Analysis of methods of estimating objective function gradient during recurrent measurements of image parameters

Methods for estimating the objective function gradient in recurrent algorithms for parameter estimation are analyzed by the example of the problem of estimating the parameters of geometric interframe image deformations. The gradient is estimated from a local sample and current estimates of measured parameters taking into account digital image sampling.     

Methods of finding gradient estimates of target function for measurement of images parameters

Taking into account the discreteness, digital images are considered and analyzed four ways to calculate the target function pseudogradient by the local sample and the current estimates of the measured parameters for the problem of estimating the parameters of interframe geometrical image distortion as an example.     

Optimization of the sampling scheme for estimating geometrical interframe image deformations

In the pseudogradient estimation of image parameters, convergence of the estimates and computational costs depend on the size and local sampling scheme of image reading used to determine the pseudogradient of the goal function. An approach is proposed for pseudogradient optimization by the selection of a local sampling scheme.     

Pseudogradient optimization of objective function in estimation of geometric interframe image deformations

An optimization criterion is suggested for the plan of counts in a local sample used to determine the pseudogradient of the objective function of estimation quality. The use of the criterion is considered in the case when the object functions are defined as the interframe difference mean square, the covariance, and the interframe correlation coefficient. The optimization is directed at increasing the convergence rate of estimates of the parameters of geometric interframe image deformations.     

Choice of finite differences in finding the goal function gradient in the estimation procedures of interframe image deformations

It is shown that, in the pseudogradient estimation algorithm of image parameters, the convergence rate of estimates depends on the method of pseudogradient calculations through the finite differences. An approach to optimize the step of finite differences on the parameters in the problem of estimating interframe geometrical image distortion is considered.     

Finding the pseudogradient of the objective function in procedures for estimation of interframe deformations of images

In the recursive estimate of parameters of interframe geometric deformations of digital images, calculating the pseudogradient from a local sample and current estimates of deformation parameters to be measured involves finding derivatives in terms of finite differences. The maximal convergence rate of estimates of the deformation parameters can be achieved when using the most informative readings of images in a local sample. Under this approach, there exist optimal values of increments in the parameters and basic axes, depending on the mismatch between estimates and correlation properties of the image. The performance of the procedures may be increased if the increments are optimized at each iteration. The potential accuracy of estimation of the parameters, as given by the Cramer-Rao inequality, serves as an optimality criterion when calculating the pseudogradient of the objective function. It is shown that the condition of maximum of information can be reduced to the condition of maximization of the ratio of the expectation of the pseudogradient to its mean square deviation. Application of optimized values of increments enables one to reduce considerably (up to several times) the computational cost with the same accuracy of estimation.     

Pseudogradient optimization in the estimation of geometric interframe image deformations

In the pseudogradient estimation of image parameters, the convergence of the estimates and the computational costs depend on the size of a local sample of image counts used to determine the pseudogradient of the objective function. An approach to pseudogradient optimization via choosing a plan of counts in the local sample is proposed. Aleksandr Grigor’evich Tashlinskii. Born 1954. Graduated from Ul’yanovsk State Technical University in 1977. Received doctoral degree in 2000. Professor of the Department of CAD Systems at Ulyanovsk State Technical University. Research interests: statistical image processing, in particular, the estimation of spatiotemporal deformations in dynamic image sequences. Author of about 250 publications, including 80 papers and 2 monographs covering the parameter estimation of spatial deformations in image sequences. Full member of the International Academy of Authors of Scientific Discoveries and Inventions and the Russian Academy of Natural Sciences. Awarded medals from these academies. Galina Leonidovna Minkina. Born 1983. Graduated from Ul’yanovsk State Technical University in 2005. Graduate student of this university. Research interests: optimization of parameters of algorithms for estimating geometrical interframe image deformations. Author of 25 publications. Galina Vladimirovna Dikarina. Born 1983. Graduated from Ul’yanovsk State Technical University in 2005. Graduate student of this university. Research interests: adaptive estimation of quantile random fields. Author of eight publications. Aleksandr Nikolaevich Repin. Born 1985. Graduated from Ul’yanovsk State Technical University in 2007. Graduate student of this university. Research interests: minimization of computational costs in the estimation of geometrical interframe image deformations and the prediction of cellular coverage. Author of four publications.     

