Curvature-Driven PDE Methods for Matrix-Valued Images

Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo’s concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.     

基于非均匀热扩散的交互式图像分割算法

交互式图像分割是图像分割中的重要分支,在现实生活和医学领域都有着广泛的应用。该文基于计算测地距离的热方法,引入了热扩散系数,提出了一种基于非均匀热扩散的交互式图像分割算法。该算法利用图像的颜色信息构造三角网格作为热扩散的媒介,首先由热方程找到距离增加的方向,再利用泊松方程还原测地距离。将前景中人工交互区域上的热流扩散速度增加,则前景不同部分之间的测地距离变小,消除了内部边界,通过设置外部边界分割限制条件,即可实现完整的前景分割。算法仅需求解两个稀疏线性方程组,鲁棒性强、精度高且更易于操作。同时,拉普拉斯算子和梯度算子的预计算可以被多次重用,减少了内存占用和时间消耗。大量交互式图像分割实验结果表明:该算法无需过多的用户交互信息,即可将现实图像中的复杂前景快速准确地分割出来。     

Heat method of non-uniform diffusion for computing geodesic distance on images and surfaces

This paper presents a non-uniform heat method to calculate geodesic distance and geodesic curves on the images and surfaces. Different from the varadhan’s formula-based heat method, our non-uniform heat method first finds the direction of distance increases by heat diffusion, and then recovers the geodesic distance by solving a Poisson equation. Various heat diffusion metrics obtained from different potentials and tensors, such as intensity-based metrics, gradient-based metrics, and anisotropy metrics et., describe the differences of geodesic distances in various regions. Combined with automatic geodesic segmentation technology, our heat method can be effectively and quickly applied to centerlines extraction and salient curves detection in images, skeleton extraction of shapes, and 3D path planning on surfaces. Two categories of discretization algorithms on scattered points and triangle meshes are more flexible and can often be used to more complicated cases. The algorithm is robust and simple to implement since it is based on solving a pair of standard sparse linear systems. Pre-calculation also greatly reduces time consumption and memory footprint.

     

基于局部密度和偏移量的图像自动分割算法

图像分割是计算机视觉领域的传统问题,也是图像分析和模式识别的关键组成部分。提出了一种不依赖于图像分割数参数的图像自动分割算法。基于超像素间的测地距离,根据其定义的局部密度和偏移量,结合K-S假设检验来分析图像最佳分割数,并给出了图像自动分割算法。大量图像分割的实验结果表明:该方法可以准确地对图像进行自动分割,达到了较好的分割效果,相比其它方法,速度更快。     

Geodesic Distance and Curves Through Isotropic and Anisotropic Heat Equations on Images and Surfaces

This paper proposes a method to extract geodesic distance and geodesic curves using heat diffusion. The method is based on Varadhan’s formula that helps to obtain a numerical approximation of geodesic distance according to metrics based on different heat flows. The heat equation can be utilized by regarding an image or a surface as a medium for heat diffusion and letting the user set at least one source point in the domain. Both isotropic and anisotropic diffusions are considered here to obtain geodesics according to their respective metrics. (1) In the part of the paper where we deal with the isotropic case, we use gray-level intensity to compute the conductivity, i.e., those pixels with gray-levels similar to the source point would have higher conductivity. The model of Perona and Malik, which inhibits heat from diffusing out of homogeneous regions, is also used for geodesic computations in this paper. The two methods are combined and used for more complicated cases. We can also use the norm of the gradient of an image as the feature in the Perona and Malik model to make the heat diffuse along boundaries and edges. (2) For the anisotropic case, we use different eigenvectors and eigenvalues to compose the diffusion tensors to concentrate heat flow along chosen directions. Furthermore, to automate the process of extracting geodesic lines, we propose two automatic methods: a new voting method and a key point method, which are both especially designed for the heat-based method. Our algorithms are tested on synthetic and real images as well as on a mesh. The results are very promising and demonstrate the robustness of the algorithms.     

