物体形状的表示与分析关键问题研究
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摘要
形状是反映物体性质的重要载体。它是目标识别、多媒体检索、医学图像分析与辅助诊断、计算机图形学与辅助设计等众多研究领域中的重要研究对象。形状蕴含着极为丰富的变化,形状的本质特性往往在一些形变中得到体现,然而又常常为另一些形变所干扰。这是因为形状变化既包含了反映物体特性的各种自身形变,也包含了由噪声、提取误差等干扰带来的外部形变。因此在构造形状表现时,一般需要该表现对各种外部干扰具有鲁棒性,还要在不同应用中对一些的自身形变具有不变性。
基于上述背景,本文主要从鲁棒性和不变性的角度出发,研究样条与多边形的形状表示,排除噪声影响,有效提取形状上的显著几何特征点；研究对相似变换不变的非刚体形变表示,衡量椎间盘形状的差异,并应用至椎间盘退变辅助诊断之中。本文主要研究内容及其创新之处如下：
1.开展基于样条的平面形状表示研究。分析了弹性二次曲线模型的几何意义,揭示了模型中能量权重因子和样条重叠度因子对模型保持形状特征的影响作用。针对原模型在表现形状时仅能“各处同性”地保持几何特征的问题,提出一种改进的弹性二次曲线模型来表现形状,通过对离散曲线演化模型获取形状各处的几何特征显著度,指导模型能量权重因子根据形状特征显著度变化,在重构形状时能够自适应地保持其几何特征。将该模型与交互式LiveWire算法相结合,应用至图像分割中。
2.开展基于样条的三维形状表示研究,提出用于曲面表示的弹性二次曲面模型,并基于该算法表示三维形状曲面。根据弹性二次曲线表示平面形状的基本思想,推广至用重叠的二次曲面来重构表示曲面,即通过重叠的参数域构造彼此重叠的二次曲面片,根据相邻面片之间的0阶与1阶不连续势能建立二次型势能函数。经过对整个曲面的逐点迭代,获得稳定且保持显著几何特征的三维曲面表示。该模型能将受到较大噪声干扰的三维人脸曲面细节较好地恢复出来。
3.研究形状的多边形高效近似及多尺度的显著特征点提取。用ε等距同构的概念描述形状多边形表示,提出构造平面凸曲线的逐级ε等距同构重构,该重构能有效地控制近似误差,且与视觉显著特征之间有明确的量化关系。在此基础上,通过对形状轮廓的特征点删除、添加、调整等机制,构造出一种近似效率高、对初始化不敏感、单参数控制的多尺度显著特征点提取／形状多边形近似算法。
4.通过描述椎间盘形状非刚体形变来提取其差异,应用于椎间盘退化辅助诊断之中。提出将椎间盘形状变换至对相似变换不变、只包含非刚体形变信息的形状空间中,通过估算此空间中两点间测地线来衡量椎间盘形状间的相似度。同时提出形状与纹理相结合的思路来更全面地反映椎间盘之间的差异。并将主动学习思路引入分类器训练之中,提出一种改进的直推式实验设计算法来更好地选择有代表性的样本送给医生标识,以期使用少量的样本也能训练出准确率较高的分类器,减轻人工标识训练样本的负担。
Shapes carry many important properties of the objects in the real world. They play a central role in research fields such as object recognition, multimedia search, medical image analysis and computer assisted design&computer graphics. The shape variations are ubiquitous. Some of the variations reveal the properties of an object while the rest conceal them. This is due to the fact that the shape variations come from both various inside factors and outside interruptions. As a result, a shape should be ideally represented in the way that it should not only be robust to all the noises but also be invariant to some of the intrinsic variations in specific applications.