Estimation of Edge Parameters and Image Blur Using Polynomial Transforms

A method is presented for detecting blurred edges in images and for estimating the following edge parameters: position, orientation, amplitude, mean value, and edge slope. The method is based on a local image decomposition technique called a polynomial transform. The information that is made explicit by the polynomial transform is well suited to detect image features, such as edges, and to estimate feature parameters. By using the relationship between the polynomial coefficients of a blurred feature and those of the a priori assumed (unblurred) feature in the scene, the parameters of the blurred feature can be estimated. The performance of the proposed edge parameter estimation method in the presence of image noise has been analyzed. An algorithm is presented for estimating the spread of a position-invariant Gaussian blurring kernel, using estimates at different edge locations over the image. First a single-scale algorithm is developed in which one polynomial transform is used. A critical parameter of the single-scale algorithm is the window size, which has to be chosen a priori. Since the reliability of the estimate for the spread of the blurring kernel depends on the ratio of this spread to the window size, it is difficult to choose a window of appropriate size a priori. The problem is overcome by a multiscale blur estimation algorithm where several polynomial transforms at different scales are applied, and the appropriate scale for analysis is chosen a posteriori. By applying the blur estimation algorithm to natural and synthetic images with different amounts of blur and noise, it is shown that the algorithm gives reliable estimates for the spread of the blurring kernel even at low signal-to-noise ratios.     

Mean fields and two-dimensional Markov random fields in image analysis

In this paper we compare two iterative approaches to the problem of pixel-level image restoration when the model contains unknown parameters. Pairwise interaction models are assumed to represent the local associations in the true scene. The first approach is a variation on the EM algorithm in which Mean-field approximations are used in the E-step and a variational approximation is used in the M-step. In the second approach, each iteration involves first restoring the image using the Iterated Conditional Modes (ICM) algorithm and then updating the parameter estimates by maximising the so-called pseudolikelihood. In addition, refinemenrs are made to the Mean-field approximation, and these are also used for restoration. The methods are compared empirically using both artificial and real noise-corrupted binary scenes. Within the comparisons the effects of using different convergence criteria for deciding when to stop the algorithms are also investigated.     

Multiscale Minimization of Global Energy Functions in Some Visual Recovery Problems

Many image analysis and computer vision problems have been expressed as the minimization of global energy functions describing the interactions between the observed data and the image representations to be extracted in a given task. In this note, we investigate a new comprehensive approach to minimize global energy functions using a multiscale relaxation algorithm. The energy function is minimized over nested subspaces of the original space of possible solutions. These subspaces consist of solutions which are constrained at different scales. The constrained relaxation is implemented via a coarse-to-fine multiresolution algorithm that yields fast convergence towards high quality estimates when compared to standard monoresolution or multigrid relaxation schemes. It also appears to be far less sensitive to local minima than standard relaxation algorithms. The efficiency of the approach is demonstrated on a highly nonlinear combinatorial problem which consists of estimating long-range motion in an image sequence on a discrete label space. The method is compared to standard relaxation algorithms on real world and synthetic image sequences.     

Two-stage procedure for parameter estimation in large-scale interconnected linear zero-memory systems

The problem of parameter estimation in interconnected complex systems composed of linear zero-memory elements is considered. A two-stage scheme for estimating system parameters is proposed, and the convergence in probability and with probability one, of the parameter estimates to the true values of system parameters, is shown. Some computational aspects of the algorithm are discussed and its recursive version is provided. The rate of convergence is also studied.     

Convergence of parameter sensitivity estimates in a stochastic experiment

To reduce the error in estimating the gradient (parameter sensitivity) of an unknown function is of great importance in stochastic optimization problems. Three kinds of parameter sensitivity estimates using the Monte Carlo method are discussed in this paper. The estimates depend on the number of replications,N, and the change in parameter,Delta d. The convergence properties asN rightarrow inftyandDelta d rightarrow 0for these estimates are obtained. The result explains many theoretical and practical issues in the study of discrete event dynamic systems, as well as continuous dynamic systems, by the Monte Carlo method. It is proved that an estimate based on averaging the gradients calculated along each sample path by a perturbation of the path is much better than the other estimates if the output functions are uniformly differentiable with probability one (w.p.1). It is also concluded that in computer simulations one should always choose the same seed for bothdandd + Delta din estimating the parameter sensitivity. Combining the results in this paper with existing stochastic approximation algorithms may yield algorithms with faster convergence.     