一种扩散张量脑脐服体图像分割算法

提出了一种基于矢量活动轮廓模型的扩散张量脑拼刀氏体图像分割算法,其利用矢量Chan-Vese模型构造了控制轮廓线演化方向的矢量符号压力函数,并将向量范数形式用于表达脑拼肌体组织的扩散张量各向异性,给出了具有全局与局部分割特性的矢量活动轮廓模型。10组真实大脑扩散张量图像分割结果表明,该算法对脑拼抵体结构的分割精确、稳定。     

Fast Asymmetric Fronts Propagation for Image Segmentation

In this paper, we introduce a generalized asymmetric fronts propagation model based on the geodesic distance maps and the Eikonal partial differential equations. One of the key ingredients for the computation of the geodesic distance map is the geodesic metric, which can govern the action of the geodesic distance level set propagation. We consider a Finsler metric with the Randers form, through which the asymmetry and anisotropy enhancements can be taken into account to prevent the fronts leaking problem during the fronts propagation. These enhancements can be derived from the image edge-dependent vector field such as the gradient vector flow. The numerical implementations are carried out by the Finsler variant of the fast marching method, leading to very efficient interactive segmentation schemes. We apply the proposed Finsler fronts propagation model to image segmentation applications. Specifically, the foreground and background segmentation is implemented by the Voronoi index map. In addition, for the application of tubularity segmentation, we exploit the level set lines of the geodesic distance map associated with the proposed Finsler metric providing that a thresholding value is given.     

基于区域中心的交互式图像前景提取方法

图像分割是从图像中提取有意义的区域,是图像处理和计算机视觉中的关键技术。而自动分割方法不能很好地处理前景复杂的图像,对此提出一种基于区域中心的交互式图像前景提取算法。针对图像前景的复杂度,很难用单一的相似区域描述前景,文中采用多个区域中心来刻画目标区域。为提升图像分割的稳定性,给出基于超像素颜色、空间位置和纹理信息的相似性度量方法;为确保图像分割区域的连通性和准确性,定义了基于超像素的测地距离计算方法。使用基于测地距离的超像素局部密度,来分析图像的若干区域中心;基于用户交互的方式来分析前景的区域中心,得到图像前景。经过大量彩色图像的仿真表明,在分割过程中利用少量的用户交互信息,可有效提升图像分割的稳定性和准确性。     

Curvature-based anisotropic geodesic distance computation for parametric and implicit surfaces

Distribution of geometric features varies with direction, including, for example, normal curvature. In this paper, this characteristic of shape is used to define a new anisotropic geodesic (AG) distance for both parametric and implicit surfaces. Local distance (LD) from a point is defined as a function of both the point and a unit tangent plane directions, and a total distance is defined as an integral of that local distance. The AG distance between points on the surface is the minimum total distance between them. The path between the points that attains the minimum is called the anisotropic geodesic path. Minimization of total distance to attain the AG distance is performed by associating the LD function with a tensor speed function that controls wave propagation in the convex Hamilton–Jacobi (H–J) equation solver. We present new distance metrics for both parametric and implicit surfaces based on the curvature tensor. In order to solve for the implicit AG, a bounded 3D H–J equation solver was developed. We present a second metric for the AG distance, a difference curvature tensor, for parametric surfaces. Some properties of both new AG distances are presented, including parameterization invariance. This AG path differs from the usual geodesic in that minimal path, i.e., lowest cost path, roughly speaking, minimizes an integral of curvature along the curve. Then, the effectiveness of the proposed AG distances as shape discriminators is demonstrated in several applications, including surface segmentation and partial shape matching.

Interactive visualization of volumetric white matter connectivity in DT-MRI using a parallel-hardware Hamilton-Jacobi solver

In this paper we present a method to compute and visualize volumetric white matter connectivity in diffusion tensor magnetic resonance imaging (DT-MRI) using a Hamilton-Jacobi (H-J) solver on the GPU (Graphics Processing Unit). Paths through the volume are assigned costs that are lower if they are consistent with the preferred diffusion directions. The proposed method finds a set of voxels in the DTI volume that contain paths between two regions whose costs are within a threshold of the optimal path. The result is a volumetric optimal path analysis, which is driven by clinical and scientific questions relating to the connectivity between various known anatomical regions of the brain. To solve the minimal path problem quickly, we introduce a novel numerical algorithm for solving H-J equations, which we call the Fast Iterative Method (FIM). This algorithm is well-adapted to parallel architectures, and we present a GPU-based implementation, which runs roughly 50-100 times faster than traditional CPU-based solvers for anisotropic H-J equations. The proposed system allows users to freely change the endpoints of interesting pathways and to visualize the optimal volumetric path between them at an interactive rate. We demonstrate the proposed method on some synthetic and real DT-MRI datasets and compare the performance with existing methods.     

