Optimum Fiducials Under Weak Perspective Projection

We investigate how a given fixed number of points should be located in space so that the pose of a camera viewing them from unknown locations can be estimated with the greatest accuracy. We show that optimum solutions are obtained when the points form concentric complete regular polyhedra. For the case of optimal configurations we provide a worst-case error analysis and use it to analyze the effects of weak perspective approximation to true perspective viewing. Comprehensive computer simulations validate the theoretical results.     

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．     

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.     

逆向投影点绘制算法

现有的点绘制算法局限于采用高斯滤波对三维空间中的点模型进行重构,而且在某些视点下绘制结果会出现“洞”．文中算法通过精确的逆向透视投影计算点模型中的每一个顶点在屏幕空间上的形状和影响因子．该算法不仅解决了绘制结果中存在“洞”的问题,而且可以将多种不同的重构滤波器统一在一个绘制框架内,在采用圆锥滤波时可以得到比高斯滤波更好的绘制质量．     

透视和透视投影变换 --论图形变换和投影的若干问题之三

讨论了透视变换的基本原理．由于与画面成一角度的平行线簇经透视变换后交于灭点,因此可采用两种不同的方法来获得透视图：一是保持画面铅垂,通过旋转物体使之与画面构成角度达到透视变换效果,得到了三种最佳透视变换矩阵;二是通过倾斜投影画面达到透视变换效果,给出了通过倾斜画面得到三灭点透视图的齐次透视变换矩阵．两种方法的灭点都是可预先控制(即可先决定灭点再决定变换矩阵)的,比较彻底地解决了透视变换矩阵元素的产生方法．给出了“对一个空间物体,一定存在另一个空间物体,使前者在画面上的透视投影与后者的平行投影是一样的,且保留了深度方向的对应关系”的证明．这个性质可使复杂的透视投影转化成简单的平行投影,使得立体图形的处理大为简化．     

透视投影下三维运动重建

单相机下,三维信息的恢复往往呈现出病态,如何在透视投影约束下恢复高质量的三维人体运动信息是计算机视觉领域一个具有挑战性的课题。提出一个扩展模型,即如何从起点出发,依次扩展到得三维空间中人体关节点的位置,从而恢复出运动信息。相对于已有的算法,提出在搜索空间中用一组最优准则得到连续平滑的扩展起点,并且在扩展过程中利用全局运动平滑假设,有效地消除了深度信息恢复时固有的二义性。最后,将结果运用于动画制作,验证提出的算法的有效性。     

加速透视投影体绘制技术研究

针对可视化中透视体绘制计算量大、耗时较长的不利因素,算法将三维体数据集按照三种主要的观察方向(X,Y,Z)抽取出切片数据,对切片数据进行错切操作,设立一个与切片平行的中间图像平面;在绘制中间图像时使用图形硬件所提供的纹理混和功能;最终图像经过中间图像的变形而得到,从而使绘制速度得到了较大提高。     

A Multi-Frame Structure-from-Motion Algorithm under Perspective Projection

We present a fast, robust algorithm for multi-frame structure from motion from point features which works for general motion and large perspective effects. The algorithm is for point features but easily extends to a direct method based on image intensities. Experiments on synthetic and real sequences show that the algorithm gives results nearly as accurate as the maximum likelihood estimate in a couple of seconds on an IRIS 10000. The results are significantly better than those of an optimal two-image estimate. When the camera projection is close to scaled orthographic, the accuracy is comparable to that of the Tomasi/Kanade algorithm, and the algorithms are comparably fast. The algorithm incorporates a quantitative theoretical analysis of the bas-relief ambiguity and exemplifies how such an analysis can be exploited to improve reconstruction. Also, we demonstrate a structure-from-motion algorithm for partially calibrated cameras, with unknown focal length varying from image to image. Unlike the projective approach, this algorithm fully exploits the partial knowledge of the calibration. It is given by a simple modification of our algorithm for calibrated sequences and is insensitive to errors in calibrating the camera center. Theoretically, we show that unknown focal-length variations strengthen the effects of the bas-relief ambiguity. This paper includes extensive experimental studies of two-frame reconstruction and the Tomasi/Kanade approach in comparison to our algorithm. We find that two-frame algorithms are surprisingly robust and accurate, despite some problems with local minima. We demonstrate experimentally that a nearly optimal two-frame reconstruction can be computed quickly, by a minimization in the motion parameters alone. Lastly, we show that a well known problem with the Tomasi/Kanade algorithm is often not a significant one.     

快速自适应模板图像修复算法

在对图像局部特性分析的基础上,提出了一种简单的非迭代自适应模板快速图像修复算法。该算法首先通过对待修复点邻域像素梯度值进行排序,估计出该点的等照度线方向,从而自适应地确定其修复模板,然后利用快进法(fast marching method)确定修复路径并完成对整个破损区域的修复。实验结果表明,该算法对边缘细节及平滑区域均有良好的修复能力,在相近的修复时间内能得到明显优于一般快速图像修复算法的修复效果。     

