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JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 1579-1591 (2008) 謝豐陽1，王嘉銘2，李俊傑2，范國清2,3 1 大華技術學院 2 國立中央大學 3 佛光大學 （ JISE ） 報告者：林維達 目錄 引言 文獻探討 研究方法 研究結果 結論 摘要 引言 Lossless image compression has been an attractive subject being studied for decades due to its importance in many applications. During recent years, many lossless image compression schemes have been proposed based on the combination of the rationale of adaptive prediction and adaptive entropy coding . In the next section, we will introduce the three adaptive predictors, MED, GAP, and MMSE, and a comparison is given among the three predictors. 無損圖像壓縮由於其在許多應用中的重要性一直是這數十年研究裡引人注意的課題。在最近幾年，許多 無損圖像壓縮方案基礎上，提出了合併適應預測和適應熵編碼的理念。 在下一節中，我們將介紹三適應預測，MED、GPA和MMSE，並比較三個預測。 文獻探討 圖1.P0相鄰像素之配置 圖2.光柵掃描順序 文獻探討 → 文獻探討 1.MED (median edge detector) a=S(P1) b=S(P2) c =S(P3) According to reference , MED predictor tends to choose a (west neighbor) when there is a horizontal edge, and to choose b (north neighbor) when there is a vertical edge. 根據文獻，MED預測當有一個水平邊緣時趨向選擇 （西鄰），且有一個垂直邊緣時選擇 B（北鄰）。 文獻探討 2.GAP (Gradient-adjusted prediction) w = S(P1) n = S(P2) nw = S(P3) ne = S(P4) ww = S(P5) nn = S(P6) nne =S(P9) which represent the north, west, northeast, northwest, north-north, west-west, and north-northeast neighbors of P0, respectively. Two gradient functions (vertical and horizontal gradients) can then be estimated by 這分別代表了以P0的北，西，東北，西北，北北，西西，北東北。 然後兩個功能梯度可以估算（垂直和水平梯度） 文獻探討 3.MMSE (minimizing the mean square errors) The purpose of MMSE-based predictors is to find an optimal linear predictor for a fixed number T (we take T= 220 here) 其MMSE的基礎預測目的是找到一個最佳線性預測的固定號 T 文獻探討 預測比較 表1.MED、GAP和MMSE一階熵碼比較 研究方法 圖像 初始化 預測 最佳化 相同 壓縮率 運算 辨識 圖3. 區塊自適應預測計劃流程圖 研究方法 表2. 每個σns和cns在環境與價值的值 研究方法 圖像 初始化 預測 最佳化 相同 壓縮率 運算 辨識 圖3. 區塊自適應預測計劃流程圖 研究結果 圖4.測試圖像集（8位元灰度） 研究結果 表3.比較編碼計畫(bpp) 研究結果 圖5.本實驗與MRP殘餘熵碼比較(a)飛機(b)狒狒(c)形狀(d)氣球 研究結果 表4.本實驗與MRP初始與最後殘餘熵值比值 表5.由原文最後殘餘熵值比較修正新的U方案 結論 In the practical view, the computational complexities of lossless image coders are usually concerned. JPEG-LS and CALIC are typical practical coders, which can compress an image in less than one second. On the other hand, TMW and MRP method are designed for finding the ultimate compression ratio. 在實踐的觀點，通常關心無損圖像編碼器的計算複雜性。JPEG-LS和CALIC是典型的實際編碼器，它 可以在不到一秒鐘壓縮圖像。另一方面，TMW和MRP的方法是專為尋找極限壓縮比。 結論 The computational complexity of our proposed method is approximate to that of MRP in encoding processes. However, the decoding process of our method is slower than MRP due to the utilization of the MMSE predictor. In addition, the initial residual entropy in the encoding process is lower than that of MRP and the initial residual entropy is relatively closer to the final residual entropy than that in MRP. 我們提出的編碼過程計算方法的複雜認為是近似 MRP的。然而，解碼過程中我們的方法慢 於 MRP的原因是利用了MMSE的預測。 此外，在初始殘餘熵編碼過程是低於MRP，而且與MRP相較下，最初的剩餘熵比較接近最 終殘餘熵比。 摘要 This paper proposes a lossless image compression scheme integrating well-known predictors and Minimum Rate Predictor (MRP). Minimum Rate Predictor is considered as one of the most successful method in coding rates for lossless grayscale image compression so far. In addition, the residual entropy of the proposed scheme in the first iteration is lower than that of MRP and is relatively closer to the final residual entropy than that in MRP. This phenomenon will allow our proposed scheme to be terminated in less iterations while maintaining a relatively good compression performance. 本文提出了一種無損圖像壓縮方案結合著名的預測和最小比率預測（MRP）。最小比率預測被認為是一 個編碼率灰度圖像無損壓縮至今最成功的方法。 此外，在第一次迭代殘餘熵比的建議計劃是低於MRP的，而且與MRP比較而言較接近最後的殘餘熵比。 這種現象將允許我們提出的計劃將停止在更少的迭代同時保持了比較好的壓縮性能。 End… & Happy New Year