Orientating at the properties of robustness and invariance, we conduct research on shape representation as well as its analysis and application in this thesis. Generally, we first propose new spline and polygonal shape representations to eliminate the noise effect, with the aim at preserving and extracting salient geometric shape features. Then we research the similar-transforms-invariant representation on non-rigid shape deformation and apply it in the computer aided diagnosis on intervertebral disc degeneration. The main contributions in the dissertation are as follows:
1. The research on planar shape representation by a new type of spline is conducted. We first analyze the geometric properties of this spline model called elastic quadratic wire (EQW) and uncover the parameters' affection on the performance of the EQW model. Taking the advantage of this, an improved version of the EQW model is proposed. The geometric feature along the contour can be adaptively preserved according to the saliency obtained by the discrete curve evolution (DCE) method. We then further incorporated the adaptive EQW model with an interactive image segmentation technique called Live Wire and apply it in extracting the objects' boundaries in a few image modalities.
2. An elastic quadratic patch (EQP) model is proposed, which is extended from the basic idea of EQW model, for robustly representing three dimensional shapes. In the model, an energy function quantifying0th and1st discontinuity is constructed based on overlapping quadratic patches for each controlling point and its neighborhood on the surface. This function is in the quadratic form and can be easily minimized explicitly through a specific vector of quadratic surface parameters. The EQP representation of the whole surface, which is as stable and geometry-preserving as the EQW model, can be then obtained through a pointwise iteration. The EQP model is able to preserve the details of the3D facial surface from the relatively high noise levels.
3. The research on planar shape representation by an efficient polygonal approximation is conducted. We describe the polygonal representation as the problem of the ε-isomerty shape reconstruction, which has some appealing properties such as the rigid descent reconstructing error and the quantitative relationship with a visual saliency metric. The mechanisms of point deleting, adding and adjusting are further proposed and incorporate into a new feature point extraction algorithm, which is efficient in approximating a shape, insensitive to arbitrary initialization and allows multiscale geometric features extraction.
4. A novel framework of computer aided diagnosis (CAD) on disc degeneration is proposed. The disc degeneration is described with both shape and texture features. We quantify the non-rigid deformation between two shapes by approximating the geodesic length in the shape space. Similarly, the texture difference is measured with Bhattacharyya distance between intensity distributions of two disc regions. Then two measures are linearly combined as the appearance feature. We also introduce the idea of active learning into the CAD framework and present an improved transductive experimental design to better select representative instances for training the classifier. This technique achieves the comparable classifying accuracy with fewer training data and therefore alleviates the physicians' burden.
基于上述背景,本文主要从鲁棒性和不变性的角度出发,研究样条与多边形的形状表示,排除噪声影响,有效提取形状上的显著几何特征点；研究对相似变换不变的非刚体形变表示,衡量椎间盘形状的差异,并应用至椎间盘退变辅助诊断之中。本文主要研究内容及其创新之处如下：
1.开展基于样条的平面形状表示研究。分析了弹性二次曲线模型的几何意义,揭示了模型中能量权重因子和样条重叠度因子对模型保持形状特征的影响作用。针对原模型在表现形状时仅能“各处同性”地保持几何特征的问题,提出一种改进的弹性二次曲线模型来表现形状,通过对离散曲线演化模型获取形状各处的几何特征显著度,指导模型能量权重因子根据形状特征显著度变化,在重构形状时能够自适应地保持其几何特征。将该模型与交互式LiveWire算法相结合,应用至图像分割中。
2.开展基于样条的三维形状表示研究,提出用于曲面表示的弹性二次曲面模型,并基于该算法表示三维形状曲面。根据弹性二次曲线表示平面形状的基本思想,推广至用重叠的二次曲面来重构表示曲面,即通过重叠的参数域构造彼此重叠的二次曲面片,根据相邻面片之间的0阶与1阶不连续势能建立二次型势能函数。经过对整个曲面的逐点迭代,获得稳定且保持显著几何特征的三维曲面表示。该模型能将受到较大噪声干扰的三维人脸曲面细节较好地恢复出来。
3.研究形状的多边形高效近似及多尺度的显著特征点提取。用ε等距同构的概念描述形状多边形表示,提出构造平面凸曲线的逐级ε等距同构重构,该重构能有效地控制近似误差,且与视觉显著特征之间有明确的量化关系。在此基础上,通过对形状轮廓的特征点删除、添加、调整等机制,构造出一种近似效率高、对初始化不敏感、单参数控制的多尺度显著特征点提取／形状多边形近似算法。
4.通过描述椎间盘形状非刚体形变来提取其差异,应用于椎间盘退化辅助诊断之中。提出将椎间盘形状变换至对相似变换不变、只包含非刚体形变信息的形状空间中,通过估算此空间中两点间测地线来衡量椎间盘形状间的相似度。同时提出形状与纹理相结合的思路来更全面地反映椎间盘之间的差异。并将主动学习思路引入分类器训练之中,提出一种改进的直推式实验设计算法来更好地选择有代表性的样本送给医生标识,以期使用少量的样本也能训练出准确率较高的分类器,减轻人工标识训练样本的负担。