A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras

We describe a mathematical and algorithmic study of the Lambertian “Shape-From-Shading” problem for orthographic and pinhole cameras. Our approach is based upon the notion of viscosity solutions of Hamilton-Jacobi equations. This approach provides a mathematical framework in which we can show that the problem is well-posed (we prove the existence of a solution and we characterize all the solutions). Our contribution is threefold. First, we model the camera both as orthographic and as perspective (pinhole), whereas most authors assume an orthographic projection (see Horn and Brooks (1989) for a survey of the SFS problem up to 1989 and Zhang et al. (1999), Kozera (1998), Durou et al. (2004) for more recent ones); thus we extend the applicability of shape from shading methods to more realistic acquisition models. In particular it extends the work of Prados et al. (2002a) and Rouy and Tourin (1992). We provide some novel mathematical formulations of this problem yielding new partial differential equations. Results about the existence and uniqueness of their solutions are also obtained. Second, by introducing a “generic” Hamiltonian, we define a general framework allowing to deal with both models (orthographic and perspective), thereby simplifying the formalization of the problem. Thanks to this unification, each algorithm we propose can compute numerical solutions corresponding to all the modeling. Third, our work allows us to come up with two new generic algorithms for computing numerical approximations of the “continuous solution of the “Shape-From-Shading” problem as well as a proof of their convergence toward that solution. Moreover, our two generic algorithms are able to deal with discontinuous images as well as images containing black shadows. First online version published in October, 2005     

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。     

关于透视变换的研究

针对透视图形变换中“二点透视图、三点透视图是经过旋转平移方法获得的”的提法进行了研究,认为该提法获得的透视图与二点透视、三点透视的基本概念不相符,实际是属于一点透视下二个灭点,三个灭点的透视图,文中分别给出二点透视图和一点透视下二个灭点的透视图,并进行了论证。     

Numerical Shape-From-Shading for Discontinuous Photographic Images

The height, u(x, y), of a continuous, Lambertian surface of known albedo (i.e., grayness) is related to u(x, y), information recoverable from a black and white flash photograph of the surface, by the partial differential equation

水平集方法中符号距离函数的快速生成

准确快速地计算任意闭合曲线的符号距离函数,是提高水平集方法的效率和稳定性的至关重要的一步。改进了基于快速步进法标记任意闭合曲线内外部的方法,优化了基于源点映射扫描方法生成距离函数值的方法。实验证明方法准确有效,进一步提高了水平集方法中符号距离函数的生成速度。     

基于曲率和中值滤波的快速推移图像修复方法*

提出了一种结合中值滤波和基于曲率扩散的图像修复方法。中值滤波修复方法对于灰度值变化比较平缓的图像,修复效果从时间性能和视觉效果上均比较好,但对于灰度值变化比较剧烈的图像,效果不能令人满意。在结合了基于曲率扩散的修复方法之后,中值滤波的不足之处得到了改善。基于曲率扩散的修复方法考虑了图像本身的几何信息,在修复图像的几何特征上有较高的准确度。图像修复顺序由已知区域向未知区域扩散时经过各破损点的时间决定,用快速推移方法计算该时间。实验表明,该算法能高效、稳定地处理破损区域的图像信息。     

改进的Fast Marching方法在医学图像分割中的应用

Fast Marching方法应用于医学图像分割取得了较好的分割结果,但是Fast Marching方法对边缘比较模糊的图像不能准确完整地分割出来。提出了一种结合像素间信任连接算法和Fast Marching方法的医学图像分割方法,首先用高斯滤波器对图像进行滤波,然后对图像用基于像素间信任连接的算法提取待分割图像中目标区域,取得较大的同质区,最后用Fast Marching方法对图像进行分割。实验结果表明,该方法对边缘模糊和目标内部存在伪边缘的医学图像能取得较好的分割结果。     

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。     

基于分组行进算法的图像修补方法

图像修补是图像恢复研究中的一个重要内容,它的目的是根据图像的现有信息来自动恢复丢失的信息。虽然图像修补的基本思想十分简单,但是许多的图像修补算法都十分复杂,而且难于实现。快速行进算法(FMM)与水平集法(Level Set)相结合进行曲线进化是一种高效的曲线进化算法,该算法的时间复杂度是O(NlbN)。Kim提出了另一种水平集的曲线进化算法——分组行进算法(GMM),该算法的时间复杂度是O(N)。受其启发,为了更快地进行图像修补,提出了一种基于GMM算法的图像修补的新算法,并研究了对GMM算法的细节改进。为了验证算法的快速性,还给出了使用Bertalmio提出的算法、Telea提出的算法以及新算法对同一幅图片进行修补的实验结果。通过比较发现,该新算法在大幅度提高修补速度的同时,仍能保持较好的修补效果。     

FMM与改进GBNN模型相结合的多AUV实时围捕算法

多自主水下机器人(AUV)实时围捕是一个综合的研究课题,包括联盟生成和目标追捕等阶段.首先,基于快速行进算法(FMM)预估围捕时间,有效形成多AUV的动态围捕联盟;然后,在追捕阶段, AUV需要立即跟踪智能逃逸机器人以防止其逃跑.为了实现这一目标,在GBNN (Glasius biological inspired neural network)模型中使用反比例函数替换指数函数计算神经元连接权值,加入额外的衰减项,并提出两点加快神经元活性传播的改进措施,使其适用于实时追捕路径规划.仿真研究表明,围捕联盟形成机制和反比例权值GBNN模型实时路径规划策略都显示出其优越性.在水下环境的多AUV协作围捕中,所提出的围捕控制算法可以提高围捕效率,减少AUV所花费的追捕距离和逃逸机器人的逃逸距离.     

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.