| 摘要: | 近年來隨著醫學影像設備的精進及普及，醫學影像數量的累積速度愈來愈快;對於醫學影像的傳輸、儲存、診斷分析、和治療支援需求日益增多，其中醫學影像壓縮和醫學影像分割技術是不可或缺的技術。在本研究中，我們基於統計推論 (statistical inference) 的原理，提出二個醫學影像壓縮方法及一個醫學影像分割方法。 在第一個醫學影像壓縮中，我們提出一個以小波 (wavelet) 為基礎具有動態預測 (adaptive prediction) 功能的無損影像壓縮方法。這個方法包含了三個主要的步驟: (i) 首先我們分析小波係數的相關性 (correlation analysis) ，透過這個分析我們挑選出一個適合用來壓縮醫學影像的lifting整數小波基底函數，並使用這個小波基底函數做影像的小波分解; (ii) 為了要決定那些小波係數應該被放在預測方程式的模型中 (那些小波係數要被當成是預測方程式中的預測變數)，才會得到最佳的預測，我們將HLi, LHi, 和 HHi (i = 1, 2, 3) 次頻帶 (subband) 上的小波係數以統計檢定 (statistical F Test) 進行檢定，經由統計檢定，我們得到三個分別對應於三個不同性質小波樹 (wavelet tree) 的預測方程式，即所謂的動態預測方法; (iii) 透過動態預測，我們得到各小波係數的預測值 (predicted value)，並由預測值與真正值 (original value) 相減計算出預測差值 (prediction error); 再以動態算術編碼法 (adaptive arithmetic encoder) 編碼預測差值。取代使用固定數目的預測變數 (predictor) 在固定的位置上做預測，我們提出以動態預測方法來克服預測變數 (predictor variables) 間的共線性問題 (multicollinearity)。我們所提的方法整合了相關性分析選擇小波基底函數，且利用動態預測挑選預測方程式中的預測變數，所以我們的方法能夠完成高準確的預測。我們也比較了其它著名的壓縮方法;在電腦斷層掃描影像 (CT)、核磁共振影像 (MRI)、和超音波影像 (ultrasound images) 的無損壓縮上，我們所提的方法能夠提供較高的壓縮率。 更進一步，為了提供多樣性region-of-interest (ROI) 的需求，包含了漸近式傳輸、多邊形ROI、多個ROI需求，我們提出了另一個具有多邊形 ROI之漸近式影像壓縮方法。首先，我們利用所提的分割及合併 (split and mergence) 演算法將凹多邊形ROI 分割成多個凸多邊形ROI，第二，我們利用列掃描方式 (row-order scan) 和動態算術編碼法來編碼這多個凸多邊形ROI裡的像點。第三，我們將影像中ROI區域內的像點以零值取代，並用lifting integer wavelet transform 來分解整個影像，第四，我們將此小波分解後的影像利用所提的第一個醫學影像壓縮方法來處理，此步驟執行完後會得到影像的預測差值;最後，我們再利用動態算術編碼法編碼預測差值。 為了要協助醫學影像上的分析和判讀，使得醫生們能夠更準確地辨識出相關的病因或症狀，我們提出一個以貝氏風險 (Bayesian risk) 為基礎的等階集合 (level set) 醫學影像分割方法。首先，影像分割問題被看作成一個影像點的分類問題。然後，透過像點分類時所造成的誤分類損失(the loss of misclassification)，我們定義相對應的貝氏風險 (Bayesian risk)。經由極小化此誤分類的風險，我們推論出能夠找到目標邊緣的等階集合演化泛函式 (level set evolution functional)。接下來，為了避免演化曲線 (propagating curves) 產生太多不規則形狀的區段和產生過多的小區域，影像的曲率 (curvature) 和梯度 (gradient) 資訊也被整合到此泛函式裡。最後，Euler-Lagrange 公式被用來推導等階集合演化方程式。比較其它等階集合方法，我們的方法是依賴像點分類最佳化決定所推導出的;所以我們的方法在理論和實務上都有可靠的信賴度。實驗也顯示這個方法能夠正確地擷取出複雜的目標物形狀，且對於多種不同的影像;例如，高雜訊低對比影像、各種類型雜訊影像、各種類型模糊影像、各類型醫學影像等，我們都能得到準確的分割結果。更進一步，我們所提的方法可以很容易的被延伸到多區域 (multiphase) 分割問題上。 在這篇論文中，統計推論是我們方法的主要基礎，在第一個方法中，由於使用相關性分析和統計檢定來完成壓縮;所以能完成較高的壓縮效果，在第二個方法中，我們將壓縮功能加以延伸，使得原方法能夠進一步地提供多樣性ROI的需求，在第三個方法中，統計決策理論 (statistical decision theories) 被整合到貝式等階集合分割方法 (Bayesian level set method) 中推導;因此所提的分割方法適合用在複雜的醫學影像分割上。 As image acquisition devices are rapidly evolving and extreme amount of medical images are daily produced, the needs for medical image transmission, storage, diagnostic analysis, and therapeutic support are ever-increasing. Among the technologies to achieve the needs mentioned above, medical image compression and segmentation are two of the indispensable technologies. In this dissertation, we propose the medical image compression and segmentation methods based on the principles of statistical inference. To achieve the compression of medical images, a lossless wavelet-based image compression method with adaptive prediction (WCAP) is proposed. The proposed method consists of three steps: (i) the correlations between wavelet coefficients are analyzed to identify a proper wavelet basis function; (ii) predictor variables are statistically test to determine which relative wavelet coefficients should be included in the prediction model; (iii) prediction differences are encoded by an adaptive arithmetic encoder. Instead of relying on a fixed number of predictors on fixed locations, we propose the adaptive prediction approach to overcome the multicollinearity problem of predictor variables. The proposed approach integrating correlation analysis for selecting wavelet basis function with