| 摘要: | 從一連串的平行切面影像重建出物體或人體器官的3D表面模型是醫學及工業上的一項重要應用；例如，偵測、診斷、模擬、及訓練等。在本論文的研究中，我們提出了三項相關技術：影像雜訊去除 (image denoising)、邊線偵測 (edge detection)、及模型重建 (model reconstruction) 來達成自動化重建表面模型的目的。首先，我們提出一個關聯隱藏馬可夫樹模式 (contextual hidden Markov tree model) 來分析影像小波係數間的關係，再配合經驗貝氏估計法 (empirical Bayesian estimation) 去除影像中的高斯雜訊。隱藏馬可夫樹模式 (hidden Markov tree model) 是作用在小波係數上的一個新穎統計模式。雖然，隱藏馬可夫樹模式可以完全描述小波係數樹狀結構的持續性 (persistence property)，但並不能將同層小波係數間的群聚性 (clustering property) 描述得很好。而我們提出的關聯隱藏馬可夫樹模式則是透過對於每個小波係數增加延伸係數 (extended coefficient) 來加強隱藏馬可夫樹模式的群聚性，而且不改變小波樹狀結構的特性。在實驗中，我們所提的關聯隱藏馬可夫樹模式作ㄧ維信號及二維影像雜訊去除，其結果幾乎都比原來的隱藏馬可夫樹模式所作的結果好；而且，對於相同雜訊去除的結果，我們的模式都比隱藏馬可夫樹模式需要更少的迴圈次數來估計參數。 其次，我們提出一個兩階段邊線偵測的方法來擷取物體輪廓。對一張影像而言，坡度影像 (gradient image) 是用來描述相鄰點間的差異。傳統的邊線偵測方法只依賴坡度影像的資訊來擷取邊線，其結果容易產生雜訊及斷線。在本研究中，我們提出了關聯濾波邊線偵測器 (contextual-filtered edge detector) 及多重解析度邊線追蹤器 (multiscale edge tracker) 的兩階段邊線偵測法來解決上述問題。邊線偵測器偵測出大部份的邊線，而追蹤器則進一步精煉出邊線結果；如此能減少雜訊及模糊的影響。而且，我們所擷取出來的邊線幾乎都是單一像素寬度的邊線，非常適合後續的直接應用。在實驗中，我們以六個小波基底函數 (wavelet basis function)，並以品質及量化的比較 (qualitative and quantitative comparisons) 方式分析我們的方法與其他方法的差異。實驗結果顯示，我們所提的方法都比其他以小波為基礎的邊線偵測器及Canny偵測器更能擷取出適當的邊線結果。 最後，我們提出一個多樣性的表面模型重建方法來從一連串的平行輪廓中重建出物體表面模型。如同大部份類似目的的方法，我們所提的方法也僅考慮兩層相鄰切片影像中物體輪廓的對應及三角化而已，而整個物體的表面模型則可經由整合所有三角網格的結果來獲得。然而，我們所提的方法比其他方法使用了更多的準則 (criterion) 及規則 (rule) 來獲得更合理及較少扭曲現象的模型。我們的方法包含了七個步驟：(i) 首先找出相鄰兩層間輪廓配對的候選者；(ii) 從候選配對輪廓中找尋特徵點 (feature point) 加以配對連結；(iii) 使用區域性追蹤法來找尋相似輪廓段落；(iv) 找尋出交錯線段並三角化該片段；(v) 找尋兩層輪廓間最近點並連結；(vi) 擷取出裂縫多邊形；最後，(vii) 我們提出一個多目標動態規畫演算法 (multi-objective dynamic programming) 將相似輪廓段落及裂縫多邊形編織成幾個三角網格，並與之前的片斷網格整合成一個完整的三角網格。比較我們的方法與其他方法，我們的方法有下列優點：(1) 每一層切片影像允許有多個及巢狀的輪廓；(2) 我們有一個合理的資料結構來描述切片影像中輪廓的關係以幫助後續的表面模型重建；(3) 我們提出的方法可多方面的考量以構建合理且較少扭曲的模型；(4) 對於複雜的模型，我們也能夠合適地重建出來。 Reconstructing 3-D surface models from a series of parallel planar cross sections of objects or bodies is important for medical and industrial applications, such as detection, diagnosis, simulation, and training. In this study, we propose three techniques: image denoising, edge detection, and model reconstruction to achieve the purpose of automatic surface model reconstruction. Firstly, we propose a wavelet-based image denoising method using the proposed contextual hidden Markov tree (CHMT) model to remove noise from images corrupted with Gaussian noise. The hidden Markov tree (HMT) model is a novel statistical model for image processing on wavelet domain. The HMT model captures the persistence property of wavelet coefficients, but lacks the clustering property of wavelet coefficients within a wavelet scale. The proposed CHMT model enhances the clustering property of the HMT model by adding extended coefficients associated with wavelet coefficients without changing the wavelet tree structure. In experiments, the proposed CHMT model produced almost better results than the HMT model produced for image denoising. Furthermore, the CHMT model needs fewer iterations of training than the HMT model needs to get the same denoised results. Secondly, a two-stage edge extraction approach is proposed to extract object contours. A gradient image describes the differences of neighboring pixels in the original image. Traditional edge detectors only depending on the gradient information will result in noised and broken edges. Here we propose the two-stage edge extraction approach with contextual-filtered edge detector and multiscale edge tracker to solve the problems. The edge detector detects most edges and the tracker refines the results as well as reduces the noised or blurred influence; moreover, the extracted results are nearly thinned edges which are suitable for further applications. Based on six wavelet basis functions, qualitative and quantitative comparisons with other methods show that the proposed approach extracts better edges than the other wavelet-based edge detectors and Canny detector extract. Finally, a versatile method for surface model reconstruction from serial planar contours is proposed. Like most similar-purposed methods, the proposed method tiles triangles between contours on every two adjacent slice images, then the surface model is constructed by aggregating all tiled triangles; however, the proposed method uses more criteria and rules than the other methods use to construct reasonable and less-distorted models. The proposed method consists of seven stages: (i) contour-pair candidates are first found between two adjacent slices; (ii) feature points on the contour pairs are extracted to link; (iii) similar contour segments are extracted by a tracking algorithm; (iv) cross lines are found to tile partial triangles; (v) near points are found to link; (vi) cleft polygons are extracted; at last, (vii) the proposed multi-objective dynamic programming algorithm is used to construct the triangulated strips formed by the extracted similar contour segments and cleft polygons. Comparing with other similar-purposed methods, the proposed method has the advantages: (i) more than one (cross) contour are allowed in a slice image; (ii) reasonable data structure describing the relationship among contours on a slice image is proposed for helping the surface reconstruction; (iii) the proposed method is versatile to construct reasonable and less-distorted models; (iv) complex models can be properly reconstructed. |
