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.     

标准正则化理论的一些推广和应用

在标准正则化理论中建议一类局部相互作用场和自适应正则项。局部相互作用场包括通常的误差项和一窗口函数。窗口的大小，取向和形状可以视具体的应用加以调整。自适应正则项用来处理不连续变化。这两项导致一对称的能量泛函。最简单的梯度下降算法通常在参数变化和有噪声时也很稳定，有效。     

一种改进的变分光流计算方法

提出一种改进的变分光流算法的能量泛函,该能量泛函的数据项由灰度不变假设和Hessian矩阵不变假设组成,并与Lucas局部光流一致方法相结合。平滑项的设计采用先各项同性平滑再各项异性平滑的策略,其中引入图像一致增强思想。实验结果证明,运用该方法进行光流计算的效果比以往变分方法有所改进。     

Freehand HDR Imaging of Moving Scenes with Simultaneous Resolution Enhancement

Despite their high popularity, common high dynamic range (HDR) methods are still limited in their practical applicability: They assume that the input images are perfectly aligned, which is often violated in practise. Our paper does not only free the user from this unrealistic limitation, but even turns the missing alignment into an advantage: By exploiting the multiple exposures, we can create a super‐resolution image. The alignment step is performed by a modern energy‐based optic flow approach that takes into account the varying exposure conditions. Moreover, it produces dense displacement fields with subpixel precision. As a consequence, our approach can handle arbitrary complex motion patterns, caused by severe camera shake and moving objects. Additionally, it benefits from several advantages over existing strategies: (i) It is robust under outliers (noise, occlusions, saturation problems) and allows for sharp discontinuities in the displacement field. (ii) The alignment step neither requires camera calibration nor knowledge of the exposure times. (iii) It can be efficiently implemented on CPU and GPU architectures. After the alignment is performed, we use the obtained subpixel accurate displacement fields as input for an energy‐based, joint super‐resolution and HDR (SR‐HDR) approach. It introduces robust data terms and anisotropic smoothness terms in the SR‐HDR literature. Our experiments with challenging real world data demonstrate that these novelties are pivotal for the favourable performance of our approach.     

Parallel implementation of the MAGPACK package for the analysis of high-nuclearity spin clusters

Molecular clusters are formed by a finite number of exchange-coupled paramagnetic centers and they are model systems between molecules and extended solids. In order to simulate their properties and extrapolate to solids, the size of the systems to be treated should be as large as possible. In this context, the use of efficient parallel codes is essential. We present the parallel programs ParAni and ParIso, for anisotropic and isotropic models, that enable the calculation of large energy matrices in parallel and the subsequent computation of the relevant spectral information. The evaluation of the matrix elements is based on the serial package Magpack that uses the irreducible tensor operators technique and takes into account all kinds of anisotropic and isotropic magnetic interactions. To obtain the eigenvalues, the energy matrix is partially diagonalized by means of the SLEPc library. The calculation of eigenvalues and eigenvectors of these spin clusters enables us to evaluate the bulk magnetic properties (magnetic susceptibility and magnetization) as well as the spectroscopic properties (inelastic neutron scattering spectra). The results are encouraging in terms of parallel efficiency and open the way to address very challenging problems.     

Relaxed sparse eigenvalue conditions for sparse estimation via non-convex regularized regression

Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regularized regression, our sparse eigenvalue based conditions are weaker than that of L1-regularization for parameter estimation and sparseness estimation. For the approximate global and approximate stationary (AGAS) solutions, almost the same conditions are also enough. We show that the desired AGAS solutions can be obtained by coordinate descent (CD) based methods. Finally, we perform some experiments to show the performance of CD methods on giving AGAS solutions and the degree of weakness of the estimation conditions required by the sharp concave regularizers.     

基于抽象匹配流的彩色图像配准模型

在抽象匹配流框架下,构造能够克服大色差问题的彩色图像配准模型.该模型中,数据项采用互相关函数作为2幅图像间的相似性度量,以解决大色差问题;正则项采用各向异性扩散滤波器约束图像演化,从而实现在演化过程中对图像特征的有效保持.扩散滤波器中的扩散系数定义为关于彩色结构张量的函数,以使图像演化能够综合各通道信息,解决了各通道所得位移场不一致而引起的色彩混迭问题.实验结果表明,文中模型对具有大色差的彩色图像能够实现有效配准.     

