Uncalibrated obstacle detection using normal flow

This paper addresses the problem of obstacle detection for mobile robots. The visual information provided by a single on-board camera is used as input. We assume that the robot is moving on a planar pavement, and any point lying outside this plane is treated as an obstacle. We address the problem of obstacle detection by exploiting the geometric arrangement between the robot, the camera, and the scene. During an initialization stage, we estimate an inverse perspective transformation that maps the image plane onto the horizontal plane. During normal operation, the normal flow is computed and inversely projected onto the horizontal plane. This simplifies the resultant flow pattern, and fast tests can be used to detect obstacles. A salient feature of our method is that only the normal flow information, or first order time-and-space image derivatives, is used, and thus we cope with the aperture problem. Another important issue is that, contrasting with other methods, the vehicle motion and intrinsic and extrinsic parameters of the camera need not be known or calibrated. Both translational and rotational motion can be dealt with. We present motion estimation results on synthetic and real-image data. A real-time version implemented on a mobile robot, is described.     

基于粒子纹理融合的流场可视化方法

基于纹理的可视化方法可以描述流场的整体结构，但传统方法计算耗时，生成可视化图像对比度比较低。从加速可视化整体流程出发，提出了一种基于粒子纹理融合的流场可视化方法。此方法首先随机产生一组噪声图像作为初始粒子分布图，然后依次将初始粒子分布图与根据流动而变形的数据网格加权融合得到粒子轨迹图，最后一帧帧彼此相邻的粒子轨迹图组成一个流场的动态显示。该方法具有独立于流场数据、绘制速度快、生成图像对比度高的特点，参数物理意义明显，不同参数选择可得到不同视觉效果的可视化输出结果，能够充分利用现有硬件图形显示加速设备,已经被成功应用于空间晶体生长实验流场数据的可视化，获得了较好的效果。     

Modeling smooth shape using subdivision on differential coordinates

Traditional subdivision schemes are applied on Euclidean coordinates (the spatial geometry of the control mesh). Although the subdivision limit surfaces are almost everywhere C² continuous, their mean-curvature normals are only C⁰. In order to generate higher quality surfaces with better-distributed mean-curvature normals, we propose a novel framework to apply subdivision for shape modeling, which combines subdivision with differential shape processing. Our framework contains two parts: subdivision on differential coordinates (a kind of differential geometry of the control mesh), and mutual conversions between Euclidean coordinates and differential coordinates. Further discussions about various strategies in both parts include a special subdivision method for mean-curvature normals, additional surface editing options, and a version of our framework for curve design. Finally, we demonstrate the improvement on surface quality by comparing the results between our framework and traditional subdivision methods.     

一个交互实时的多分辨率地形绘制系统

本文设计并实现了一个交互实时的多分辨率地形绘制系统，介绍了系统的组成、实时优化方法的以及地形几何和纹理数据表示和管理方法，并通过一实例对地形绘制系统的性能进行了评价。从绘制结果看，系统对地形进行实时优化时折衷考虑了国象绘制质量和绘制速率，在图象质量没有有明显退化的情况下极大地改善了地形绘制的性能。     

Determining shape and motion from non-overlapping multi-camera rig: A direct approach using normal flows

In this paper, we explore how a wide field-of-view imaging system that consists of a number of cameras in a network arranged to approximate a spherical eye can reduce the complexity of estimating camera motion. Depth map of the imaged scene can be reconstructed once the camera motion is there. We present a direct method to recover camera motion from video data, which neither requires establishment of feature correspondences nor recovery of optical flow, but from normal flow which is directly observable. With a wide visual field, the inherent ambiguities between translation and rotation disappear. Several subsets of normal flow pairs and triplets can be utilized to constraint the directions of translation and rotation separately. The intersection of solution spaces arising from normal flow pairs or triplets yields the estimate on the direction of motion. In addition, the larger number of normal flow measurements so resulted can be used to combat the local flow extraction error. Rotational magnitude is recovered in a subsequent stage. This article details how motion recovery can be improved with the use of such an approximate spherical imaging system. Experimental results on synthetic and real image data are provided. The results show that the accuracy of motion estimation is comparable to those of the state-of-the-art methods that require to use explicit feature correspondences or full optical flows, and our method has a much faster computational speed.     