面向运动分割优化的变分光流计算方法研究

面向运动分割的需求,围绕变分光流计算中的运动边缘保留问题,对反应-扩散式光流计算模型中的扩散张量设计与改进方法进行系统深入研究。 在分析已有设计方法的基础上,提出了一种融合图像和流场信息驱动的扩散张量设计方法,并利用该扩散张量建立光流计算模型,然后在多尺度计算框架下给出了相应的偏微分方程数值计算方法。 理论分析与对比实验结果表明,这种设计方法能有效克服现有方法提取运动边缘不精确的缺点,更准确地刻画出运动边缘,提高光流的计算精度。     

基于差异性累积与子空间传播的法向估计算法

以分割为基础的法向估计算法主要是通过法向的差异来构造点之间的相似性.针对由于距离属性的缺失,使这类算法对于紧邻面及一些光滑曲面的估计结果并不理想的问题,提出基于差异性累积与子空间传播的法向估计算法,利用最短路将法向的差异性和点的位置信息相融合.首先,对于部分点的邻域,找到邻域点间的最短路,通过叠加最短路中点的法向差异,计算点之间的相似性;然后,利用谱分割对邻域进行分割,选择一子邻域估计此点的法向;最后,为了提高效率,提出法向约束的子空间结构传播算法,其余邻域的分割结果由已有的分割结果进行推断.在Fandisk等仿真数据和Armadillon等真实扫描数据上的实验结果表明,文中算法能准确地恢复模型的尖锐特征,有效地克服噪声及非均匀采样.     

GACV: Geodesic-Aided C-V method

A novel algorithm for image segmentation is proposed. The proposed method incorporates geodesic curves and C-V method to raise active contours’ performance on image segmentation. Moreover, we extend our method to color images. By practical experiments, it is verified that our model obtains better results than original methods, especially with respect to images within holes, complex background, weak edges, and noise.     

结合Gabor滤波器和扩展LTP算子的无监督纹理图像分割

目的 现实中的纹理往往具有类型多样、形态多变、结构复杂等特点,直接影响到纹理图像分割的准确性。传统的无监督纹理图像分割算法具有一定的局限性,不能很好地提取稳定的纹理特征。本文提出了基于Gabor滤波器和改进的LTP（local ternary pattern）算子的针对复杂纹理图像的纹理特征提取算法。方法 利用Gabor滤波器和扩展LTP算子分别提取相同或相似纹理模式的纹理特征和纹理的差异性特征,并将这些特征融入到水平集框架中对纹理图像进行分割。结果 通过实验表明,对纹理方向及尺度变化较大的图像、复杂背景下的纹理图像以及弱纹理模式的图像,本文方法整体分割结果明显优于传统的Gabor滤波器、结构张量、拓展结构张量、局部相似度因子等纹理分割方法得到的结果。同时,将本文方法与基于LTP的方法进行对比,分割结果依然更优。在量化指标方面,将本文方法与各种无监督的纹理分割方法就分割准确度进行对比,结果表明,在典型的纹理图像上,本文方法准确度达到97%以上,高于其他方法的分割准确度。结论 提出了一种结合Gabor滤波器和扩展LTP算子的无监督多特征的纹理图像分割方法,能够较好地提取相似纹理模式的特征和纹理的差异性特征,且这些纹理特征可以很好地融合到水平集框架中,对真实世界复杂纹理图像能够得到良好的分割效果。     