Simulation of lognormal random fields with varying resolution scale and local average for Darcy flow

The paper presents a new method for generating isotropic realizations of a random field with varying resolution scales and local block averages in one, two, or three dimensions. The random field has a lognormal distribution as found for the hydraulic conductivity in Darcy's flow in hydrology. We also present a fast method for generating anisotropic realizations of aGaussian random field using superposition of harmonic modes. Both methods are implemented in a software package which is presented. The realizations of the rescaled random field are made up ofupscaled local averages of the underlying random field which are consistentwith the level of resolution and which can be conditioned. The approach is motivated by the need to represent engineering properties aslocal averages and to be able to easily condition the realizations to incorporate known data or to change the resolution within sub-regions. The numerical results show that the method is very efficient computationally.     

Optic Flow in Harmony

Most variational optic flow approaches just consist of three constituents: a data term, a smoothness term and a smoothness weight. In this paper, we present an approach that harmonises these three components. We start by developing an advanced data term that is robust under outliers and varying illumination conditions. This is achieved by using constraint normalisation, and an HSV colour representation with higher order constancy assumptions and a separate robust penalisation. Our novel anisotropic smoothness is designed to work complementary to the data term. To this end, it incorporates directional information from the data constraints to enable a filling-in of information solely in the direction where the data term gives no information, yielding an optimal complementary smoothing behaviour. This strategy is applied in the spatial as well as in the spatio-temporal domain. Finally, we propose a simple method for automatically determining the optimal smoothness weight. This method bases on a novel concept that we call “optimal prediction principle” (OPP). It states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence. The benefits of our “optic flow in harmony” (OFH) approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used Middlebury optic flow benchmark.     

基于改进光流场模型的大脑图像配准

将光流场模型引入大脑图像配准,针对Horn模型会造成图像严重模糊的问题,在微分光流场模型的一般框架下,构造具有边缘保持和一致性增强能力的流驱动各向异性扩散方程作为正则项,以增强配准过程的特征保持能力;采用非二次惩罚函数作为数据项,以增强模型的鲁棒性.最后利用文中模型对大脑图像进行配准实验,得到了较为准确的结果.     

Nonet-Cartesian Grid Method for Shock Flow Computations

A nonet-Cartesian grid method, based on anisotropic/isotropic refinement, is presented for solving the Euler equations in gas dynamic problems. Grids are generated automatically, by the recursive subdivision of a single cell into nine subcells for isotropic nonet-Cartesian grids and into three subcells independently in each direction for anisotropic nonet-Cartesian grids, encompassing the entire flow domain. The grid generation method is applied here to steady inviscid shock flow computation. A finite difference formulation for the Euler equation using nonet-Cartesian grids is used to treat complex two-dimensional configuration. Results using this approach are shown to be competitive with other methods. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.     

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.     

Image retrieval via isotropic and anisotropic mappings

This paper presents an approach for content-based image retrieval via isotropic and anisotropic mappings. Isotropic mappings are defined as mappings invariant to the action of the planar Euclidean group on the image space—invariant to the translation, rotation and reflection of image data, and hence, invariant to orientation and position. Anisotropic mappings, on the other hand, are defined as those mappings that are correspondingly variant. Structure extraction (via a perceptual grouping process) and color histogram are shown to be representations of isotropic mappings. Texture analysis using a channel energy model comprised of even-symmetric Gabor filters is considered to be a representation of anisotropic mapping. An integration framework for these mappings is developed. Results of retrieval of outdoor images by query and by classification using a nearest neighbor classifier are presented.     

A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Diminishing (TVD) limiter, an improved finite-volume method is developed to solve the advection term with significant reduction of numerical diffusion and oscillation errors. In addition, a coordinate transformation is introduced to simplify the diffusion term with the Green-Gauss theorem used to deal with the anisotropic effect based on unstructured mesh. The new scheme is validated against three benchmark cases with separated and combined advection and diffusion transport processes involved. Results show that the scheme performs better than existing methods in predicting the advective transport, particularly when a sharp concentration front is in presence. The model also provides a sound solution for the anisotropic diffusion phenomenon. Anisotropic diffusion has been largely neglected by existing flow models based on unstructured mesh, which usually treat the diffusion process as being isotropic for simplicity. Based on the flow field provided by the ELCIRC model, the developed transport model was successfully applied to simulate the transport of a hypothetical conservative tracer in a bay under the influence of tides.     

