基于高阶LLF和WENO算法的透视SFS

透视投影下从明暗恢复形状(SFS)问题,通常通过结合静态HamiltonJacobi(HJ)方程和快速扫描方法来求解。为进一步优化静态HJ方程的求解精度,改善透视SFS的恢复结果,采用了高阶局部LaxFriedrichs(LLF)通量分裂格式,以提高待求量的偏导数的精度;同时采用了改进的加权本质无振荡(WENO)格式,使得算法只计算整格点值,并且利用修正的光滑因子得到比WENO更高的精度。对合成图像和实际图像的实验结果表明,可以有效提高透视投影SFS问题的恢复精度。     

利用等值线跟踪的快速步进法

针对由明暗重构三维形状及普遍意义上的Eikonal偏微分方程求解问题,提出一种基于等值线跟踪的快速步进法,通过跟踪等值线的传播,利用迎风格式对等值线附近的扩展区域进行单遍或两遍更新,使求解过程具有O（N）复杂度．实验结果表明,该方法改进了已有快速步进法的速度和精度,可有效地处理多源问题及由明暗重构形状问题,且在复杂情形下速度优于快速扫描法．     

基于自适应网格的快速步进法

针对形状重建及Eikonal方程求解问题,提出了一种根据曲面曲率动态地对网格进行细化的快速步进法,证明了该方法在一阶差分情形下符合因果律,在实现中利用哈希表对邻接点进行快速定位。实验结果表明,该方法较已有方法计算误差小,对噪声适应力较强,可有效处理从明暗恢复形状问题。     

由单幅图像重构表面形状的B样条变分法研究

针对SFS（Shape From Shading)问题中的Lagrange乘子难题,经过B样条插值,将SFS问题的积性、光滑性限制隐含、消除Lagrange乘子的不利影响,采用B样条变分法解决了SFS问题;并根据B样条特殊结构,设计了SFS问题变分格式的层次基变换共轭梯度加速度法,初步的计算实例表明,此方法在精度、速度上有所提高,效果令人满意。     

基于表面局部最高点估计的明暗恢复形状算法

基于数据逼近强约束的针图恢复算法是近年来提出的一种较为成功的从明暗恢复形状（shape from shading）的算法,但由于该算法在非垂直光线下得到的初始化针图的误差较大,并且不能保证法向量有解或有唯一解,为了解决SFS算法存在的问题,提出了一种改进的SFS算法。该改进算法从分析非垂直光线下图像梯度图与针图之间的关系入手,首先检测图像局部最亮点位置;然后根据照度方程估计表面局部最高点的位置,同时对梯度方向进行调整,并建立方程组;最后针对方程组解的不同情况,提出了相应的处理方法。改进后的算法,对于垂直光线和非垂直光线下的情况同样有效,从而扩大了基于数据逼近强约束的SFS算法的适用范围。从合成图像和实际图像的实验结果可以看出,采用改进的算法可以得到比基于数据逼近强约束的算法更接近真实表面的初始化针图和初始化高度。     

从阴影恢复形状的径向基函数反射模型研究

目的 为解决传统阴影恢复形状（SFS）算法由于光源方向初始信息估计不准确,恢复的物体表面过于光滑,3维表面形状误差较大等问题,建立了基于径向基函数神经网络的反射模型,并对传统的神经网络进行了改进。方法 建立的基于径向基函数（SFS）神经网络的从阴影恢复形状反射模型代替了传统方法中采用的理想朗伯体表面反射模型。该模型利用径向基函数优秀的局部映射和函数逼近能力来处理SFS问题,通过网络训练过程中的权值代替物体所受到的初始光源信息,解决了传统算法在进行计算时,必须已知光源参数的限制。在该网络模型中添加自适应学习率算法,加速网络的收敛和训练速度。结果 针对SFS问题处理的两幅经典合成图像以及两幅实际图像进行了实验,实验结果表明,改进后的算法在3维视觉效果和3维形状信息的恢复方面都明显优于传统算法。归一化后的3维高度误差结果相比传统算法缩小了60%以上,而且同时适用合成图像和实际图像;自适应学习率的加入,使得网络的训练速度大大加快,对一幅128×128像素的图像,运算速度提升了50%。结论 本文针对SFS问题建立了基于RBF神经网络的从阴影恢复形状反射模型,利用网络模型中的参数代替SFS问题中的初始光源信息,通过最优化方法求解SFS问题。并针对传统的神经网络固定学习率造成网络收敛速度慢,容易陷入局部极小值的问题,加入了自适应学习率算法。实验结果表明,改进后的算法在处理该SFS问题时表现了优秀的性能,适用范围更广,收敛速度更快。     