A model for real-time on-surface flows

Simulating fluid flows for visualization purposes is known to be one of the most challenging fields of the computer graphics domain. While rendering vast liquid areas has been widely addressed this last decade, few papers have tackled the problematic of on-surface flows, even though real-time applications such as drive simulators or video games could greatly benefit from such methods. We present a novel empirical method for the animation of liquid droplets lying on a flat surface, the core of our technique being a simulation operating on a 2D grid which is implementable on GPU. The wetted surface can freely be oriented in space and is not limited to translucent materials, the liquid flow being governed by external forces, the viscosity parameter and the presence of obstacles. Furthermore, we show how to simply incorporate in our simulation scheme two enriching visual effects, namely absorption and ink transport. Rendering can be achieved from an arbitrary view point using a GPU image based raycasting approach and takes into account the refraction and reflection of light. Even though our method doesn’t benefit from the literature of fluid mechanics, we show that convincing animations in terms of realism can be achieved in real-time.     

Viscosity Solutions of a Level-Set Method for Anisotropic Geometric Diffusion in Image Processing

We discuss the existence of viscosity solutions for a class of anisotropic level-set methods which can be seen as an extension of the mean-curvature motion with a nonlinear anisotropic diffusion tensor. In an earlier work (Mikula et al. in Comput. Vis. Sci. 6(4):197–209, [2004]; Preusser and Rumpf in SIAM J. Appl. Math. 62(5):1772–1793, [2002]) we have applied such methods for the denoising and enhancement of static images and image sequences. The models are characterized by the fact that—unlike the mean-curvature motion—they are capable of retaining important geometric structures like edges and corners of the level-sets. The article reviews the definition of the model and discusses its geometric behavior. The proof of the existence of viscosity solutions for these models is based on a fixed point argument which utilizes a compactness property of the diffusion tensor. For the application to image processing suitable regularizations of the diffusion tensor are presented for which the compactness assumptions of the existence proof hold. Finally, we consider the half relaxed limits of the solutions of auxiliary problems to show the compactness of the solution operator and thus the existence of a solution to the original problem.     

基于交叉熵及曲线进化的图像分割算法

该文提出一种新的图像分割算法,从目标和背景区域的差异性出发,利用信息论中的交叉熵作为衡量标准,构造能量函数,通过最小化能量即可得到分割结果。在最小化能量函数时,运用最陡梯度下降法导出曲线进化方程,然后考虑噪声的影响提出了改进模型,并用水平集方法来表示此曲线进化方程,利用快速水平集方法来进行数值求解。最后的仿真结果证明了本文算法的有效性。     

Construction of simplified boundary surfaces from serial-sectioned metal micrographs

We present a method for extracting boundary surfaces from segmented cross-section image data. We use a constrained Potts model to interpolate an arbitrary number of region boundaries between segmented images. This produces a segmented volume from which we extract a triangulated boundary surface using well-known marching tetrahedra methods. This surface contains staircase-like artifacts and an abundance of unnecessary triangles. We describe an approach that addresses these problems with a voxel-accurate simplification algorithm that reduces surface complexity by an order of magnitude. Our boundary interpolation and simplification methods are novel contributions to the study of surface extraction from segmented cross-sections. We have applied our method to construct polycrystal grain boundary surfaces from micrographs of a sample of the metal tantalum.     

空间晶体生长实验中流场的动态显示研究

矢量场可视化是科学计算可视化研究的重要方向.对于复杂环境条件下大数据量矢量场的可视化,传统的方法运算量大,实时性难以满足要求.以空间晶体生长实验中的流场数据可视化为应用背景,针对目前常用方法的不足,引入了一种全新的基于图像的流场可视化方法--IBFV方法,并对该方法的机理进行了深入地分析和研究,给出了一种基于OpenGL图形库的简单实现算法,最终应用于布里奇曼晶体生长实验中流场数据的实时动态显示.实践证明此方法独立于流场数据,具有良好的适用性和直观性,并具有极高的速度,在当前普通PC机上可以实现50fps的动态显示帧频,得到连续无抖动的流场动态图像仿真.     

