Accurate optical flow computation under non-uniform brightness variations

In this paper, we present a very accurate algorithm for computing optical flow with non-uniform brightness variations. The proposed algorithm is based on a generalized dynamic image model (GDIM) in conjunction with a regularization framework to cope with the problem of non-uniform brightness variations. To alleviate flow constraint errors due to image aliasing and noise, we employ a reweighted least-squares method to suppress unreliable flow constraints, thus leading to robust estimation of optical flow. In addition, a dynamic smoothness adjustment scheme is proposed to efficiently suppress the smoothness constraint in the vicinity of the motion and brightness variation discontinuities, thereby preserving motion boundaries. We also employ a constraint refinement scheme, which aims at reducing the approximation errors in the first-order differential flow equation, to refine the optical flow estimation especially for large image motions. To efficiently minimize the resulting energy function for optical flow computation, we utilize an incomplete Cholesky preconditioned conjugate gradient algorithm to solve the large linear system. Experimental results on some synthetic and real image sequences show that the proposed algorithm compares favorably to most existing techniques reported in literature in terms of accuracy in optical flow computation with 100% density.     

空域中基于正则化的自适应超分辨率图像复原

对于模糊图像的复原问题,从正则化技术克服问题病态性的思想出发,研究了一种有效的超分辨率图像复原方法.在Nguyen等人的正则图像复原框架的基础上,根据Roberts交叉梯度算子构造正则项,从自适应的角度生成正则化参数,并用共轭梯度法求解该模型的目标泛函极小值.计算机仿真结果表明,该方法可较好的再现图像的重要信息,复原图像的相对误差降低,同时,峰值信噪比和主观视觉效果方面都有明显的提高.     

大型稀疏线性方程组新的ICCG方法

有限元线性方程组的系数矩阵一般具有稀疏性和对称性的特点,全稀疏存贮方法就是利用这些特点,只存贮对称部分的非零元素,采用链表式管理,即节省存贮空间,又便于动态更改．在完全Cholesky分解的基础上,构造出了新的预处理方法,应用适当的对角元修正策略,得到了一种新的ICCG方法,能够确保方程组高效准确的分解和求解．数值算例证明该算法在时间和存贮上都较为占优,可靠高效,能够应用于有限元线性方程组的求解．     

A General Motion Model and Spatio-Temporal Filters for Computing Optical Flow

Traditional optical flow algorithms assume local image translational motion and apply simple image filtering techniques. Recent studies have taken two separate approaches toward improving the accuracy of computed flow: the application of spatio-temporal filtering schemes and the use of advanced motion models such as the affine model. Each has achieved some improvement over traditional algorithms in specialized situations but the computation of accurate optical flow for general motion has been elusive. In this paper, we exploit the interdependency between these two approaches and propose a unified approach. The general motion model we adopt characterizes arbitrary 3-D steady motion. Under perspective projection, we derive an image motion equation that describes the spatio-temporal relation of gray-scale intensity in an image sequence, thus making the utilization of 3-D filtering possible. However, to accommodate this motion model, we need to extend the filter design to derive additional motion constraint equations. Using Hermite polynomials, we design differentiation filters, whose orthogonality and Gaussian derivative properties insure numerical stability; a recursive relation facilitates application of the general nonlinear motion model while separability promotes efficiency. The resulting algorithm produces accurate optical flow and other useful motion parameters. It is evaluated quantitatively using the scheme established by Barron et al. (1994) and qualitatively with real images.     

Preconditioned edge-preserving image deblurring and denoising

Preconditioned conjugate gradient (PCG) algorithms have been successfully used to significantly reduce the number of iterations in Tikhonov regularization techniques for image restoration. Nevertheless, in many cases Tikhonov regularization is inadequate, in that it produces images that are oversmoothed across intensity edges. Edge-preserving regularization can overcome this inconvenience but has a higher complexity, in that it involves non-convex optimization. In this paper, we show how the use of preconditioners can improve the computational performance of edge-preserving image restoration as well. In particular, we adopt an image model which explicitly accounts for a constrained binary line process, and a mixed-annealing algorithm that alternates steps of stochastic updating of the lines with steps of preconditioned conjugate gradient-based estimation of the intensity. The presence of the line process requires a specific preconditioning strategy to manage the particular structure of the matrix of the equivalent least squares problem. Experimental results are provided to show the satisfactory performance of the method, both with respect to the quality of the restored images and the computational saving.     

