| 摘要: | 影像分割是將影像根據其視覺或物理意義切割成前景和背景，在影像處理和電腦視覺的領域皆扮演重要角色。目前常見的方法有：直方圖閥值法、區域生長分割法、群集法、顯式動態邊緣模型及層集法。其中，層集法（隱式動態邊緣模型）已被證實為一大有可為的方法，屬於變分法的一種，分割的求解過程，是將切割曲線與欲切割的圖像相關的能量泛函最小化。雖然在影像分割及邊緣為基礎的物體追蹤上是個可靠的工具，層集法普遍受限於一些限制，像是對初始曲線敏感，和大量的計算時間。此外，目前通用的模型較難處理複雜背景或遮蔽效應。
本研究旨在建立層集法以處理影像分割中的挑戰──包括遮蔽效應和複雜背景，以及計算效能。在第一個模型中，我們將欲分割物體的形態優先知識加入能量泛函，使能量泛函包含資料項和形態項。資料項，取材自區域法，自影像強度資訊中演化出輪廓。形態優先項，定義為演化輪廓和參考輪廓的距離，依據參考輪廓來限制目標輪廓的演化。為了處理形態變異，我們以主成份分析法來建立參考形狀，並將形態項轉譯為模糊能量生成函數。在模型中，為了對齊參考形狀、演化形狀和訓練資料中的形狀，我們應用不變矩方法和形狀正規化程序直接計算形變程度，而非利用常見的梯度下降法。此外，為了最小化能量泛函，我們直接計算能量的轉變，此方法因而能有效率的處理具複雜背景和遮蔽效應的影像，同時增進計算速度，並且避免梯度下降法需處理的時間步長選擇問題。
第二個模型仍舊處理具複雜背景和物件遮蔽。我們導入核心密度預測法，用來估計訓練資料中的形態特徵以建立優先形態。配合不變矩方法和形狀正規化以對齊形態，為了能較快速的收斂，我們將層集方程式表示成以B-spline為基底的連續函數的線性組合。此外，我們也延伸模型至應用至多相位層集法的問題上，並將此延伸版本應用於追縱心臟MR影像的左心室位置。相較於常見的形態優先之主動輪廓模型，此模型表現出幾項優勢，例如，避免解偏微分方程會遇到的缺點。更有甚者，我們提出的模型減少了計算時間並快迅地收斂至分割解。
簡言之，此論文提出了兩個形態優先為基礎的層級法，有效率地解決影像分割中的複雜背景和遮蔽效應。此模型可應用於批次處理影像分割的工作。實驗結果顯示，我們提出的模型與其他現存方法之成效可並駕齊驅。
;Image segmentation plays an important role in the field of image processing and computer vision. The goal of image segmentation is to partition an image into semantic parts including foreground and background. There have been many methods for image segmentation such as histogram thresholding, region-growing, clustering, explicit active contours, and level set methods. Among them, level set methods (or implicit active contours) are shown to be a promising approach to perform the segmentation tasks. Level set methods belong to variational methods in which the segmentation solution is derived by minimizing an energy functional associated with the curve itself and features of image to segment. Although being a promising approach for image segmentation and contour-based object tracking, level set methods generally suffer from some drawbacks such as initial curve sensitivity and high computational cost. In addition, common models meet difficulties when dealing with images in the presence of clutter and occlusion.
This dissertation aims at developing level set models to handle challenges in segmentation of objects under occlusion and cluttered background as well as computational cost.Particularly, in the first model, to deal withimages in the presence of clutter and occlusion, we encoded the shape prior knowledge of desired object into energy functional which includes a data term and a shape term. The data term, inspired from the region-based approach, evolves the contour relied on the image intensity information. The shape prior term, defined as the distance between the evolving shape and a reference one, constrains the evolution of the contour with respect to the reference shape. To handle shape variability, we build the reference shape through Principal Component Analysis approach, and encode the shape term into a fuzzy energy formulation. Especially, in this model, to align the reference shape and the evolving one as well as the shapes in the training data, we employ moment invariant approach and shape normalization procedure that directly calculates the shape transformation, instead of using common gradient descent approach. In addition, to minimize the energy functional, we utilize a direct method to calculate the alteration of the energy.The proposed model therefore can deal with images with cluttered background and object occlusion in an effective way. Moreover, it also improves the computational speed, and avoids difficulties associated with time step selection issue in gradient descent based approaches.
In the second model, also for segmenting imageswith cluttered background and occluded objects, we employ kernel density estimation to estimate shapes’ features in the set of training shapes to construct the shape prior. Along with utilizing the moment invariant approach and shape normalization procedure to align the shapes, for a fast convergence, we represent the level set functions as linear combinations of continuous basic function expressed on B-spline basics. Moreover, we also extend the model into multiphase formulation case and apply the extended version to segment and track the left ventricle from cardiac MR images. The model therefore reveals some advantages, such as avoiding shortcomings associated with solving a set of partial differential equations as in the conventional shape prior-based models. Moreover, the proposed model reduces computation time and fast converges to segmentation solutions.
In sum, this dissertation presents two supervised level set models to perform image segmentation tasks. In the first model, the shape prior knowledge of the desired objects is encoded into energy functional via performing principal component analysis on shapes in the given training data. The alignment between the shapes is achieved by utilizing moment invariant approach and shape normalization procedure. The segmentation solution is derived by directly calculating the changes in value of energy functional. In the second model, the shape prior term is constructed by employing kernel density estimation on the given training shapes. The level set functions are represented by a linear combination of continuous functions expressed on B-spline basic function. The proposed models are applied to segment a vast number of images and experimental results show the desired performances of our proposed models. |