predictor variable selection is fully achieving high accuracy of prediction. Comparing with several state-of-the-art methods, the proposed approach achieves a higher compression ratio on computed tomography (CT), magnetic resonance (MRI), and ultrasound images. Moreover, to provide the variety requirements of region of interest (ROI) coding containing progressive transmission, polygon-shaped ROI, and multiple ROIs, we further propose another progressive lossy-to-lossless compression technique. Firstly, split and mergence algorithms were proposed to separate concave ROIs into smaller convex ROIs. Secondly, row-order scan and an adaptive arithmetic coding were used to encode the pixels in ROIs. Thirdly, a lifting integer wavelet transform was used to decompose the original image in which the pixels in the ROIs had been replaced by zeros. Fourthly, the WCAP method was used to obtain predicted coefficients for difference encoding. Finally, the adaptive arithmetic coding was also adopted to encode the differences between the original and corresponding predicted coefficients. The proposed method only needs less shape information to record the shape of ROI and provides a lossy-to-lossless coding function; thus the approach is suitable for achieving the variety of ROI requirements including polygon-shaped ROI and multiple ROIs. Experimental results show that the proposed lossy-to-lossless coding with ROI function reduces bit rate as comparing with the MAXSHIFT method in JPEG2000. To assist doctors to analyze and explore the medical images, a level set method based on the Bayesian risk is proposed, so that doctors can make better diagnosis and accurately examine disease symptoms. At first, the image segmentation is formulated as a classification of pixels. Then the Bayesian risk is formed by the losses of pixel classification. Through minimizing the risk of misclassification, the level set evolution functional is deduced for finding the boundaries of targets. To prevent the propagating curves from generating excessively irregular shapes and lots of small regions, curvature and gradient of edges in the image are integrated into the functional. Finally, the Euler-Lagrange approach is used to find the iterative level set equation from the derived functional. Comparing with other level-set methods, the proposed approach relies on the optimum decision of pixel classification; thus the approach has more reliability in theory and practice. Experiments show that the proposed approach can accurately extract the complicated shape of targets and is robust for various types of images including high-noisy and low-contrast images. Moreover, the algorithm is extendable for multiphase segmentation. In this dissertation, we proposed medical image compression and segmentation methods which are mainly derived from the statistical inferences. In the first technique, we adopt correlation analysis to identify a proper wavelet basis function, and statistical F test to adaptively select predictor variable; thus the proposed WCAP approach can achieve high compression ratio on various medical images. In the second technique, we further extended the lossless compression technique to provide the variety of ROI requirements. In the third technique, the statistical decision theories are integrated into the derivation of Bayesian level set method; thus the proposed segmentation method is suitable for complicated medical image segmentation. |