Mapping Conjugate Gradient Algorithms for Neutron Diffusion Applications onto SIMD, MIMD, and Mixed-Mode Machines

The performance of conjugate gradient (CG) algorithms for the solution of the system of linear equations that results from the finite-differencing of the neutron diffusion equation was analyzed on SIMD, MIMD, and mixed-mode parallel machines. A block preconditioner based on the incomplete Cholesky factorization was used to accelerate the conjugate gradient search. The issues involved in mapping both the unpreconditioned and preconditioned conjugate gradient algorithms onto the mixed-mode PASM prototype, the SIMD MasPar MP-1, and the MIMD Intel Paragon XP/S are discussed. On PASM , the mixed-mode implementation outperformed either SIMD or MIMD alone. Theoretical performance predictions were analyzed and compared with the experimental results on the MasPar MP-1 and the Paragon XP/S. Other issues addressed include the impact on execution time of the number of processors used, the effect of the interprocessor communication network on performance, and the relationship of the number of processors to the quality of the preconditioning. Applications studies such as this are necessary in the development of software tools for mapping algorithms onto either a single parallel machine or a heterogeneous suite of parallel machines.     

Optical flow with an intensity-weighted smoothing

Matching algorithms which use image structure such as edges and junctions cannot perform well on unstructured images. For such images, global gradient-based methods may be more appropriate. Some of the assumptions involved in applying discretized conservation equations such as the optical flow equation are discussed and an intensity-weighted method of estimating dense displacement fields is presented, which attempts to avoid some of the problems of the standard methods. The only derivative required is the intensity gradient, and the method includes procedures for automatic parameter evaluation. The algorithm is expected to perform better than conventional algorithms on images without strong texture, as is demonstrated on the test set of images     

不完全乔莱斯基分解预优共轭梯度的模型

在超分辨率影像重建中，基于最大后验估计(MAP)框架的重建方法具有较大的优势，应用非常广泛。然而，常用的迭代求解方法如最速下降法、共轭梯度法等收敛速度慢、处理时间长，经常难以满足实际处理的需要。该文在MAP框架的基础上，提出了基于不完全乔莱斯基分解预优共轭梯度的模型求解方法，即在迭代求解过程中利用不完全乔莱斯基分解构造预优矩阵，降低系数矩阵的条件数，从而提高收敛速度，节省处理时间。实验结果证明，该方法是有效的、可行的。     

A non-conforming finite element method for solving a least-square formulation of tricomi's problem

The purpose of this work is to solve in the plane Tricomi's equation of mixed type by means of global least-square formulation. The resolution is obtained with Zienkiewicz's finite element which verifies the patch test, and the incomplete Cholesky conjugate gradient algorithm (ICCG) yields very fast convergence. The least-square formulation is still applicable when a non-linear term is introduced, and the solution is searched for by Newton's method.     

基于梯度曲面面积与稀疏约束的图像平滑方法

针对纹理图像在平滑过程中低对比度边缘易丢失和纹理细节抑制不彻底等问题,提出基于梯度曲面面积与稀疏约束的图像平滑方法。首先,将图像视作三维空间中的二维嵌入曲面,再在此基础上分析图像的几何特征并提出梯度曲面面积约束正则化项,以提高纹理抑制性能;其次,根据图像的统计特性,建立L₀梯度稀疏与自适应梯度曲面面积约束的混合正则化约束图像平滑模型;最后,采用交替方向乘子法对非凸非光滑的优化模型进行高效求解。通过纹理抑制、边缘检测、纹理增强和图像融合等方面的实验结果可知,所提出的图像平滑算法克服了L₀梯度最小化平滑方法易造成的阶梯效应和欠滤波等缺陷,能够在去除大量纹理信息的同时保持并锐化图像显著的边缘轮廓。