一种改进的几何活动轮廓模型

针对传统的几何活动轮廓模型在分割具有凹形边界时,演化曲线不能准确定位的缺点,提出了一种改进的几何活动轮廓模型,该模型通过在原模型的演化方程中增加一个正的常数项,使得演化曲线在未到达目标边界时,加速曲线演化,而在到达边界附近时,该加速项逐渐减小为零,从而能够很好的完成对凹形边界的分割.实验证明,该方法不仅能够分割具有凹形边界的目标,还能够使演化过程加速,提高几何活动轮廓模型的分割速度.     

求解图像分割CV模型的BB算法

给出图像分割的一种新算法——BB算法.该方法的优点在于利用迭代过程中当前点和前一点的信息确定搜索步长,从而更有效地搜索最优解.为此,首先通过变分水平集方法将CV模型转化为最优化问题;其次,将BB算法引入该优化问题进行求解;然后,对BB算法进行收敛性分析,为该算法应用在CV模型中提供了理论依据;最后将该方法与已有的最速下降法、共轭梯度法的分割结果进行比较.结果表明,跟其他两种方法相比,BB算法在保证较好分割效果的前提下,提高了算法的速度和性能.     

快速均值漂移图像分割算法研究

Mean shift算法是一种搜索与样本点分布最接近模式的非参数统计方法.但它是一种迭代统计方法,要保证较高的数值计算精度需要较多的迭代次数,耗费较长的计算时间.为克服这一缺点,提出快速均值漂移图像分割算法.该算法在每次迭代时以前一次的聚类中心集合T动态地更新样本集S,并通过使用直方图缩小样本点的搜索范围进一步加快算法的收敛速度.实验结果表明该方法在保证图像分割质量的同时具有较快的收敛速度.     

改进的水平集方法及其在图像分割中的应用

为了稳定水平集函数的演化过程,提出了一种改进的距离规则化水平集方法,新方法与传统的距离规则化方法相比,能更好地维持水平集函数的符号距离函数特性.为了检验新方法的性能,首先将其应用到基于边缘的主动轮廓模型中并用于图像分割,实验结果表明新方法能有效提高分割效率和精度.同时,还将新方法应用到一种改进的基于区域的主动轮廓模型中,实验结果不仅进一步验证了新方法的有效性,还表明新方法能改善初始位置的鲁棒性.     

椭球面上平面曲线类型的闭测地线

通过对椭球面上平截线的研究,找出了椭球面上所有平面曲线类型的闭测地线.     

平行映射下保测地线的曲面

利用古典微分几何方法,讨论了在平行映射下测地线不变的曲面若干局部性质;研究了该类曲面的测地坐标系,并最终得出满足该条件的曲面只有三类.     

几种特殊曲面上的测地线

具体刻画了柱面、锥面、旋转曲面上测地线的几何特征,所得结果一方面匡正了某些文献关于锥面上测地线的错误断言,一方面推广了现有文献关于旋转曲面上测地线几何性质的描述.     

Morse指标和闭测地线的稳定性

令ind(c)为n+1维Riemann流形M上闭测地线c的Morse指标.我们证明:对于闭测地线c,如果它是定向的且n+ind(c)是奇数,或它是非定向的且n+ind(c)为偶数,则c不稳定.Poincaré的一个著名定理说Riemann面上的极小闭测地线是不稳定的,我们的结果是该结论的一个推广.     

基于元胞自动机模型的图像分割算法

针对图像处理中的图像分割任务,我们提出了一个基于模糊元胞自动机模型的图像分割算法.将元胞自动机原理中的演化规则换为模糊规则建立模糊元胞自动机模型,使图像中灰度水平介于目标和背景之间的像素得以更好地归类,从而得到较好的图像分割结果.     

基于EM算法和小波多尺度边缘检测的活动轮廓模型初始化

本文研究了活动轮廓模型初始化的问题.利用EM算法和小波多尺度边缘检测的方法,获得了活动轮廓模型的外部能量函数和初始曲线,并对于具体的X射线图像给出了实验结果和该算法的有效性.     

