、ML-HP學習演算法	17
表2.2、ML-HP追蹤演算法	17
表4.1、Multi-Layered ESDP學習演算法	34
表4.2、Multi-Layered ESDP追蹤演算法	34
表5.1、攝影機規格表	39
表5.2、電腦規格表	39
表5.3、四個隨機蕨偵測器的參數設定	43
表5.4、平面追蹤處理時間比較	50
表5.5、多平面處理時間	58

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