近年來紋理影像分割已越來越多採用多維分析法來進行。一張影像通常先經由一組紋理瀘波器處理，產生一張多維影像，其中每一個像素對應一組頻率特徵。常被採用之紋理瀘波器像是小波轉換(wavelet transform)或賈柏瀘波器(Gabor filters)。雖然這些特徵增加了紋理之間的類別分離度，但是瀘波過程中，由於尺度函數或瀘波視窗於紋理交接處跨越不同類別，也可能於相鄰紋理的邊界附近產生混合像素，反而造成分類錯誤，導致像是鋸齒狀和三明治夾層狀等不規則邊界。此外，在均值區域經常發生破碎形狀的分割，這通常由於離群像素（outlier）或是類別分離度低的緣故。此研究的目的即在改善紋理分割的這些缺陷。
　　我們提出了一個適用於多類別紋理分割的多重蛇輪廓競爭模型。為了達成多類別多物體追縱的目的，我們設計了基於情境式機率(contextual probabilities)的蛇輪廓外力而非用於傳統蛇輪廓模型的梯度值。紋理分割的過程包含三步驟：首先，利用小波轉換或賈柏瀘波器在影像中來萃取出有用的紋理特徵；第二步，利用以馬可夫隨機場(Markov random field)為基礎的分類器在影像上來產生下一步驟將定義輪廓外力的情境式機率；第三步，多個蛇輪廓在設定初始位置之後開始成長，當蛇輪廓之間的競爭到達平衡時，決定了紋理之間邊界的位置。
　　本篇論文琢磨了一些輪廓拓譜的問題。例如，當蛇輪廓成長遭遇離群像素或非均質區域可能造成蛇輪廓自我交錯(self-intersection)的問題，我們藉由偵測在蛇輪廓內較小的交錯迴路並決策基於規則：順時針則保留並持續和內部的類別競爭；反時針則移除並更正分類錯誤的區域，來解決問題。另一個輪廓拓譜問題是因為促使輪廓圓滑的內力造成收斂到角落(連接點)的困難，我們建立了一個拉鏈的技巧，讓蛇輪廓盡可能的接近角落。
　　我們以合成的Brodatz紋理庫影像、自然影像和遙測影像來測試效能的好壞。實驗結果顯示，輪廓的內力與蛇輪廓自我交錯處理，可以消除均質區域的破碎分割，定義的類別內部正確率增加到幾乎100%。此外，蛇輪廓競爭達到平衡時，邊緣可以正確地界定，並且邊界附近的正確率增加了3~15%。由這量化分析我們證實了以上視覺效果上重大的改進。

　　The multiband analysis has been increasingly adopted nowadays for textured image segmentation. An image is usually processed through a series of texture filters, such as wavelet transforms or Gabor filters, to yield a set of features for a pixel and thus form a multi-band image. Although adding these features increase class separability between textures, the filtering operations may as well generate mixed pixels near boundaries, where a scaling function or a filter window crosses different classes. Misclassification of the mixed pixels may lead to irregular boundaries, such as zigzag and sandwich boundaries. In addition, fragmented segmentation often occurs in a homogeneous region due to outliers or poor class separability. Our objective is to mitigate these defects in texture segmentation.
　　We propose a multi-snake competition model for multiclass texture segmentation. In order to fulfill the purpose of multiclass multiobject tracking, we redesign the external forces of snakes based on contextual probabilities rather than the gradient magnitudes used in the classic snake model. The texture segmentation process consists of three stages. First, wavelet transforms (or Gabor filters) are applied to the image to extract effective texture features. In the second stage, an MRF-based classifier is applied to the image to produce contextual probabilities, which will be used in the next stage to define the external forces of snakes. In the third stage, a number of snakes are initiated and start growing. As the competition between snakes arrives at a balance, the locations of boundaries between textures are finalized.
　　In this study, we also address several contour topology problems. As a snake grows, the self-intersection problem may arise when the snake encounters outliers or heterogeneous regions. We overcome the problem by detecting the smaller intersect loop in a snake and making a decision based on the rule: clockwise to remain and keep competing with the inner classes; anticlockwise to remove and correct the misclassified region. Another contour topology problem is the difficult convergence to corners (conjunction points) because of the internal force, which enforces the smoothness of the contour. We have developed a zipper technique for snakes to approach corners as closely as possible.
　　Tests have been performed on synthesized Brodatz texture images, natural images and a remote sensing image. The experimental results show that the proposed self-intersection treatment and the internal forces of snakes can eliminate the fragmented segmentation in a homogeneous region, where the defined interior accuracy increased to almost 100%. Besides, reliable boundaries were obtained as snakes reached a competition balance and gave an increment of 3-15% near the boundary. This quantitative analysis confirms these significant improvements in visualization.

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