| 摘要: | 影像分割 (image segmentation) 是影像處理中的基本工作，可視為分析影像時的前處理。紋理 (texture) 則是影像的重要特徵之一，可用來識別影像中某些有興趣的物件或區域。此外，紋理分割在視覺感知應用上具有相當的重要性，可以應用於工業自動化檢測、文件影像區塊分割、影像擷取、生物醫學影像分析，及遙測影像；例如，空照圖、衞照圖，與合成孔徑雷達影像的分析。如何從影像中找出代表紋理特徵的資訊是非常具有挑戰性的工作。基本上，紋理在影像內容中，看似具有特殊規則性的變化，但其中又包含了許多難以分析的細節。主要的問題在於，真實紋理影像在方向上或尺度上並非完全具備一致性的變化。
一般而言，紋理分割的演算方法可以廣泛地區分為四種：結構性 (structural)、統計 (statistical)、模式 (model-based)，及時頻資料轉換 (transform) 方法。結構性方法以紋理成份做為紋理特徵的樣板做分類。統計性方法是計算相鄰影像像素的一階、二階或更高階的統計量，並將其當作紋理的區域特性做分類。模式方法則將影像資料建構成機率模式或線性組合模式，以模式參數做為區分不同紋理的依據。時頻資料轉換方法則是透過傅利葉轉換、Gabor轉換、或小波轉換等工具，將影像資料轉換為頻率域資訊，藉由分析頻率特性以區分不同紋理類別。
由於小波轉換不僅提供了頻率資訊，同時還保留了空間資訊；而且建立在小波係數上的隱藏馬可夫樹 (hidden Markov tree, HMT)，具有小波係數的統計特性，能夠對紋理影像提供良好的表達方式。所以我們的研究即以小波樹狀資料結構為基礎建立模式參數執行紋理影像分割。
紋理分割包含了紋理樣本訓練與紋理像素分類的兩個階段。在紋理樣本訓練階段中，每一種紋理樣本的特徵都會被擷取出來；而在紋理像素分類階段，則擷取像素特徵，並與已知類別的紋理樣本特徵比對，最後將每一個影像區塊分類為適當的紋理類別。
在本研究中，我們提出了一個基於關聯式隱藏馬可夫樹 (contextual hidden Markov tree, CHMT) 模式做多重解析度紋理影像分割的方法。在紋理樣本訓練階段，我們利用高斯混合模型 (Gaussian mixture model, GMM) 建構影像小波係數的關聯式隱藏馬可夫樹模式，以EM演算法 (expectation-maximization algorithm) 訓練紋理樣本的關聯式隱藏馬可夫樹模式之參數，將此參數做為紋理特徵的表示式。隱藏馬可夫樹模式是一個樹狀結構的機率模式，在不同尺度間的小波係數具有繼承特性 (persistence property)，但缺少同一尺度內係數的聚集特性 (clustering property)。我們在隱藏馬可夫樹中額外增加小波係數與其鄰近點的連結，可同時獲得小波係數間強健的繼承特性與弱的聚集特性，而成為同時保有不同尺度間與同一尺度內小波係數關聯性的關聯式隱藏馬可夫樹模式。
在紋理影像分割階段，我們採用貝氏分割 (Bayesian segmentation) 方法，利用關聯式隱藏馬可夫樹模式參數計算各種尺度之分割影像在各個紋理模型參數下的最大相似度 (maximum likelihood)，選擇具有最大相似度的紋理類別做為分割結果。最後，以邊界精細化 (boundary refinement) 方法依照不同解析度的分割結果，區分出同質區域及邊界區域。同質區域傾向採用低解析度的分割結果，而邊界區域則傾向採用高解析度的分割結果。
更進一步的研究，由於離散小波轉換 (discrete wavelet transform, DWT) 缺少移動不變 (shift invariance) 與多方向性 (directionality) 的特性，我們改用雙重樹狀結構的複數小波包轉換 (complex wavelet packet transform, CWPT) 取代原本的離散小波轉換執行紋理分割；如此除了改進了移動不變與多方向性的特性外，因小波包轉換將高頻成份再分解，可以得到更多的高頻資訊，有助於紋理細節的分析。
我們所提出的 “基於關聯式隱藏馬可夫樹模式做多重解析度紋理影像分割” 方法具有以下幾項優點：(1)多尺度分析使得影像分割結果不受固定尺寸之分類視窗的影響。(2)高斯混合模型的小波係數可以有效地表現具非穩態信號特性的紋理特徵。(3)關聯式隱藏馬可夫樹模式同時俱備不同尺度間小波係數的關聯性與影像中鄰近點小波係數的關聯性。(4)以複數小波包轉換取代離散小波轉換，除了增加中高頻資訊分析能力外，並強化了信號移動不變與具備多方向的特性。
我們使用人工合成的紋理影像和空照影像驗證我們所提的紋理分割方法，並與其他方法比較。我們提出的關聯式隱藏馬可夫樹模式，結合了不同尺度間小波係數強健的繼承特性，以及同尺度間微弱的聚集特性。關聯式隱藏馬可夫樹模式與假設小波係數互相獨立的隱藏馬可夫模式，或是僅有小波係數不同尺度繼承特性的隱藏馬可夫樹模式比較，都能有更好的紋理特徵表達能力。因此，在實驗中，在在顯示我們的方法有較好紋理影像分割效能。;Image segmentation is a fundamental task in image processing applications. It is usually taken as a pre-processing for analyzing images. Textures are important appearance features in images those can be used to identify objects or regions of interesting; thus, texture segmentation plays an important role in visual perception. Texture segmentation has been used to industrial automatic inspection, document image segmentation, image retrieval, biomedical image analysis, and remote sensing image applications such as aerial photos, multispectral satellite images, and synthetic aperture radar images. How to express the information of textures is always a challenge task. In general, Texture characteristics are variant with special regularity in pixel values; however, textures contain many details those are hard to understand. The main hard issue is that texture contents always involve non-uniform variations in orientation and scaling.
In general, the algorithms of texture segmentation are broadly classified into structural, statistical, model-based, and transform approaches. Structural methods use texture elements to describe textures. Statistical methods use gray-level relationships between neighboring pixels to describe the local texture properties in the first-order, the second-order, or higher-order statistics. Model-based methods model images as different probability or linear combination models and use the model parameters to describe the texture features. The transform methods transfer images into the frequency domain using Fourier, Gabor, or wavelet transform. Then the frequency properties are used to discriminate from distinct textures.
