Priors with Coupled First and Second Order Differences for Manifold-Valued Image Processing

We generalize discrete variational models involving the infimal convolution (IC) of first and second order differences and the total generalized variation (TGV) to manifold-valued images. We propose both extrinsic and intrinsic approaches. The extrinsic models are based on embedding the manifold into an Euclidean space of higher dimension with manifold constraints. An alternating direction methods of multipliers can be employed for finding the minimizers. However, the components within the extrinsic IC or TGV decompositions live in the embedding space which makes their interpretation difficult. Therefore, we investigate two intrinsic approaches: for Lie groups, we employ the group action within the models; for more general manifolds, our IC model is based on recently developed absolute second order differences on manifolds, while our TGV approach uses an approximation of the parallel transport by the pole ladder. For computing the minimizers of the intrinsic models, we apply gradient descent algorithms. Numerical examples demonstrate that our approaches work well for certain manifolds.     

基于主观对比度的变分图像融合方法

局部对比度在图像融合领域中扮演着重要角色.图像融合的目的是将原图像中的重要信息保留到融合结果中去.韦伯定律告诉我们不同背景下的同样的灰度变化给人的干支是不同的,所以一个理想的图像处理算法必须考虑视觉原理.本文考虑了人类视觉系统(HVS),将量化的主观对比度从源图像保留到融合结果中.利用临界可分辨率(JND)作为量化度量,多通道图像的感知对比度作为融合的目标.构造了一个泛函极值问题来寻找融合结果,使得融合结果的主观对比度尽可能接近我们的目标.使用变分法可以得到Euler-Lagrange方程,然后利用梯度下降的迭代算法来求解.试验结果表明,本文的方法具有很好的主观感知效果.     

First and Second Order SMO Algorithms for LS-SVM Classifiers

Least squares support vector machine (LS-SVM) classifiers have been traditionally trained with conjugate gradient algorithms. In this work, completing the study by Keerthi et al., we explore the applicability of the SMO algorithm for solving the LS-SVM problem, by comparing First Order and Second Order working set selections concentrating on the RBF kernel, which is the most usual choice in practice. It turns out that, considering all the range of possible values of the hyperparameters, Second Order working set selection is altogether more convenient than First Order. In any case, whichever the selection scheme is, the number of kernel operations performed by SMO appears to scale quadratically with the number of patterns. Moreover, asymptotic convergence to the optimum is proved and the rate of convergence is shown to be linear for both selections.     

基于变分的图像增强算法和伪彩色映射

提出了一种新的基于变分方法的灰度图像增强算法。将灰度图像的对比度场进行线性放大作为目标图像的对比度场,在图像显示和打印的动态范围约束条件下。利用变分方法求解出增强的图像,使其具有最接近于目标对比度场的对比度。若把目标对比度进一步作动态范围压缩后,将此方法应用到彩色图像的亮度分量中去(色度和饱和度不变)。并根据人类视觉感知的统计特性将结果图进行伪彩色映射,得到视觉效果更佳的彩色图像。这种增强方法不需要人为选定待增强图像区域。实验结果表明了该图像增强方法的有效性。当图像中含有极其微弱的有用的局部对比度信息时,效果尤佳。     

A Novel Variational Image Model: Towards a Unified Approach to Image Editing

In this paper we propose a unified variational image editing model. It interprets image editing as a variational problem concerning the adaptive adjustments to the zero- and first-derivatives of the images which correspond to the color and gradient items. By varying the definition domain of each of the two items as well as applying diverse operators, the new model is capable of tackling a variety of image editing tasks. It achieves visually better seamless image cloning effects than existing approaches. It also induces a new and efficient solution to adjusting the color of an image interactively and locally. Other image editing tasks such as stylized processing, local illumination enhancement and image sharpening, can be accomplished within the unified variational framework. Experimental results verify the high flexibility and efficiency of the proposed model.     

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.     

A Variational Approach for the Segmentation of the Left Ventricle in Cardiac Image Analysis

In this paper we propose a level set method to segment MR cardiac images. Our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints. The visual information is expressed through a gradient vector flow-based boundary component and a region term that aims at best separating the cardiac contours/regions according to their global intensity properties. In order to deal with misleading visual support, an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance. The resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme, the Additive Operator Splitting. Encouraging experimental results are provided using real data.     