Model-based brightness constraints: on direct estimation ofstructure and motion

We describe a direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of Horn and Weldon (1988) to three views. Adding the third view enables us to solve for motion and compute a dense depth map of the scene, directly from image spatio-temporal derivatives in a linear manner without first having to find point correspondences or compute optical flow. We describe the advantages and limitations of this method which are then verified with experiments using real images     

Reliable and Efficient Computation of Optical Flow

In this paper, we present two very efficient and accurate algorithms for computing optical flow. The first is a modified gradient-based regularization method, and the other is an SSD-based regularization method. For the gradient-based method, to amend the errors in the discrete image flow equation caused by numerical differentiation as well as temporal and spatial aliasing in the brightness function, we propose to selectively combine the image flow constraint and a contour-based flow constraint into the data constraint by using a reliability measure. Each data constraint is appropriately normalized to obtain an approximate minimum distance (of the data point to the linear flow equation) constraint instead of the conventional linear flow constraint. These modifications lead to robust and accurate optical flow estimation. We propose an incomplete Cholesky preconditioned conjugate gradient algorithm to solve the resulting large and sparse linear system efficiently. Our SSD-based regularization method uses a normalized SSD measure (based on a similar reasoning as in the gradient-based scheme) as the data constraint in a regularization framework. The nonlinear conjugate gradient algorithm in conjunction with an incomplete Cholesky preconditioning is developed to solve the resulting nonlinear minimization problem. Experimental results on synthetic and real image sequences for these two algorithms are given to demonstrate their performance in comparison with competing methods reported in literature.     

一种基于遗传算法的脑MR图像去偏移场模型

由于磁共振图像(magnetic resonance images,MRI)常含有偏移场而影响后继图像分割,针对这种图像的分割,采用Legendre多项式基函数来拟合偏移场,可以去除偏移场对图像分割的影响。当使得恢复图像的信息熵达到最小时,则求得的偏移场最优。在求偏移场的过程中,需要求解基函数的参数,由于传统的梯度下降法易陷入局部最优,为解决此问题,提出将遗传算法引入到参数求解过程中,然而传统的遗传算法不仅时间复杂度高,且易陷入局部最优,为此需对遗传算法进行改进,使得不仅更容易得到全局最优解,且时间复杂度较低。实验证明,该改进算法可以得到精确的偏移场,并可得到准确的分割结果。     

Variational Optic Flow Computation with a Spatio-Temporal Smoothness Constraint

Nonquadratic variational regularization is a well-known and powerful approach for the discontinuity-preserving computation of optic flow. In the present paper, we consider an extension of flow-driven spatial smoothness terms to spatio-temporal regularizers. Our method leads to a rotationally invariant and time symmetric convex optimization problem. It has a unique minimum that can be found in a stable way by standard algorithms such as gradient descent. Since the convexity guarantees global convergence, the result does not depend on the flow initialization. Two iterative algorithms are presented that are not difficult to implement. Qualitative and quantitative results for synthetic and real-world scenes show that our spatio-temporal approach (i) improves optic flow fields significantly, (ii) smoothes out background noise efficiently, and (iii) preserves true motion boundaries. The computational costs are only 50% higher than for a pure spatial approach applied to all subsequent image pairs of the sequence.     

Lucas/Kanade Meets Horn/Schunck: Combining Local and Global Optic Flow Methods

Differential methods belong to the most widely used techniques for optic flow computation in image sequences. They can be classified into local methods such as the Lucas–Kanade technique or Bigün's structure tensor method, and into global methods such as the Horn/Schunck approach and its extensions. Often local methods are more robust under noise, while global techniques yield dense flow fields. The goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways; (i) We juxtapose the role of smoothing/regularisation processes that are required in local and global differential methods for optic flow computation. (ii) This discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches: It yields dense flow fields that are robust against noise. (iii) Spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method. (iv) We propose a simple confidence measure for optic flow methods that minimise energy functionals. It allows to sparsify a dense flow field gradually, depending on the reliability required for the resulting flow. Comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure.     

Curve-skeleton extraction using iterative least squares optimization

A curve skeleton is a compact representation of 3D objects and has numerous applications. It can be used to describe an object's geometry and topology. In this paper, we introduce a novel approach for computing curve skeletons for volumetric representations of the input models. Our algorithm consists of three major steps: 1) using iterative least squares optimization to shrink models and, at the same time, preserving their geometries and topologies, 2) extracting curve skeletons through the thinning algorithm, and 3) pruning unnecessary branches based on shrinking ratios. The proposed method is less sensitive to noise on the surface of models and can generate smoother skeletons. In addition, our shrinking algorithm requires little computation, since the optimization system can be factorized and stored in the pre-computational step. We demonstrate several extracted skeletons that help evaluate our algorithm. We also experimentally compare the proposed method with other well-known methods. Experimental results show advantages when using our method over other techniques.     