基于在线磨粒和改进RAGA-PPC传动箱磨损状态评估研究

针对装甲车辆传动箱油液中磨损颗粒收集滞后,数据维数高,设备磨损权重难以确定问题。使用安装在传动箱上的在线油液磨粒传感器采集数据,建立变速箱磨损状态的7个评价指标。采用罚函数法构建投影指标模型（PPC）,降低数据维数。为了避免初始值和初始搜索方向引起的局部收敛,采用改进加速遗传算法（RAGA）求解最佳投影方向。得到最佳投影方向后将7个指标投影到低维数据空间,分析投影边界值得到运行投影范围。通过分析在线数据投影值落点,得到设备的磨损状态。该方法提高了寻优速度和判别精度,实现了更有效的传动箱磨损状态评估。     

梯度约束SFS的月面地形重构

目的 解决月面着陆器在下降过程中可能得不到足够的匹配点进行着陆区地形恢复的问题。方法 基于特征边缘线梯度比例约束的明暗恢复形状（shape from shading）算法。首先以Lommel-Seeliger模型模拟月表反射情况,建立辐照度方程;然后以地形特征边缘提取结果为基础,经过最小二乘拟合与表面光滑模型约束后,演化得到剩余影像点的梯度比例因子,实现对辐照度方程的正则化约束。结果 经过测试得到模拟影像的平均相对恢复精度可以达到-0.199,真实影像月面可以达到0.051和0.022。结论 本文算法能够有效地进行3维地形恢复,且恢复精度优于经典SFS算法中对实际地形恢复效果最好的Tsai算法。     

基于粗糙表面模型的三维形貌恢复研究

文中提出了一种针对粗糙物体的表面反射模型,即用Oren-Nayar模型代替通用的朗伯体表面反射模型(Lamber-tian surface reflection model),并基于透视投影从明暗恢复形状(shape from shading),对图像进行三维重建,此三维重建具有很高的现实意义.实验用该模型对两幅较粗糙的真实图像进行重建并与在朗伯体模型下得到的结果进行比较,实验结果表明对于粗糙物体文中方法能得到较好的恢复效果,说明本SFS方法是有效且收敛的.     

基于互补约束规划模型的投影Barzilai-Borwein梯度算法求解绝对值方程

在绝对值方程◢Ax-|x|=b◣问题有解情形下,给出了求解绝对值问题的一种新方法。首先建立了一等价求解绝对值问题的互补约束规划模型,进而利用新模型中的非负约束给出了求解绝对值问题投影Barzilai-Borwein（BB）梯度算法。数值实验结果表明了该方法的有效性。     

Optimal Algorithm for Shape from Shading and Path Planning

An optimal algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the height of the reconstructed surface is a weighted distance. A consistent numerical scheme based on Sethian's fast marching method is used to compute the reconstructed surface. The surface is a viscosity solution of an Eikonal equation for the vertical light source case. For the oblique light source case, the reconstructed surface is the viscosity solution to a different partial differential equation. A modification of the fast marching method yields a numerically consistent, computationally optimal, and practically fast algorithm for the classical shape from shading problem. Next, the fast marching method coupled with a back tracking via gradient descent along the reconstructed surface is shown to solve the path planning problem in robot navigation.     

Spherical surface parameterization for perspective shape from shading

We propose a new mathematical formulation for perspective shape from shading (PSFS) problems. Our approach is based on representing the unknown surface as a spherical surface, expressed by Euclidean distance to the optical centre, as opposed to the traditional representation by distance from the image plane. We show that our parameterization is better suited for perspective camera models and results in simpler models and equations for classical PSFS problems with a light source in the optical centre. The unknown distance field satisfies a simple isotropic Eikonal equation on the unit sphere in the case of a Lambertian surface reflection model. This is in contrast to previous methods with depth field parameterization, which result in anisotropic equations. Adding light attenuation to the model, we show that the distance field satisfies an Eikonal type of equation with a zero order term. We show how both Eikonal equations can be approximated by very efficient Fast Marching methods. A number of numerical tests and examples are provided to demonstrate our approach, and to compare with previous work. Our results indicate competitive accuracy and computational time that are several orders of magnitude faster than state-of-the-art iterative algorithms. A preliminary investigation indicates that our method could be used in more general PSFS problems.     

Multi-stencils fast marching methods: a highly accurate solution to the eikonal equation on cartesian domains

A wide range of computer vision applications require an accurate solution of a particular Hamilton-Jacobi (HJ) equation known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multistencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, two stencils cover 8-neighbors of the point, whereas in 3D space, six stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.     