基于变分光流估计的肺部4D-CT图像超分辨率重建

由于受到扫描时间和照射剂量的限制,肺部4D-CT数据中纵向采样率远小于面内采样率.为了得到更高质量的肺部图像,从医学图像固有的自相似性出发,提出了一种基于局部和全局相结合的变分光流估计的图像序列超分辨率重建技术,用于提高4D-CT图像重建质量.首先,构建了一个用于求解肺部4D-CT不同相位图像之间的光流场的变分光流模型;然后,利用快速交替方向乘子法求解该模型,得到不同相位图像之间的光流场;最后,基于光流场,并利用非局部迭代反投影超分辨率重建算法,实现了高分辨率肺部图像的重建.实验结果表明：与已有算法相比,本方法在增强图像纹理结构的同时更好地保留了图像的轮廓.     

A Scalable Approach for Variational Data Assimilation

Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a large and computationally expensive problem. Here we focus on scalable methods that makes DA applications feasible for a huge number of background data and observations. We present a scalable algorithm for solving variational DA which is highly parallel. We provide a mathematical formalization of this approach and we also study the performance of the resulted algorithm.     

一种融合纹理的三维图像重建快速实现方法

为了得到完整的三维模型,介绍了一种融合纹理的三维图像重建快速实现方法。通过对不同视角的深度图像的手动粗配准、ICP算法精配准以及全局配准得到这些深度图像的旋转平移矩阵。通过vrippack,三维重建出完整的三维图像,用TextureStitcher对得到的三维图像进行纹理映射,从而实现融合纹理的三维图像的快速重建。文中在论述配准算法主要思想和实现步骤的同时,也用实验验证了方法的可行性与通用性。     

A Variational Framework for Exemplar-Based Image Inpainting

Non-local methods for image denoising and inpainting have gained considerable attention in recent years. This is in part due to their superior performance in textured images, a known weakness of purely local methods. Local methods on the other hand have demonstrated to be very appropriate for the recovering of geometric structures such as image edges. The synthesis of both types of methods is a trend in current research. Variational analysis in particular is an appropriate tool for a unified treatment of local and non-local methods. In this work we propose a general variational framework for non-local image inpainting, from which important and representative previous inpainting schemes can be derived, in addition to leading to novel ones. We explicitly study some of these, relating them to previous work and showing results on synthetic and real images.     

结合FCMS与变分水平集的图像分割模型

提出了一个结合融合空间约束的模糊C均值（Fuzzy C means with spatial constraints,FCMS）聚类与变分水平集的图像模糊聚类分割模型.在该模型中引入了一个基于图像局部信息和空间信息的外部模糊聚类能量,从而可以获取精确的局部图像的空间特征,使得本文模型对噪声图像的聚类分割具有较强的鲁棒性.采用不同类型的实验图像,将本文模型与10个不同类型的图像分割模型进行了对比实验,实验结果显示本文模型能克服图像中噪声影响并取得较满意的聚类分割结果.     

基于混合基稀疏图像表示的压缩传感图像重构

单一基函数不能对同时包含边缘和纹理信息的自然图像进行最优压缩传感图像重构. 本文根据Meyer的卡通--纹理图像模型和生物视觉原理, 用拉普拉斯塔式分解和圆对称轮廓波分别表示图像的光滑成分和边缘成分, 并构造了窄带轮廓波变换实现纹理成分的稀疏表示. 三种稀疏变换的基函数分别与视觉皮层中的侧膝体、简单细胞及栅格细胞的感受野类似. 结合三种图像稀疏表示方法和凸集交替投影算法提出了基于混合基稀疏表示的压缩传感图像重构算法. 实验结果表明,与基于块匹配三维变换迭代收缩的图像重构算法比较, 本文算法能获得更高的图像重构质量.     

小波构造变正则参数变分模型在带噪图像恢复中的应用

在利用正则化方法构造变分模型进行图像去噪时,其正则参数往往选择为恒定值．文中利用小波分解的层次性和带噪图像中噪声所具有的时频特点,构造出变正则参数的变分模型．在不同的小波分解层,通过选择不同的正则参数从而达到自适应去噪的目的．     

A Fourier Domain Framework for Variational Image Registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well. We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach.

A Restricted Second Order Logic for Finite Structures

We introduce a restricted version of second order logic SO^ωin which the second order quantifiers range over relations that are closed under the equivalence relation ≡^kofkvariable equivalence, for somek. This restricted second order logic is an effective fragment of the infinitary logicL^ω_∞ω, but it differs from other such fragments in that it is not based on a fixed point logic. We explore the relationship of SO^ωwith fixed point logics, showing that its inclusion relations with these logics are equivalent to problems in complexity theory. We also look at the expressibility of NP-complete problems in this logic.