Gaussian curvature using fundamental forms for binary voxel data

Local curvature characterizes every point of a surface and measures its deviation from a plane, locally. One application of local curvature measures within the field of image and geometry processing is object segmentation. Here, we present and evaluate a novel algorithm based on the fundamental forms to calculate the curvature on surfaces of objects discretized with respect to a regular three-dimensional grid. Thus, our new algorithm is applicable to voxel data, which are created e.g. from computed tomography (CT). Existing algorithms for binary data used the Gauss map, rather than fundamental forms. For the calculation of the fundamental forms, derivatives of a surface in tangent directions in every point of the surface have to be computed. Since the surfaces exist on grids with restricted resolution, these derivatives have to be discretized. In the presented method, this is realized by projecting the tangent plane onto the discrete object surface. The most important parameter of the proposed algorithm is the size of the chosen window for the calculation of the gradient. The size of this window has to be selected according to object size as well as with respect to distances between objects. In our experiments, an algorithm based on the Gauss map provided inconsistent values for simple test objects, whereas our method provides consistent values. We report quantitative results on various test geometries, compare our method to two algorithms working on gray value data and demonstrate the practical applicability of our novel algorithm to CT-reconstructions of Greenlandic firn.     

Mesh Parametrization Driven by Unit Normal Flow

Based on mesh deformation, we present a unified mesh parametrization algorithm for both planar and spherical domains. Our approach can produce intermediate frames from the original meshes to the targets. We derive and define a novel geometric flow: ‘unit normal flow (UNF)’ and prove that if UNF converges, it will deform a surface to a constant mean curvature (CMC) surface, such as planes and spheres. Our method works by deforming meshes of disk topology to planes, and spherical meshes to spheres. Our algorithm is robust, efficient, simple to implement. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexities. Our experiments show that our algorithm can be a competing alternative approach to other state-of-the-art mesh parametrization methods. The unit normal flow also suggests a potential direction for creating CMC surfaces.     

Extracting Structure from Optical Flow Using the Fast Error Search Technique

In this paper, we present a globally optimal and computationally efficient technique for estimating the focus of expansion (FOE) of an optical flow field, using fast partial search. For each candidate location on a discrete sampling of the image area, we generate a linear system of equations for determining the remaining unknowns, viz. rotation and inverse depth. We compute the least squares error of the system without actually solving the equations, to generate an error surface that describes the goodness of fit across the hypotheses. Using Fourier techniques, we prove that given an N × N flow field, the FOE, and subsequently rotation and structure, can be estimated in operations. Since the resulting system is linear, bounded perturbations in the data lead to bounded errors.We support the theoretical development and proof of our technique with experiments on synthetic and real data. Through a series of experiments on synthetic data, we prove the correctness, robustness and operating envelope of our algorithm. We demonstrate the utility of our technique by applying it for detecting obstacles from a monocular sequence of images.     

Topology optimization of flow domains using the lattice Boltzmann method

We consider the optimal design of two- (2D) and three-dimensional (3D) flow domains using the lattice Boltzmann method (LBM) as an approximation of Navier-Stokes (NS) flows. The problem is solved by a topology optimization approach varying the effective porosity of a fictitious material. The boundaries of the flow domain are represented by potentially discontinuous material distributions. NS flows are traditionally approximated by finite element and finite volume methods. These schemes, while well established as high-fidelity simulation tools using body-fitted meshes, are effected in their accuracy and robustness when regular meshes with zero-velocity constraints along the surface and in the interior of obstacles are used, as is common in topology optimization. Therefore, we study the potential of the LBM for approximating low Mach number incompressible viscous flows for topology optimization. In the LBM the geometry of flow domains is defined in a discontinuous manner, similar to the approach used in material-based topology optimization. In addition, this non-traditional discretization method features parallel scalability and allows for high-resolution, regular fluid meshes. In this paper, we show how the variation of the porosity can be used in conjunction with the LBM for the optimal design of fluid domains, making the LBM an interesting alternative to NS solvers for topology optimization problems. The potential of our topology optimization approach will be illustrated by 2D and 3D numerical examples.