基于局部连接度和差异度算子的水平集纹理图像分割

目的 复杂纹理的图像分割一直是图像分割的难题,现有的一些纹理图像分割方法主要通过提取图像确定方向的灰度变化特征或者提取图像的局部灰度相似性特征得到特征图像,从而进行纹理图像的分割,然而,自然纹理中普遍存在局部形态相似和方向不确定的现象,导致现有方法不能准确地分割纹理图像。方法 本文提出局部连接算子和局部差异算子来描述局部纹理的形态相似性和局部纹理的差异度。一方面,通过设定一定阈值,将局部区域的灰度差异分为两类,分析两类差异的分布特征,从而提取图像的形态特性及局部连接度算子;另一方面,设置一种无方向性的灰度差异分析算子,提取图像局部的灰度差异值从而得到局部差异度算子。两个算子结合以更好地提取纹理图像的局部特征,然后通过融合局部相似度特征、局部差异度特征和灰度信息,构造水平集能量泛函,进而通过最小化能量泛函实现纹理图像分割。结果 相比基于Gabor变换、结构张量、局部相似度因子的纹理分割方法,提出的局部算子能够更好地区分自然图像的不同纹理区域,且对实验图像的平均分割准确率高达97%,远高于其他方法。因此,提出的模型对于自然纹理图像具有更好的分割效果。结论 本文提出了两种新颖的纹理特征局部描述子：局部连接度算子和局部差异度算子,能够有效地提取纹理特征,且有一定的互补性。实验表明,提出的方法对于复杂自然纹理图像具有良好的分割效果。     

融合高斯混合模型的测地线脑肿瘤分割方法

脑肿瘤分割是计算机辅助脑病诊断的基础。为提高脑肿瘤分割精度,提出一种融合高斯混合模型的测地线脑肿瘤分割方法。根据相邻2个像素点间互相到达时间构造离散且带有权重的网格图,通过高斯混合模型估计每个像素点属于目标物体的罚度,并融合高斯混合模型的概率密度差异表示区域属性与边缘属性构成能量函数,利用快速最短路径算法求解前景与背景间的测地线距离,并根据该距离最小化能量函数,得到脑肿瘤的分割结果。利用10组脑部核磁共振图像数据对算法进行评估,结果表明,该算法分割结果与金标准的重叠率在0.60~0.85之间,可有效避免局部最优解的情况,对非匀质区域具有较好的分割效果。     

Efficient foreground extraction using RGB-D imaging

Image segmentation is one of the most important topics in the field of computer vision. As a result, many image segmentation approaches have been proposed, and interactive methods based on energy minimization such as GrabCut, have shown successful results. Automating the entire segmentation process is, however, very difficult because virtually all interactive methods require a considerable amount of user interaction. We believe that if additional information is provided to users in order to guide them effectively, the amount of interaction required can be reduced. Consequently, in this paper we propose an efficient foreground extraction algorithm, which utilizes depth information from RGB-D sensors such as Microsoft Kinect and offers users guidance in the foreground extraction process. Our approach can be applied as a pre-processing step for interactive and energy-minimization-based segmentation approaches. Our proposed method is able to segment the foreground from images and give hints that reduce interaction with users. In our method, we make use of the characteristics of depth information captured by RGB-D sensors and describe them using information from the structure tensor. Further, we show experimentally that our proposed method separates foreground from background sufficiently well for real world images.     

Vesselness enhancement diffusion

We propose a new anisotropic diffusion filter to enhance the local coherence of multiscale tubular structures on 2D images. The proposed filter uses a diffusion tensor with diffusion direction and strength determined by the local structure, and chooses automatically for each pixel the diffusion tensor scale. In this paper, we show how this filter enhances X-ray coronary angiographic images to facilitate vessel segmentation. To this aim, we present experimental results of the performance of the filter on synthetic and real images.     

三维人体点云模型多约束肢体分割

针对人体点云模型的肢体分割这一动作识别和虚拟重建领域的重要问题,提出了一种基于分类骨架线、测地距离、特征点和姿态分析的多约束肢体分割算法,通过生成点云模型的分类骨架线,配合测地距离获得人体各部位粗分割点云集,利用测地路径方法实现关键特征点的定位,并利用曲线拟合方式进行定位优化,针对头颈、上肢、下肢和躯干之间关联部位的解剖学特征,构造多种约束条件,对各部位粗分割点云集进行了优化再分割。实验结果表明,所提算法对站姿条件下的不同动作、不同体型、不同精度人体点云模型均能取得与视觉理解相吻合的分割效果。通过该算法得到的肢体各部分点云数据可用于姿态分析等后续研究。