A Study of a Convex Variational Diffusion Approach for Image Segmentation and Feature Extraction

We analyze a variational approach to image segmentation that is based on a strictly convex non-quadratic cost functional. The smoothness term combines a standard first-order measure for image regions with a total-variation based measure for signal transitions. Accordingly, the costs associated with discontinuities are given by the length of level lines and local image contrast. For real images, this provides a reasonable approximation of the variational model of Mumford and Shah that has been suggested as a generic approach to image segmentation.The global properties of the convex variational model are favorable to applications: Uniqueness of the solution, continuous dependence of the solution on both data and parameters, consistent and efficient numerical approximation of the solution with the FEM-method.Various global and local properties of the convex variational model are analyzed and illustrated with numerical examples. Apart from the favorable global properties, the approach is shown to provide a sound mathematical model of a useful locally adaptive smoothing process. A comparison is carried out with results of a region-growing technique related to the Mumford-Shah model.     

Direct Visible Surface Interpolation

The computation of visible surfaces is usually formulated in a regularization framework based on thin-plate and membrane splines. When discretized, this formulation leads to large sparse linear systems. Most surface interpolation methods solve these sparse systems with iterative methods. Here we explore the use of direct methods. Through a careful analysis of the regularization operator, we derive direct methods that efficiently make use of all zeros in the sparse discretization of the operator. Experimental results show that, compared with iterative interpolation methods, the direct methods we present are competitive in general, and they provide significant speed-ups for problems involving discontinuities. In addition to their use in visible-surface interpolation, the presented methods also support very efficient time integration for deformable surfaces.     

New Riemannian techniques for directional and tensorial image data

This paper develops new geometrical filtering and edge detection algorithms for processing non-Euclidean image data. We view image data as residing on a Riemannian manifold, and we work with a representation based on the exponential map for this manifold together with the Riemannian weighted mean of image data. We show how the weighted mean can be efficiently computed using Newton's method, which converges faster than the gradient descent method described elsewhere in the literature. Based on geodesic distances and the exponential map, we extend the classical median filter and the Perona-Malik anisotropic diffusion technique to smooth non-Euclidean image data. We then propose an anisotropic Gaussian kernel for image filtering, and we also show how both the median filter and the anisotropic Gaussian filter can be combined to develop a new edge preserving filter, which is effective at removing both Gaussian noise and impulse noise. By using the intrinsic metric of the feature manifold, we also generalise Di Zenzo's structure tensor to non-Euclidean images for edge detection. We demonstrate the applications of our Riemannian filtering and edge detection algorithms both on directional and tensor-valued images.     

Anisotropic diffusion with generalized diffusion coefficient function for defect detection in low-contrast surface images

In this paper, an anisotropic diffusion model with a generalized diffusion coefficient function is presented for defect detection in low-contrast surface images and, especially, aims at material surfaces found in liquid crystal display (LCD) manufacturing. A defect embedded in a low-contrast surface image is extremely difficult to detect, because the intensity difference between the unevenly illuminated background and the defective region is hardly observable and no clear edges are present between the defect and its surroundings.The proposed anisotropic diffusion model provides a generalized diffusion mechanism that can flexibly change the curve of the diffusion coefficient function. It adaptively carries out a smoothing process for faultless areas and performs a sharpening process for defect areas in an image. An entropy criterion is proposed as the performance measure of the diffused image and then a stochastic evolutionary computation algorithm, particle swarm optimization (PSO), is applied to automatically determine the best parameter values of the generalized diffusion coefficient function. Experimental results have shown that the proposed method can effectively and efficiently detect small defects in various low-contrast surface images.     

