On the \Gamma-limit of the Mumford-Shah functional

We study by means of -convergence the asymptotics of the rescaled Mumford-Shah functional

Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods

Let I: be a given bounded image function, where is an open and bounded domain which belongs to ⁿ. Let us consider n=2 for the purpose of illustration. Also, let S={x_i}_i be a finite set of given points. We would like to find a contour , such that is an object boundary interpolating the points from S. We combine the ideas of the geodesic active contour (cf. Caselles et al. [7,8]) and of interpolation of points (cf. Zhao et al. [40]) in a level set approach developed by Osher and Sethian [33]. We present modelling of the proposed method, both theoretical results (viscosity solution) and numerical results are given. AMS subject classification 49L25, 74G65, 68U10     

基于灰色关联分析的医学图像分割

医学图像分割处理为临床诊断、病理分析、治疗提供可靠的依据。为了分割出图像中感兴趣的区域,提出了一种基于灰色理论区域生长分割算法。该方法利用灰色关联理论对图像进行关联性分析,根据像素间全局和局部的关联度,指导区域生长的分割和停止。该方法的最大不同之处在利用灰色理论进行关联性分析,不需要大量数据的统计,算法简单,高效。实验证明,该方法能够有效地分割出目标区域,并且具有一定的抗噪能力,是一种较为有效的图像分割新方法。     

基于均值漂移和模糊积分融合的高光谱图像分割

针对高光谱图像的特殊性,给出了一种基于均值漂移和模糊积分融合的高光谱图像分割算法。依据高光谱图像各波段间高度的相关性将其分为若干组,通过主成分分析对各波段子集进行降维。在此基础上,采用均值漂移算法计算各波段子集图像的聚类中心进而实现分割,再利用模糊积分融合各波段子集的分割结果。仿真结果证明了该算法的有效性。     

Collimation and enhancement of elastic transverse waves in two-dimensional solid phononic crystals

In this Letter, we numerically investigate the propagation characteristics of elastic transverse waves emitted by line sources embedded inside two-dimensional (2D) solid phononic crystals (PCs). The results show that collimation and enhancement of elastic transverse waves can be achieved at the band edge frequencies. We find that the collimation effect originates from the flat equifrequency contours (EFCs) at the band edge of appropriately designed 2D solid PCs. It is shown that, in addition to geometric symmetry, appropriate constituent material combination is essential to obtain flat EFCs at the band edge. A highly directional and enhanced elastic transverse wave source with a half power angular width of only 5.6° and an enhancement factor of 530 is realized simply by utilizing a finite-size 2D solid PC structure.     

A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium

In this paper, we develop an algorithm for the segmentation of the pervious lumen of the aorta artery in computed tomography (CT) images without contrast medium, a challenging task due to the closeness gray levels of the different zones to segment. The novel approach of the proposed procedure mainly resides in enhancing the resolution of the image by the application of the algorithm deduced from the mathematical theory of sampling Kantorovich operators. After the application of suitable digital image processing techniques, the pervious zone of the artery can be distinguished from the occluded one. Numerical tests have been performed using 233 CT images, and suitable numerical errors have been computed and introduced ex novo to evaluate the performance of the proposed method. The above procedure is completely automatic in all its parts after the initial region of interest (ROI) selection. The main advantages of this approach relies in the potential possibility of performing diagnosis concerning vascular pathologies even for patients with severe kidney diseases or allergic problems, for which CT images with contrast medium cannot be achieved.     

Mathematical Modeling to Simulate the Movement of Contaminants in Groundwater

The objectives of this paper are twofold. Firstly, we formulate a system of partial differential equations that models the contamination of groundwater due to migration of dissolved contaminants through unsaturated to saturated zone. A closed form solution using the singular perturbation techniques for the flow and solute transport equations in the unsaturated zone is obtained. Indeed, the solution can be used as a tool to verify the accuracy of numerical models of water flow and solute transport. The second part of this paper, deals with how the water level in a water reserve drops due to pumping water out of a well that is some distance away.     

Modeling of MIG/MAG welding with experimental validation using an active contour algorithm applied on high speed movies

This paper investigates some issues in physical modeling of metal inert gas/metal active gas (MIG/MAG) welding process in the short arc mode. In this mode, a metal supply is molten in the arc state and then transferred to the weld pool during the short-circuit state. A hybrid model having two distinct continuous states whose switchings are controlled by two guard conditions is proposed. Due to the complexity of the physical phenomena involved in the welding process, simplifications are used to obtain a model accounting for the main physical contributions but simple enough to yield an efficient, fast and numerically tractable simulator which can be used intensively for evaluating different control strategies. In an attempt to validate the proposed model, different measurements have been made including supply voltage and current sampled synchronously with high speed digital video. In order to extract some relevant quantities representative of the metal transfer from image sequences, an active contour algorithm is developed and tested. The effectiveness of the proposed model in the prediction of major tendencies of a welding process, especially in the arc state, is shown using experimental data. Some limitations of the model during the metal transfer are also stressed and possible remedies are then proposed.     

场景轮廓的动态规划立体匹配算法

立体匹配算法是三维重建的关键步骤。由于实际场景中经常存在大片灰度相近的区域,稠密三维重建存在计算时间长、实时性差的问题。采用了场景的轮廓来重建场景的方法。基于场景中相邻点之间的视差应当是连续的假设,解决了轮廓在匹配时存在的"噪点"的问题,利用动态规划法对轮廓上各个点的视差进行约束以及求解最优解。由于提取轮廓后需要匹配的点数大为减少,用时可减少为原来的10%,得到与场景一致的轮廓视差图。     

Automatic segmentation of cerebral white matter hyperintensities using only 3D FLAIR images

Magnetic Resonance (MR) white matter hyperintensities have been shown to predict an increased risk of developing cognitive decline. However, their actual role in the conversion to dementia is still not fully understood. Automatic segmentation methods can help in the screening and monitoring of Mild Cognitive Impairment patients who take part in large population-based studies. Most existing segmentation approaches use multimodal MR images. However, multiple acquisitions represent a limitation in terms of both patient comfort and computational complexity of the algorithms. In this work, we propose an automatic lesion segmentation method that uses only three-dimensional fluid-attenuation inversion recovery (FLAIR) images. We use a modified context-sensitive Gaussian mixture model to determine voxel class probabilities, followed by correction of FLAIR artifacts. We evaluate the method against the manual segmentation performed by an experienced neuroradiologist and compare the results with other unimodal segmentation approaches. Finally, we apply our method to the segmentation of multiple sclerosis lesions by using a publicly available benchmark dataset. Results show a similar performance to other state-of-the-art multimodal methods, as well as to the human rater.