基于三角域快速行进法的地震波走时计算

地震波走时计算是地震资料解释处理技术的重要组成部分,本文根据复杂地层构造中速度场分布的特点,设计了一种采用快速行进法基于三角网格的走时计算方法,针对计算效率优化和快速行进法在三角域上的计算格式进行了重点的研究,并根据地层限定条件对速度场进行网格剖分,在三角网格上用快速行进算法计算各点走时。与基于矩形网格的差分方法相比,该方法不需要对速度场边界进行任何平滑,无须通过细分网格来提高计算精度 可根据不同地质构造的复杂度进行变网格大小的剖分,网格剖分数目相对较少。最后通过计算实例进行了验证。     

Improving Shape from Shading with Interactive Tabu Search

Optimisation based shape from shading (SFS) is sensitive to initialization: errors in initialization are a significant cause of poor overall shape reconstruction. In this paper, we present a method to help overcome this problem by means of user interaction. There are two key elements in our method. Firstly, we extend SFS to consider a set of initializations, rather than to use a single one. Secondly, we efficiently explore this initialization space using a heuristic search method, tabu search, guided by user evaluation of the reconstruction quality. Reconstruction results on both synthetic and real images demonstrate the effectiveness of our method in providing more desirable shape reconstructions.     

A numerical modelling for the extraction of decay regions from color images of monuments

An innovative application focused on the segmentation of decay zones from images of stone materials is presented. The adopted numerical approach to extract decay regions from the color images of monuments provides a tool that helps experts analyze degraded regions by contouring them. In this way even if the results of the proposed procedure depend on the evaluation of experts, the approach can be a contribution to improving the efficiency of the boundary detection process. The segmentation is a process that allows an image to be divided into disjoint zones so that partitioned zones contain homogeneous characteristics. The numerical method, used to segment color images, is based on the theory of interface evolution, which is described by the eikonal equation. We adopted the fast marching technique to solve the upwind finite difference approximation of the eikonal equation. The fast marching starts from a seed point in the region of interest and generates a front which evolves according to a specific speed function until the boundary of the region is identified. We describe the segmentation results obtained with two speed functions, attained by the image gradient computation and color information about the object of interest. Moreover, we present the extension of the working modality of the method by introducing the possibility to extract the regions not only in a local way but also in a global way on the entire image. In this case, in order to improve the segmentation efficiency the application of the fast marching technique starts with more seed points defined as seed regions. The study case concerns the impressive remains of the Roman Theatre in the city of Aosta (Italy). In the image segmentation process the color space L^∗a^∗b^∗$L^{\ast }{a}^{\ast }{b}^{\ast }$ is utilized.     

Multiphase image segmentation using a phase-field model

In this paper, we propose a new, fast, and stable hybrid numerical method for multiphase image segmentation using a phase-field model. The proposed model is based on the Allen-Cahn equation with a multiple well potential and a data-fitting term. The model is computationally superior to the previous multiphase image segmentation via Modica-Mortola phase transition and a fitting term. We split its numerical solution algorithm into linear and a nonlinear equations. The linear equation is discretized using an implicit scheme and the resulting discrete system of equations is solved by a fast numerical method such as a multigrid method. The nonlinear equation is solved analytically due to the availability of a closed-form solution. We also propose an initialization algorithm based on the target objects for the fast image segmentation. Finally, various numerical experiments on real and synthetic images with noises are presented to demonstrate the efficiency and robustness of the proposed model and the numerical method.     

Symmetric Shape-from-Shading Using Self-ratio Image

In this paper, we present a symmetric shape-from-shading (SFS) approach to recover both shape and albedo for symmetric objects. Lambertian surfaces with unknown varying albedo and orthographic projections are assumed. In our formulation of symmetric SFS, we have two image irradiance equations. One is the standard equation used in SFS, and the other is a self-ratio image irradiance equation. This new image irradiance equation relates the self-ratio image which is defined as the ratio of two-halves of the input image to light source and surface shape. The introduction of the self-ratio image facilitates the direct use of symmetry cue. Based on the self-ratio image, a new model-based symmetric source-from-shading algorithm is also presented. We then propose symmetric SFS algorithms to recover both shape and albedo from a single image and present experimental results.The new symmetric SFS scheme has one important property: the existence of a unique (global) solution which consists of unique (local) solutions at each point simultaneously obtained using the intensity information at that point and the surrounding local region and the assumption of a C ² surface. Proofs for the existence of a unique solution in the cases of unknown constant and non-constant albedos are provided.