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象徵圖片所組成。為了能夠從影像資料庫中尋找出我們有興趣的資料，我們必須有能力推論組成圖片的物件彼此之間的空間關係。空間關係推理的技術已經被應用在影像資料庫上，「二維字串」這樣的空間索引技術就是相當成功的一個案例。在這篇論文中，為了讓圖像比對能夠更為精確，我們將既有的比對由3個層次增加為6個。Lee和Hsu完整地推演出在一維空間中兩兩物件之間的空間關係總共有13種，他們單純地將這13種空間關係應用到二維平面上，進而推導出169種空間關係，但是，他們卻忽略了考慮「方位」並不存在於一維空間上，卻存在於二維空間中。因此，單單169種空間關係無法完整地詮釋在二維空間中兩兩物件彼此之間所形成的空間關係所有可能出現的情形。為了解決這樣的窘境，我們以原本的169空間關係為基礎，連帶將九個「方位」的空間關係一併考慮，進而整理出在二維平面上的空間關係應該有289種之多。再則為了使問題簡化，在過去針對空間圖像索引所提出的一系列方法中，會將圖片中的每一個物體用最小矩形來表示，因此，實際上我們是藉由最小矩形來推導出圖片中兩兩物件的空間關係。由此可知，圖片中物件彼此之間真實的空間關係與藉由最小矩形所推導出來的空間關係會有所出入，我們提議將物件彼此之間的空間關係—拓樸關係—這樣的資訊也一併紀錄下來，這樣就可以解決因最小矩形所帶來的困擾。一個好的存取方法可以讓我們有效率地從擁有龐大資料的影像資料庫中擷取出我們想要的資訊，簽章檔案可以被視為一種篩子，事先將不適當的資訊過濾掉。為了要完整地表達二維平面上兩兩物件之間的空間關係，以及解決最小矩形所帶來空間關係上模稜兩可的困擾，我們提出了以擷取相似圖形為主的一個混合方式為基礎的簽章技術。在效能模擬程式中，拿我們提出的方法，和Lee等人所提出的以2D B-string為基礎的簽章方法做比較之後，可以顯示出，我們提出的簽章方法其辨正率較高，並且，用來儲存簽章檔案所需要的空間也相對地較少。在某些情形下，我們的方法其辨正率可以高達42.18%，在相同的情況下，Lee等人所提出的簽章方法卻只能達到16.66%的辨正率。而在儲存空間的需求方面，在最糟糕的情形下，我們需要1686個位元來儲存簽章檔案；然而，在任何情形下，Lee等人所提出的方法總是需要2015個位元這樣多的儲存空間。

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. 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. Spatial reasoning techniques have been applied to pictorial database, in particular those using 2D strings as an index representation have been successful. In this thesis, we extend the existing three levels of type-i similarity to more levels to aid similarity retrieval more precisely. There are 13 spatial operators which
were introduced by Lee and Hsu to completely represent spatial relationships in 1D space. But, they just combined the 13 spatial relationships on x- and y-axis to represent the spatial relationships in 2D space by 13 times 13 =
169 spatial relationships. However, the 169 spatial relationships are still not sufficient to show all kinds of spatial relationships between any two objects in 2D space. For example, the directional relationships, like North or South West, exist in 2D space and is difficult to be deducted from those 13 spatial operators. Thus, we add the nine directional relationships to the
169 spatial relationships in 2D space. In this way, we can distinguish up to 289 spatial relationships in 2D space. Moreover, in our proposed strategy, we also take care of the problem caused by the MBRs. In most of the previous approaches for iconic indexing, for simplifying the concerns, they apply the MBRs of two objects to define the spatial relationship
between them. The topological relationships, however, between objects can be quite different from the spatial relationship of their respective $MBR$s. Therefore, sometimes, it is hard to correctly describe the spatial relationship of the objects in terms of the relationships between their corresponding MBRs. To improve this drawback resulted from MBRs, we adopting the concept of topological relationships in our proposed strategy. Good access methods for large image databases are important for efficient retrieval. The signature files can be viewed as a preselection searching filter to prune off the unsatisfied images. In order to solve the ambiguity of the MBRs and to present the spatial
relationships in two dimensional space completely, we propose a hybrid approach-based signature extraction method for similarity retrieval. From our simulation study, we show that our approach can provide a higher rate of a correct match and requires a smaller storage cost than Lee et al.'s 2D B-based signature approach. In some case, the correct match rate based on our
proposed strategy can be up to 42.18%, while it is just 16.66% in Lee et al.'s strategy. Moreover, the worst case of the storage cost required in our proposed strategy is 1686 bits. But, it always needs 2015 bits in Lee et al.'s strategy.

1.Introduction . . . 1
1.1 Problems in Image Databases . . . 1
1.2 Iconic Indexing . . . 2
1.3 Access Methods . . . 7
1.4 Similarity etrieval . . . 9
1.5 Motivations . . . 10
1.6 Organization of the Thesis . . . 18
2. A Survey of Iconic Indexing Strategies . . . 19
2.1 2D trings . . . 19
2.2 2D C-Strings . . . 21
2.3 9DLT Matrix . . . 22
2.4 2D B-Strings . . . 25
2.4.1 Representation . . . 25
2.4.2 Spatial Relationships . . . 27
2.4.3 Query Types and Similarity Retrieval . . . 28
2.4.4 Access Methods . . . 30
2.4.4.1 Signature Files of 2D B-Strings . . . 32
2.4.4.2 Access Method for Retrieval by Objects . . . 33
2.4.4.3 Access Method for Type-0 Similarity Retrieval . . . 33
2.4.4.4 Access Method for Type-1 Similarity Retrieval . . . 35
2.4.4.5 Access Method for Type-2 Similarity Retrieval . . . 37
2.4.4.6 Integration of All Type-i Signature Files . . . 38
2.5 Zhou and Ang's DT Approach . . . 39
3. The Hybrid Approach . . . 44
3.1 The Extended Type-i Similarity . . . 45
3.2 Four New Spatial Strings . . . 51
3.2.1 Spatial Category Strings (SCS) . . . 52
3.2.2 Nine Direction Code Strings (DCS) . . . 54
3.2.3 Identication Number Strings (INS) . . . 55
3.2.4 Topological Relationship Strings (TRS) . . . 62
3.3 Record Signatures and Block Signatures . . . 65
3.3.1 An Example . . . 71
3.4 Object and Type-i Similarity Retrieval . . . 73
3.4.1 Query of Object Similarity . . . 73
3.4.2 Query of Type-0 Similarity . . . 75
3.4.3 Query of Type-1 Similarity . . . 76
3.4.4 Query of Type-1.5 Similarity . . . 78
3.4.5 Query of Type-2 Similarity . . . 80
3.4.6 Query of Type-2.5 Similarity . . . 80
3.4.7 Query of Type-3 Similarity . . . 81
4. Performance Study . . . 82
4.2 Simulation Results . . . 84
5. Conclusion . . . 95
5.1 Summary . . . 95
5.2 Future Work . . . 96

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