一個影像資料庫儲存了大量的影像資料與相關的資訊，這些影像資料與資訊是由真實的影像圖片與相對應的符號圖片所組成。影像資料庫系統的相似程度擷取的應用當中，空間關係是一個相當重要的參考因素。為了能夠從影像資料庫中尋找出有興趣的資料，必須有能力推論組成圖片的物件彼此之間的空間關係。隨著數位相機和影像處理軟體的普及，許多的影像資料可以輕易地旋轉或翻轉。也就是說，這些影像可以被旋轉到特定的角度、水平翻轉或垂直翻轉。一個穩固的影像相似擷取架構，可以辨識出各種影像轉換，例如：變形、放大縮小、旋轉、或任意的轉換組合。目前已發表的空間相似擷取演算法可以歸納成三種類型：符號圖像投射類型、幾何空間類型、與圖學技術比對類型。符號圖像投射可以保留物件中與空間有關的重要資訊，例如：長度、寬度、以及座落位置。然而，許\\多以符號圖像投射為主的物件索引技術對於圖像的翻轉與旋轉相當敏感。因此，以空間關係搜尋圖像時，如果指定的空間關係方位和資料庫中儲存不一致，搜尋的結果會遺漏符合條件的影像。為了解決這個問題，學者們整理出影像轉換後，空間關係變化的規則。並提供一組條件式，將空間關係對應到轉變後的結果。然而，這組條件式由一系列的條件判斷所組成，導致運算沒有效率。在這本博士論文中，首先，我們將上述的條件式分成三種類型。根據這樣的分類，細心地為每一個空間關係指定一個16位元長度的位元字串。這樣的對應，可以將空間關係的轉換根據我們提出的位元運算—intra-exchange—來完成。此位元運算的時間複雜度為O(1)的CPU運算時間。除此之外，我們設計了一個物件索引技術來儲存物件之間的空間關係。此索引技術稱為Unique Bit Pattern Matrix。處理影像相似擷取時，我們不需要從索引中推導出原來的影像，再透過旋轉或翻轉此影像來獲得相對應的索引。然後根據推導出來的索引做相似度比對。相反地，透過位元運算和矩陣運算，我們的索引技術可以直接推導出影像旋轉或翻轉之後相對應的索引。透過推導出的索引來做相似度比對，可以保證我們設計的索引機制不會遺漏符合使用者條件的影像。在效能評估中，首先分析我們設計的索引機制在進行相似度擷取的時間複雜度。接著，我們呈現透過模擬測試效能的結果。結果顯示，我們的索引機制的效能表現，遠比以條件式為主的索引機制還要優異。依據影像中所包含的物件個數的不同，效能的提升介於13.64% 和53.23% 之間。

A symbolic image database system is a system in which a large amount of image data and their related information are represented by both symbolic images and physical images. Spatial relationships are important issues for similarity-based retrieval in many image database applications. How to perceive spatial relationships among the components in a symbolic image is an important criterion to find a match between the symbolic image of the scene object and the one being store as a modal in the symbolic image database. With the popularity of digital cameras and the related image processing software, a sequence of images are often rotated or flipped. That is, those images are transformed in the rotation orientation or the reflection direction. A robust spatial similarity framework should be able to recognize image variants such as translation, scaling, rotation, and arbitrary variants. Current retrieval by spatial similarity algorithms can be classified into symbolic projection methods, geometric methods, and graph-matching methods. Symbolic projection could preserve the useful spatial information of objects, such as width, height, and location. However, many iconic indexing strategies based on symbolic projection are sensitive to rotation or reflection. Therefore, these strategies may miss the qualified images, when the query is issued in the orientation different from the orientation of the database images. To solve this problem, researchers derived the rule of the change of spatial relationships in image transformation, and proposed a function to map the spatial relationship to its related transformed one. However, this mapping consists of several conditional statements, which is time-consuming. Thus, in this dissertation, first, we classify the mapping into three cases and carefully assign a 16-bit unique bit pattern to each spatial relationship. Based on the assignment, we can easily do the mapping through our proposed bit operation, intra-exchange, which is a CPU operation and needs only the complexity of O(1). Moreover, we propose an efficient iconic index strategy, called Unique
Bit Pattern matrix strategy (UBP matrix strategy) to record the
spatial information. In this way, when doing similarity retrieval, we do not need to reconstruct the original image from the UBP matrix in order to obtain the indexes of the rotated and flipped image. Conversely, we can directly derive the index of the rotated or flipped image from the index of the original one through bit operations and the matrix manipulation. Thus, our proposed strategy can do similarity retrieval without missing the qualified database images. In our performance study, first, we analyze the time
complexity of the similarity retrieval process of our proposed strategy. Then, the efficiency of our proposed strategy according to the simulation results is presented. We show that our strategy outperforms those mapping strategies based on different number of objects in an image. According to the different number of objects in an image, the percentage of improvement is between 13.64% and 53.23%.

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Image Content Descriptor . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Spatial Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Retrieval by Spatial Similarity . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Iconic Indexing Based on Symbolic Projection . . . . . . . . . . . . . 11
1.5 Motivations and Contributions . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . 18
2. A Survey of Iconic Indexing Strategies . . . . . . . . . . . . . . . . 19
2.1 2D Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 2D C-Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 2D B-Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 2D Projection Interval Relationships . . . . . . . . . . . . . . . . . . 28
2.5 Zhou and Ang's DT Approach . . . . . . . . . . . . . . . . . . . . . . 34
2.6 An Unique-ID-Based Matrix Strategy . . . . . . . . . . . . . . . . . . 39
2.7 Virtual Images for Similarity Retrieval . . . . . . . . . . . . . . . . . 43
2.8 2D Z-string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.9 9D-SPA Representation for Spatial Relationships . . . . . . . . . . . 47
2.10 9DLT Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.11 Triangular Spatial Relationship . . . . . . . . . . . . . . . . . . . . . 53
2.12 Archival and Retrieval Based on The B-Tree Structure . . . . . . . . 54
2.13 Archival and Retrieval Based on Statistic Measurements . . . . . . . 56
2.14 A Logarithmic Search Time Strategy for Exact Match Retrieval . . . 58
3. The Unique Bit Pattern Matrix Strategy . . . . . . . . . . . . . . . 61
3.1 Rules of Image Rotation and Re
ection . . . . . . . . . . . . . . . . . 61
3.2 The Matrix Manipulation and the Proposed Bit Operation . . . . . . 66
3.3 Unique Bit Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4 Spatial Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5 The Unique Bit Pattern Matrix . . . . . . . . . . . . . . . . . . . . . 73
3.6 Deriving Indices of The Rotated and Flipped Images . . . . . . . . . 76
3.7 Similarity Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4. Performance Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.1 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2 Future Research Direction . . . . . . . . . . . . . . . . . . . . . . . . 99
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

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