A fractional order derivative based active contour model for inhomogeneous image segmentation

Segmenting intensity inhomogeneous images is a challenging task for both local and global methods. Some hybrid methods have great advantages over the traditional methods in inhomogeneous image segmentation. In this paper, a new hybrid method is presented, which incorporates image gradient, local environment and global information into a framework, called adaptive-weighting active contour model. The energy or level set functions in the framework mainly include two parts: a global term and local term. The global term aims to enhance the image contrast, and it can also accelerate the convergence rate when minimizing the energy function. The local term integrates fractional order differentiation, fractional order gradient magnitude, and difference image information into the well-known local Chan–Vese model, which has been shown to be effective and efficient in modeling the local information. The local term can also enhance low frequency information and improve the inhomogeneous image segmentation. An adaptive weighting strategy is proposed to balance the actions of the global and local terms automatically. When minimizing the level set functions, regularization can be imposed by applying Gaussian filtering to ensure smoothness in the evolution process. In addition, a corresponding stopping criterion is proposed to ensure the evolving curve automatically stops on true boundaries of objects. Dice similarity coefficient is employed as the comparative quantitative measures for the segmented results. Experiments on synthetic images as well as real images are performed to demonstrate the segmentation accuracy and computational efficiency of the presented hybrid method.     

Finslerian extensions of geodesic active fields for digital image registration

The present work extends the already established prolific geodesic active field methodology of Riemannian type, which generalizes the Casseles-Kimmel-Sapiro weighted length problem, and a direction dependent Finslerian structure is proposed as alternative for the GAF image registration process. The proposed extension relies on the direction-dependent 0-homogeneous associated weight metric tensor and aims to achieve the minimization of the absolute error in the case of motion detection. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new active contour model for shape extraction

We propose a new active contour model for shape extraction of objects in grey‐valued two‐dimensional images based on an energy‐minimization formulation. The energy functional that we consider takes into account the two requirements of object isolation and smoothness of the contour. After deriving the Euler–Lagrange equations corresponding to the energy functional, we bring out some important geometric properties of a solution to these equations. The discussion on our solution method—with the help of which we try to minimize the energy functional by evolving an initial curve—also focuses on how to prescribe the initial curve fully automatically. The effectiveness of our algorithms is demonstrated with the help of experimental results. Copyright © 2000 John Wiley & Sons, Ltd.     

A novel variational model for image segmentation

In this paper, we propose a new variational model for image segmentation. Our model is inspired by the complex Ginzburg-Landau model and the semi-norm defined by us. This new model can detect both the convex and concave parts of images. Moreover, it can also detect non-closed edges as well as quadruple junctions. Compared with other methods, the initialization is completely automatic and the segmented images obtained by using our new model could keep fine structures and edges of the original images very effectively. Finally, numerical results show the effectiveness of our model.     

Using shapes correlation for active contour segmentation of uterine fibroid ultrasound images in computer-aided therapy

Segmenting the lesion regions from the ultrasound (US) images is an important step in the intra-operative planning of some computer-aided therapies. High-Intensity Focused Ultrasound (HIFU), as a popular computer-aided therapy, has been widely used in the treatment of uterine fibroids. However, such segmentation in HIFU remains challenge for two reasons: (1) the blurry or missing boundaries of lesion regions in the HIFU images and (2) the deformation of uterine fibroids caused by the patient’s breathing or an external force during the US imaging process, which can lead to complex shapes of lesion regions. These factors have prevented classical active contour-based segmentation methods from yielding desired results for uterine fibroids in US images. In this paper, a novel active contour-based segmentation method is proposed, which utilizes the correlation information of target shapes among a sequence of images as prior knowledge to aid the existing active contour method. This prior knowledge can be interpreted as a unsupervised clustering of shapes prior modeling. Meanwhile, it is also proved that the shapes correlation has the low-rank property in a linear space, and the theory of matrix recovery is used as an effective tool to impose the proposed prior on an existing active contour model. Finally, an accurate method is developed to solve the proposed model by using the Augmented Lagrange Multiplier (ALM). Experimental results from both synthetic and clinical uterine fibroids US image sequences demonstrate that the proposed method can consistently improve the performance of active contour models and increase the robustness against missing or misleading boundaries, and can greatly improve the efficiency of HIFU therapy.     

On a nonlocal model of image segmentation

We understand an image as binary grey ‘alloy’ of a black and a white component and use a nonlocal phase separation model to describe image segmentation. The model consists in a degenerate nonlinear parabolic equation with a nonlocal drift term additionally to the familiar Perona-Malik model. We formulate conditions for the model parameters to guarantee global existence of a unique solution that tends exponentially in time to a unique steady state. This steady state is solution of a nonlocal nonlinear elliptic boundary value problem and allows a variational characterization. Numerical examples demonstrate the properties of the model.Dedicated to Klaus Kirchgässner on the occasion of his 70th birthdayReceived: November 12, 2002; revised: April 8, 2003