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。     

基于自适应Eikonal方程的改进透视SFS算法

PFMM（perspective fast marching method）是一种有效解决透视投影下从明暗恢复形状（SFS）问题的方法,但是适应条件受限,且对初始数据的精度较为敏感。本文通过对Eikonal方程系数的分析,提出了在透视投影下基于自适应Eikonal方程的PFMM,解决了PFMM对初始数据过于依赖的问题,是PFMM的推广。对合成图像的实验表明本文算法比PFMM精度更高,对透视投影下SFS问题可以得到比较好的结果。     

基于SFS原理的SMT焊点表面三维重构技术研究

基于明暗重构形状原理重构表面组装焊点的表面三维形状过程是:先通过图像采集设备,采集到SMT焊点图像,使用相关的图像处理技术,对SMT焊点图像进行处理;根据一个确定的反射模型建立物体表面形状与图像亮度之间的约束关系和物体表面形状的先验知识建立物体表面形状参数的约束关系,然后对这些约束关系联立求解,可得到物体表面的三维形状.同时针对不可接受SMT焊点图像重构出的三维图像不够理想的缺点进行了改进.在阐述其基本思想和原理的基础上,结合实例介绍了该技术的实现方法与步骤,对其中焊点图像的获取与处理、焊点三维重构技术算法等主要内容与关键技术进行了研究和探讨,并对结果进行了分析验证.     

基于SFS方法的三维表面重建算法研究

SFS(由明暗恢复形状)方法研究是计算机三维视觉研究领域中的一个重要分支.以朗伯体光照漫反射模型为基础,对物体表面图像明暗恢复其表面高度和梯度的抽象模型进行分析,研究基于朗伯体定律求解受光点梯度的算法及SFS方法的实现原理.     

基于明暗恢复法的三维重建算法分析

明暗恢复形状法是计算机视觉领域的热门问题。明暗恢复法是通过一张照片的灰度信息恢复物体表面形状的一种方法。本文从数学角度度分析了SFS问题,并提出了三种解法:直接法求解,变分法求解和采用优化理论理论求解。并分析比较了这三种方法的适用范围和各自的典型算法。最后分析了SFS问题的发展趋势和难点问题。     

结合快速步进法的Level Set人体足部图像分割

针对Level set算法运算速度较慢和易产生边缘泄露的不足,引入了结合快速步进的Level Set算法,提出了一套完整的分割人体足部骨骼图像技术路线.修正了原始"光切片"图像噪声多的不足,通过预处理去除噪声,增强边缘;设定分割初始点和运算参数,运行改进的Level set算法提取骨骼区域;运行形态学开操作进行边缘断裂和毛刺修复.实验结果表明,该处理流程具有较好的准确度和鲁棒性,与经典Level Set算法相比,改进的算法能提高19%～36%的运行速度.     

一种改进的快速步进图像修复算法

图像修复是数字图像处理的重要内容，可用于恢复图像中小的破损区域、文字去除以及目标物体隐藏。基于水平集应用的快进修复算法可以简单快速且有效地修复数字图像中的破损区域，但对边缘的保持能力不够。针对这一问题提出了改进方案。利用梯度排序来保持图像内部的边缘，实验结果也表明改进后的修复结果要优于原算法。     

一种改进的快速步进图像修复算法

图像修复是数字图像处理的重要内容,可用于恢复图像中小的破损区域、文字去除以及目标物体隐藏。基于水平集应用的快进修复算法可以简单快速且有效地修复数字图像中的破损区域,但对边缘的保持能力不够。针对这一问题提出了改进方案。利用梯度排序来保持图像内部的边缘,实验结果也表明改进后的修复结果要优于原算法。     

基于多粒度匹配的高超速飞行体三维重构方法

针对高超速飞行体在飞行过程中能获取到的图像信息较少,无法完全复现其轮廓信息,提出一种基于多粒度匹配的三维重构优化方法。首先通过两台高分辨率CCD相机正交的阴影照相站系统采集高超速飞行体多幅图像信息,利用图像分割技术提取物体的二维轮廓;然后采用改进的SFS算法求解出物体表面各点的相对高度和表面法向量,恢复其三维形貌;最后使用图像拼接优化技术实现高超速飞行体表面的三维重构。并经过实体模型的三维重构验证所提方法的可行性及有效性。     

基于混合反射模型的SFS有限元方法的研究

提出了基于混合反射模型的由明暗恢复物体三维形状的有限元算法。用正方形面元逼近光滑曲面,把曲面表示为所有节点基函数的线性组合;基于既含有漫反射成分又有镜面反射成分的混合模型,结合节点基函数,将反射图线性化。考虑数字图像的特点,直接使用离散形式的SFS问题的亮度约束形式,用最小化方法得到高度满足的线性方程;使用Kaczmarz算法计算出表面三维形状。使用合成图像和实际图像验证该文算法的有效性,探讨了该算法的性能。     