The wavelet transform not only provides frequency information but also keeps the resolutions on spatial domain. Moreover, the hidden Markov tree (HMT) model based on wavelet domain captures the statistical properties of the wavelet coefficients and is suitable for expressing an image with singularities. Therefore, we focus our attention on the study of texture image segmentation on model based method, especially for the wavelet-based HMT models.
Texture segmentation is generally separated into two stages, one is training and the other is segmentation. The training stage extracts features of all kinds of textures in training samples. The segmentation stage extracts the features from segmented images and compares the features with all texture features from training samples. Then every image region is classified into the most feasible texture class.
In this study, we propose a multiscale texture image segmentation method based on contextual hidden Markov tree (CHMT) models. In training stage, we construct the CHMT model based on wavelets using Gaussian mixture model (GMM) and then train the model parameters as textures information using the expectation-maximization algorithm. The HMT model is a probabilistic model with tree structure for capturing persistence properties of wavelet coefficients without considering clustering properties. We here proposed the CHMT model to enhance the clustering properties of the HMT model by adding extended coefficients associated with wavelet coefficients in every scale. The CHMT model keeps stronger wavelet persistence property and weaker clustering property, simultaneously.
In texture image segmentation stage, we adapt the Bayesian segmentation technique to compute the maximum likelihood between the segmented image and each texture in training set. We use CHMT model parameters to compute likelihoods for every dyadic square at every scale in an image which will be segmented. Then the boundary refinement method distinguishes the each dyadic square into homogenous region or boundary region by the segment results from every scale. The segmentation result of homogenous region follows the result of coarser scale and boundary region follows the result of finer scale.
In the above approach, the discrete wavelet transform (DWT) lacks of shift invariances and directional sensitivities. We replace the DWT by a complex wavelet packet transform (CWPT) to include the properties of shift invariances and directional sensitivities. At the same time, the wavelet packet captures more high and intermediate frequency information that will help for analyzing the details of textures.
The proposed method provides several superior properties. First, the multiscale analysis makes the segmentation results be independence from the size of classification window. Second, the wavelet coefficients with GMM present the non-steady signals efficiently. Third, the CHMT model takes into account both inter and intra dependences between coefficients, simultaneously. Fourth, using the dual tree CWPT, the high and intermediate frequency components of the image are taken as important features to analysis textures. Moreover, the dual-tree CWPT has nearly shift invariant properties and good directional sensitivities which benefit the results of texture segmentation.
At last, we demonstrate the performance of the proposed methods on synthetic and aerial images; moreover, the comparison with other methods is also provided to show the effectiveness of combinations of stronger wavelet persistence and weaker clustering properties in the proposed methods. |
