Researches of the Coding Tree Assignment Scheme with Improved Search Order Coding Technique to the Compression of Vector Quantization Indices

Vector Quantization (VQ) is a popular compression technique for images. It can efficiently compress images with a very small capacity of storage. Recently, some low complexity index coding schemes have been proposed for further coding the output indices of VQ by making use of the correlation between neighboring vector-quantized blocks. Search-Order Coding (SOC) is one of the well-known schemes. It is a lossless compression for VQ indices, does not introduce extra quality degradation and requires a small amount of computation. In this dissertation, we propose three lossless VQ index compression algorithms to enhance the coding efficiency of the original VQ. Coding Tree Assignment Scheme with Improved Search-Order Coding algorithms (CTAS-ISOC) are first proposed to enhance the coding efficiency of the original SOC by exploiting the correlations of the neighboring blocks using the left-pair and upper-pair patterns in the index domain. The essential techniques consist of three major elements: the Neighboring Index Code Assignment (NICA), the Left-pair Search-Order Coding (LSOC), and the Upper-pair Search-Order Coding (USOC). The NICA approach assigns a short code to the current index by using the statistics on the indices of the neighboring blocks. The LSOC (USOC) compares the current left (upper) index pair with previous index pairs in a predefined search path. Since the predefined search path is exploited with a correlation viewpoint, both LSOC and USOC achieve better compression than the original SOC. Experimental results demonstrate the effectiveness of the proposed scheme in comparison with some existing popular lossless index coding schemes. Since the computation time of LSOC and USOC in the proposed CTAS-ISOC scheme depends on the selection of the search range in the index map, and both algorithms are based on the concept of SOC, the computation complexity is larger than SOC. Thus, we propose the Modified Coding Tree Assignment Scheme (MCTAS) to further improve the coding performance of CTAS-ISOC by the Dynamic Index Table Coding (DITC). The DITC technique exploits the correlation of neighboring index pairs not in the original vector-quantized index map but in the temporarily constructed index table that has been classified and updated for each current index. The searching matched index in a previously qualified index table results in low time complexity. In addition, the identical index table can be regenerated in the reconstruction process of the index map at the decoder end. Experimental results show the time complexity of MCTAS is more efficient than that of CTAS-ISOC. Due to the dynamic index table is updated whlie the index is generated online from VQ decoder every time, the new discussion is that how to improve the performance of updating the dynamic index table. Therefore, we further present an efficient lossless compression algorithm, the Coding Tree Assignment Scheme with Principal Index-Pattern Coding Algorithm (CTAS-PIPCA), to encode image VQ. The new coding model is designed on the basis of the schemes proposed in the previous works to further improve the coding performance of CTAS-ISOC by PIPCA. The PIPCA technique , instead of ISOC in CTAS-ISOC, exploits the correlation of neighboring index-pairs not in the original vector-quantized index map but in the principal index-pattern table which is generated from the two dimensional histogram of index-patterns in the training stage. The searching matched index in the principal index-pattern table results in lower time complexity than CTAS-ISOC. The results also show that the proposed technique apparently reduces the bit rate as compared to the conventional VQ and other existing popular lossless index coding schemes, such as SOC and CTAS-ISOC.