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。     

Shape-from-Shading Under Perspective Projection

Shape-from-Shading (SfS) is a fundamental problem in Computer Vision. A very common assumption in this field is that image projection is orthographic. This paper re-examines the basis of SfS, the image irradiance equation, under a perspective projection assumption. The resultant equation does not depend on the depth function directly, but rather, on its natural logarithm. As such, it is invariant to scale changes of the depth function. A reconstruction method based on the perspective formula is then suggested; it is a modification of the Fast Marching method of Kimmel and Sethian. Following that, a comparison of the orthographic Fast Marching, perspective Fast Marching and the perspective algorithm of Prados and Faugeras on synthetic images is presented. The two perspective methods show better reconstruction results than the orthographic. The algorithm of Prados and Faugeras equates with the perspective Fast Marching. Following that, a comparison of the orthographic and perspective versions of the Fast Marching method on endoscopic images is introduced. The perspective algorithm outperformed the orthographic one. These findings suggest that the more realistic set of assumptions of perspective SfS improves reconstruction significantly with respect to orthographic SfS. The findings also provide evidence that perspective SfS can be used for real-life applications in fields such as endoscopy.This research has been supported in part by Tel-Aviv University fund, the Adams Super-Center for Brain Studies, the Israeli Ministry of Science, the ISF Center for Excellence in Applied Geometry, the Minerva Center for geometry, and the A.M.N. fund.     

基于Fast Marching方法的多目标点路径规划的研究

目前,水下自主机器鱼已经被应用于对水域多个目标点依次进行水质监测,因此有必要研究多个目标点的路径规划。针对遍历多个目标点的路径规划问题,提出一种Multi-Direction Fast Marching（MDFM）方法和遗传算法相结合的路径规划方法。该方法首先使用MDFM方法对工作站和多个目标点两两之间进行路径规划,然后使用遗传算法规划出遍历所有点的最短路径,最后通过仿真实验验证算法的可行性。     

UAVs Mission Planning with Imposition of Flight Level through Fast Marching Square

Many proposed activities to be carried out by unmanned aerial vehicles (UAVs) in urban environments require a control over the altitude for different purposes. Energy saving and minimization of costs are some of these objectives. This work presents a method to impose a flight level in a mission planning carried out by a UAV in a 3D urban environment. The planning avoids all obstacles encountered in the environment and maintains a fixed flight level in the majority of the trajectory. The method used as planner is the Fast Marching Square (FM²) method, which includes two adjustment parameters. Depending on the values of these parameters, it is possible to introduce into the planning an altitude constraint, as well as to modify the smoothness of the trajectory and the safety margins from the obstacles. Several simulated experiments have been carried out in different situations obtaining very good results.     

A Fast Marching Method for the Area Based Affine Distance

In a previous paper, it was proved that the area based affine distance of a convex region in the plane satisfies a non-homogeneous Monge-Ampère differential equation. Based on this equation, in this paper we propose a fast marching method for the computation of this distance. The proposed algorithm has a lower computational complexity than the direct method and we have proved its convergence. And since the algorithm allows one to obtain a connection from any point of the region to the boundary by a path of decreasing distance, it offers a dynamic point of view for the area based affine distance.

Fast Image Inpainting Based on Coherence Transport

High-quality image inpainting methods based on nonlinear higher-order partial differential equations have been developed in the last few years. These methods are iterative by nature, with a time variable serving as iteration parameter. For reasons of stability a large number of iterations can be needed which results in a computational complexity that is often too large for interactive image manipulation.Based on a detailed analysis of stationary first order transport equations the current paper develops a fast noniterative method for image inpainting. It traverses the inpainting domain by the fast marching method just once while transporting, along the way, image values in a coherence direction robustly estimated by means of the structure tensor. Depending on a measure of coherence strength the method switches continuously between diffusion and directional transport. It satisfies a comparison principle. Experiments with the inpainting of gray tone and color images show that the novel algorithm meets the high level of quality of the methods of Bertalmio et al. (SIG-GRAPH ’00: Proc. 27th Conf. on Computer Graphics and Interactive Techniques, New Orleans, ACM Press/Addison-Wesley, New York, pp. 417–424, 2000), Masnou (IEEE Trans. Image Process. 11(2):68–76, 2002), and Tschumperlé (Int. J. Comput. Vis. 68(1):65–82, 2006), while being faster by at least an order of magnitude.     

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.