梯度向量流的各向异性扩散分析

为了解决梯度向量流力场(gradient vector flow,简称GVF)难以进入目标凹部的问题,提出了一种新的主动轮廓模型外力场——各向异性梯度向量流.GVF的扩散项是各向同性且光滑性强的拉普拉斯算子,它在各个方向的扩散速度相同.拉普拉斯算子根据图像的局部结构可分为沿边界法线和切线方向的扩散,沿切线方向的扩散具有增强边界的作用,而法线方向扩散具有去除噪音、扩散力场的作用.基于分析二者在扩散过程中的作用,提出了一种各向异性梯度向量流扩散方法,切线和法线方向的扩散速度可以根据图像的局部结构自适应地选择.实验结果表明,与GVF相比,所提出的方法考虑了扩散过程中法线和切线方向的不同作用,能够进入细长的凹部,并改进了分割结果.     

各向异性多尺度自相似随机场与地形构建

在长期自然环境的作用下,实际的地形表面是一个各向异性、非线性的2维场,且地形的自相似特性在整个尺度空间上并非恒定的,而是与度量的尺度范围相关。由于传统的自相似随机场的构建方法并不能准确反映地形的实际特性,因此提出一种首先应用多尺度自相似随机场构建各向同性地形表面,然后引入表征各向异性的结构滤波器,再通过谱变换构建具有各向异性的多尺度自相似地形的方法。实验结果表明,该地形构建方法不仅能够反映实际地形的自相似性依尺度而变化的特点,而且能构建山脉的走向。     

A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods

Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.     

基于形状的二维灰度图象插值

内插是三维重建中的一个重要步骤 .一般传统的插值算法大体可分为灰度插值和基于对象形状的插值两种 .其中直接的灰度插值对二值及灰度图象均适用 ,但结果在多数情况下并不准确 ;而基于形状的插值 ,早期仅适用于二值图象 .近来 ,人们将两者较好地结合起来 ,使得基于形状的插值同样适用于灰度图象 .为了克服直接灰度插值易造成较严重的轮廓模糊问题及为克服 Chuang等人提出用基于形状的插值方法求得的对应点易产生偏差的问题 ,提出了一种新的基于形状的二维灰度图象插值算法 .该算法首先采用数学形态学的方法分别对两幅源图象进行膨胀和腐蚀 ,用于确定插值图象的轮廓 ;然后对轮廓内的点 ,分别找出其在两幅源图象上的对应点 ,再通过灰度的线性插值来求得此点的灰度 ,进而得到最终的插值图象 .实验结果表明 ,此算法得到的插值结果是令人满意的 .     

Optic flow field segmentation and motion estimation using a robustgenetic partitioning algorithm

Optic flow motion analysis represents an important family of visual information processing techniques in computer vision. Segmenting an optic flow field into coherent motion groups and estimating each underlying motion is a very challenging task when the optic flow field is projected from a scene of several independently moving objects. The problem is further complicated if the optic flow data are noisy and partially incorrect. In this paper, the authors present a novel framework for determining such optic flow fields by combining the conventional robust estimation with a modified genetic algorithm. The baseline model used in the development is a linear optic flow motion algorithm due to its computational simplicity. The statistical properties of the generalized linear regression (GLR) model are thoroughly explored and the sensitivity of the motion estimates toward data noise is quantitatively established. Conventional robust estimators are then incorporated into the linear regression model to suppress a small percentage of gross data errors or outliers. However, segmenting an optic flow field consisting of a large portion of incorrect data or multiple motion groups requires a very high robustness that is unattainable by the conventional robust estimators. To solve this problem, the authors propose a genetic partitioning algorithm that elegantly combines the robust estimation with the genetic algorithm by a bridging genetic operator called self-adaptation     

Scene segmentation from visual motion using global optimization

This paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow. The maximum a posteriori (MAP) criterion is used to formulate what the best segmentation or interpretation of the scene should be, where the scene is assumed to be made up of some fixed number of moving planar surface patches. The Bayesian approach requires, first, specification of prior expectations for the optic flow field, which here is modeled as spatial and temporal Markov random fields; and, secondly, a way of measuring how well the segmentation predicts the measured flow field. The Markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous, and that their images are likely to move quite smoothly across the image plane. To compute the flow predicted by the segmentation, a recent method for reconstructing the motion and orientation of planar surface facets is used. The search for the globally optimal segmentation is performed using simulated annealing.