向量量化(Vector Quantization, VQ) 是一種很普遍的影像壓縮技術，並且具有很高的壓縮效率使得影像的平均位元率可以有效地降低。近年來，一些低複雜度的索引值編碼技術相繼被發表在各影像期刊中，這些技術利用了編碼簿或索引值圖中各方塊的關聯性或其他數學特性，進一步地將影像經過向量量化輸出後的索引值再進行第二次的壓縮而得到更高的壓縮效率。例如，搜尋順序編碼(Search-Order Coding, SOC)就是其中最著名的演算法，它具有無失真再壓縮索引值不會產生額外品質的減損且只需要少量的運算量。 在本論文中，我們提出三種應用索引值壓縮演算法運用於傳統的向量量化編碼中，進而更加提高原始向量量化的編碼壓縮率。首先提出的第一種演算法為編碼樹法結合改良型搜尋順序編碼技術(Coding Tree Assignment Scheme with Improved Search-Order Coding algorithms, CTAS-ISOC)，此演算法利用在索引值圖中具有相鄰關係的左索引對及上索引對圖樣用以改善原始的SOC 編碼技術。CTAS-ISOC包含三個主要技術組合而成:鄰近索引值指定法(Neighboring Index Code Assignment, NICA) 、左索引對搜尋順序編碼法(Left-pair Search-Order Coding, LSOC)及上索引對搜尋順序編碼法(Upper-pair Search-Order Coding, USOC)等三種技術。NICA方法是根據鄰近方塊排列的情況及出現的機率統計結果決定了目前輸入的索引值方塊應該與那些鄰近的方塊做匹配比對；LSOC(USOC)則是以目前輸入的左(上)索引對與索引值圖中的索引對依照順時針方向依序進行匹配的比較，由於索引對利用了圖形中的索引值方塊關聯性，進而能有效地改善原始SOC的編碼效能。實驗結果顯示所提出的CTAS-ISOC與其他近來所提出的無失真索引值編碼技術具有明顯的壓縮率提升。 由於CTAS-ISOC中的LSOC或USOC此兩種方法是SOC方法的再衍伸，在數學上的運算複雜度是類似的，不過其運算時間與在索引值圖中搜尋的範圍大小有關，因此，LSOC或USOC的運算量會比SOC來得大一些。於是我們提出改良式的編碼樹法(Modified Coding Tree Assignment Scheme, MCTAS)，利用了動態索引值表編碼演算法(Dynamic Index Table Coding, DITC)改善了CTAS-ISOC 中的LSOC或USOC的編碼效率；DITC演算法是利用了每次輸入索引值時動態建立分類的左索引對及上索引對的索引對表，改善了LSOC(USOC) 必須在索引值圖中重複執行尋找符合左(上)索引值的合格索引對的動作，並且以改良的編碼順序執行匹配，進而改善編碼的效率。此外，相同的左索引對及上索引對的索引對表亦可以在解碼端透過索引值圖重建的過程中動態產生出來，而不需要透過傳輸的方式建立。實驗結果顯示MCTAS比CTAS-ISOC有更低的位元率且亦降低了運算複雜度。 由於DITC是線上處理時根據每次向量量化產生出來的索引值再動態建立左(上)索引對表，因此，如何改善每次動態產生索引對表成為新的課題。我們提出了編碼樹法結合主要索引值圖樣編碼演算法(Coding Tree Assignment Scheme with Principal Index-Pattern Coding Algorithm, CTAS-PIPCA)來改善CTAS-ISOC及CTAS-DITC編碼效率。其中的PIPCA方法主要為透過離線訓練的方式，以統計出現的左(上)索引對機率，建立編碼所需的左索引對及上索引對值表。如此在編碼過程中只需查表進行編碼動作，完全不需要在索引值圖中做任何匹配的動作，進而減低運算量且也達到良好的編碼壓縮率。實驗結果顯示CTAS-PIPCA與其他索引值壓縮法(例如SOC, MSOC, LCIC, ICS, AICS, and ISAIAL)具有更高的壓縮率及較低的位元率，亦說明本論文所提的技術能有效地提高VQ影像之壓縮率。Abstract i 摘 要 iv Acknowledgement vii Contents ix Figure Captions xii Table Captions xiv Chapter 1 Introduction 1 1.1 Research Motivation 1 1.2 Research Contributions 3 1.3 Dissertation Organization 4 Chapter 2 Related Techniques 6 2.1 Review of the Vector Quantization 6 2.2 Review of VQ Index Compression 8 2.2.1 Review of the Search Order Coding Algorithm 10 2.3 Review of the Shannon-Fano Coding Algorithm 12 Chapter 3 The Coding Tree Assign ment Scheme with Improved Search-Order Coding Algorithm (CTAS-ISOC) 15 3.1 The CTAS-ISOC Technique 15 3.1.1 Coding Tree Assignment Scheme (CTAS) and Neighboring Index Code Assignment (NICA) 17 3.1.2 Left-Pair Search-Order Coding (LSOC) 22 3.1.3 The LSOC (USOC) Encoding Algorithm 24 3.1.4 Upper-Pair Search-Order Coding (USOC) 26 3.2 Experimental Results 27 3.3 Conclusions 34 Chapter 4 Index Compression for Vector Quantization Using Modified Coding Tree Assignment Scheme 35 4.1 The Modified Coding Tree Assignment Scheme 35 4.1.1 Structure of the Proposed Coding Algorithm 37 4.1.2 Dynamic Index Table Coding (DITC) 41 4.2 Experiment Results and Discussion 52 4.3 Conclusions 56 Chapter 5 Index Compression for Vector Quantization Using Principal Index-Pattern Coding Algorithm 57 5.1 The Proposed Coding Algorithm 57 5.1.1 Principal Index-Pattern Coding Algorithm (PIPCA) 59 5.1.2 The Coding Tree Assignment Scheme with Principal Index-Pattern Coding Scheme (CTAS-PIPCA) 67 5.2 Comparison with JPEG2000 73 5.3 Conclusions 75 Chapter 6 Complexity analysis 76 6.1 Computation Complexity of the CTAS-ISOC Coding Scheme 76 6.2 Computation Complexity of the MCTAS Coding Scheme 80 6.3 Computation Complexity of the CTAS-PIPCA Coding Scheme 83 Chapter 7 Conclusion 85 References 87 Publication List 9