Weighted and extended total variation for image restoration and decomposition

In various information processing tasks obtaining regularized versions of a noisy or corrupted image data is often a prerequisite for successful use of classical image analysis algorithms. Image restoration and decomposition methods need to be robust if they are to be useful in practice. In particular, this property has to be verified in engineering and scientific applications. By robustness, we mean that the performance of an algorithm should not be affected significantly by small deviations from the assumed model. In image processing, total variation (TV) is a powerful tool to increase robustness. In this paper, we define several concepts that are useful in robust restoration and robust decomposition. We propose two extended total variation models, weighted total variation (WTV) and extended total variation (ETV). We state generic approaches. The idea is to replace the TV penalty term with more general terms. The motivation is to increase the robustness of ROF (Rudin, Osher, Fatemi) model and to prevent the staircasing effect due to this method. Moreover, rewriting the non-convex sublinear regularizing terms as WTV, we provide a new approach to perform minimization via the well-known Chambolle's algorithm. The implementation is then more straightforward than the half-quadratic algorithm. The behavior of image decomposition methods is also a challenging problem, which is closely related to anisotropic diffusion. ETV leads to an anisotropic decomposition close to edges improving the robustness. It allows to respect desired geometric properties during the restoration, and to control more precisely the regularization process. We also discuss why compression algorithms can be an objective method to evaluate the image decomposition quality.     

Ultrasound speckle reduction by a SUSAN-controlled anisotropic diffusion method

An ultrasound speckle reduction method is proposed in this paper. The filter, which enhances the power of anisotropic diffusion with the Smallest Univalue Segment Assimilating Nucleus (SUSAN) edge detector, is referred to as the SUSAN-controlled anisotropic diffusion (SUSAN_AD). The SUSAN edge detector finds image features by using local information from a pseudo-global perspective. Thanks to the noise insensitivity and structure preservation properties of SUSAN, a better control can be provided to the subsequent diffusion process. To enhance the adaptability of the SUSAN_AD, the parameters of the SUSAN edge detector are calculated based on the statistics of a fully formed speckle (FFS) region. Different FFS estimation schemes are proposed for envelope-detected speckle images and log-compressed ultrasonic images. Adaptive diffusion threshold estimation and automatic diffusion termination criterion are employed to enhance the robustness of the method. Both synthetic and real ultrasound images are used to evaluate the proposed method. The performance of the SUSAN_AD is compared with four other existing speckle reduction methods. It is shown that the proposed method is superior to other methods in both noise reduction and detail preservation.     

一维热传导问题时变边界上热通量重构问题

具有Neumann边界条件的抛物方程的初边值问题是偏微分方程研究领域的一类经典问题.正问题是由已知的边界条件和初始条件来求区域温度场的问题.如果边界条件不足,但给出了区域内部的一些额外信息,这样便构成了一类热通量重构的反问题.本文讨论了一维热传导问题时动边界上的热通量重构问题,借助于位势理论方法,引入密度函数,将反问题本质上转化为一类关于密度函数的具有弱奇性核的第一类Volterra积分方程,采用了Tikhonov正则化,在正则化参数的选取上采用了后验的模型函数方法,数值结果验证了反演方法的有效性.     

一种偏好于查询子流形的半监督图像检索算法

在基于反馈的图像检索中,由于被用户标记为相关和不相关的图像数较少,使得检索问题变成了一个典型的小样本问题.流形可表达数据在低维空间中的内在几何结构,流形正则化的目的是利用这种几何结构来约束解空间,以使最优解能反映数据本身的几何分布.为了解决反馈检索中的小样本问题,本文在流形正则化框架下提出一个新的半监督图像检索算法.在新算法中,流形正则化项只依赖于文中定义的查询子流形,而不依赖于数据集的全局结构.在两个图像集上的实验结果对比表明,本文提出的新算法在检索效果上优于现有的4种state-of-the-art算法.     

基于混合最小二乘支持向量机网络模型的非线性系统辨识

针对基于输入输出数据的非线性系统辨识问题,提出一种新的混合最小二乘支持向量机(LS-SVMs)网络模型及相应的学习算法.该算法将系统的辨识问题动态自适应的划分为若干子问题,将支持向量机(SVM)用于各子模块辨识;通过分析模型的统计学特性,给出基于整体框架优化的系统参数辨识方法.针对系统中参数相关联的特性,采用期望条件最大化(ECM)算法对其进行条件辨识,同时结合正则化理论和最小二乘法,保证各专家模块的结构风险最小化辨识原则.试验结果表明,该方法兼具良好的辨识精度和泛化性能.