Shapes carry many important properties of the objects in the real world. They play a central role in research fields such as object recognition, multimedia search, medical image analysis and computer assisted design&computer graphics. The shape variations are ubiquitous. Some of the variations reveal the properties of an object while the rest conceal them. This is due to the fact that the shape variations come from both various inside factors and outside interruptions. As a result, a shape should be ideally represented in the way that it should not only be robust to all the noises but also be invariant to some of the intrinsic variations in specific applications.
Orientating at the properties of robustness and invariance, we conduct research on shape representation as well as its analysis and application in this thesis. Generally, we first propose new spline and polygonal shape representations to eliminate the noise effect, with the aim at preserving and extracting salient geometric shape features. Then we research the similar-transforms-invariant representation on non-rigid shape deformation and apply it in the computer aided diagnosis on intervertebral disc degeneration. The main contributions in the dissertation are as follows:
1. The research on planar shape representation by a new type of spline is conducted. We first analyze the geometric properties of this spline model called elastic quadratic wire (EQW) and uncover the parameters' affection on the performance of the EQW model. Taking the advantage of this, an improved version of the EQW model is proposed. The geometric feature along the contour can be adaptively preserved according to the saliency obtained by the discrete curve evolution (DCE) method. We then further incorporated the adaptive EQW model with an interactive image segmentation technique called Live Wire and apply it in extracting the objects' boundaries in a few image modalities.
2. An elastic quadratic patch (EQP) model is proposed, which is extended from the basic idea of EQW model, for robustly representing three dimensional shapes. In the model, an energy function quantifying0th and1st discontinuity is constructed based on overlapping quadratic patches for each controlling point and its neighborhood on the surface. This function is in the quadratic form and can be easily minimized explicitly through a specific vector of quadratic surface parameters. The EQP representation of the whole surface, which is as stable and geometry-preserving as the EQW model, can be then obtained through a pointwise iteration. The EQP model is able to preserve the details of the3D facial surface from the relatively high noise levels.
3. The research on planar shape representation by an efficient polygonal approximation is conducted. We describe the polygonal representation as the problem of the ε-isomerty shape reconstruction, which has some appealing properties such as the rigid descent reconstructing error and the quantitative relationship with a visual saliency metric. The mechanisms of point deleting, adding and adjusting are further proposed and incorporate into a new feature point extraction algorithm, which is efficient in approximating a shape, insensitive to arbitrary initialization and allows multiscale geometric features extraction.
4. A novel framework of computer aided diagnosis (CAD) on disc degeneration is proposed. The disc degeneration is described with both shape and texture features. We quantify the non-rigid deformation between two shapes by approximating the geodesic length in the shape space. Similarly, the texture difference is measured with Bhattacharyya distance between intensity distributions of two disc regions. Then two measures are linearly combined as the appearance feature. We also introduce the idea of active learning into the CAD framework and present an improved transductive experimental design to better select representative instances for training the classifier. This technique achieves the comparable classifying accuracy with fewer training data and therefore alleviates the physicians' burden.
引文
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