Simultaneous parameter estimation and segmentation of Gibbs randomfields using simulated annealing

An adaptive segmentation algorithm is developed which simultaneously estimates the parameters of the underlying Gibbs random field (GRF)and segments the noisy image corrupted by additive independent Gaussian noise. The algorithm, which aims at obtaining the maximum a posteriori (MAP) segmentation is a simulated annealing algorithm that is interrupted at regular intervals for estimating the GRF parameters. Maximum-likelihood (ML) estimates of the parameters based on the current segmentation are used to obtain the next segmentation. It is proven that the parameter estimates and the segmentations converge in distribution to the ML estimate of the parameters and the MAP segmentation with those parameter estimates, respectively. Due to computational difficulties, however, only an approximate version of the algorithm is implemented. The approximate algorithm is applied on several two- and four-region images with different noise levels and with first-order and second-order neighborhoods     

一种全自动稳健的图像拼接融合算法

提出了一种全自动稳健的图像拼接融合算法。此算法采用Harris角检测算子进行特征点提取，使提取的精度达到了亚像素级，然后以特征点邻域灰度互相关法进行特征点匹配得到了初步的伪匹配集合，并运用稳健的RANSAC算法将伪匹配点集合划分为内点和外点，在内点域上运用LM优化算法精确地估计出了图像间的点变换关系，最后采用颜色插值对交接处进行颜色过渡。整个算法自动完成，它对有较大误差或错误的特征点数据迭代过滤，并用提纯后的数据来做模型估计，因而对图像噪声和特征点提取不准确有强健的承受能力。在参数估计时，以特征点的坐标位置误差而不是亮度误差来构造优化函数，克服了以往算法对光照的敏感性，使算法更具有实用性。实验结果表明，该算法融合效果比较理想，鲁棒性强，具有较高的使用价值。     

基于分裂EM算法的GMM参数估计

期望最大化(Expectation Maximization,EM)算法是一种求参数极大似然估计的迭代算法,常用来估计混合密度分布模型的参数。EM算法的主要问题是参数初始化依赖于先验知识且在迭代过程中容易收敛到局部极大值。提出一种新的基于分裂EM算法的GMM参数估计算法,该方法从一个确定的单高斯分布开始,在EM优化过程中逐渐分裂并估计混合分布的参数,解决了参数迭代收敛到局部极值问题。大量的实验表明,与现有的其他参数估计算法相比,算法具有较好的运算效率和估算准确性。     

Estimation of illuminant direction, albedo, and shape from shading

A robust approach to the recovery of shape from shading information is presented. Assuming uniform albedo and Lambertian surface for the imaging model, two methods for estimating the azimuth of the illuminant are presented. One is based on local estimates on smooth patches, and the other method uses shading information along image contours. The elevation of the illuminant and surface albedo are estimated from image statistics, taking into consideration the effect of self-shadowing. With the estimated reflectance map parameters, the authors then compute the surface shape using a procedure that implements the smoothness constraint by requiring the gradients of reconstructed density to be close to the gradients of the input image. The algorithm is data driven, stable, updates the surface slope and height maps simultaneously, and significantly reduces the residual errors in irradiance and integrability terms. A hierarchical implementation of the algorithm is presented. Typical results on synthetic and images are given to illustrate the usefulness of the approach     

基于改进栈式稀疏去噪自编码器的图像去噪

为了提高栈式稀疏去噪自编码器（SSDA）的图像去噪性能,解决计算复杂度高,参数不易调节,训练收敛速度慢等问题,提出了一种栈式边缘化稀疏去噪自编码器（SMSDA）的图像去噪方法。首先,由于边缘化去噪自编码器（MDA）具有收敛速度快这一特性,对SDA网络损失函数作边缘化处理,形成边缘化稀疏去噪自编码器（MSDA）,使其同时满足边缘性和稀疏性。其次,将多个MSDA堆叠构成深度神经网SMSDA,为避免模型参数局部最优,采用非监督逐层训练法分别训练每一层网络,再用BP算法对整个网络微调,从而获得最优权重。最后,用SMSDA对给定图像去噪。仿真结果表明,较SSDA而言,所提算法在降低计算复杂度、提高收敛速度的同时,拥有较高峰值信噪比（PSNR）,且保留了更多原始图像的细节信息,具有更好的降噪性能。     

自适应变异差分算法与Powell算法相结合的医学图像配准

图像配准是医学图像处理中的关键技术。文中提出一种自适应差分算法(Difference Algorithm,DE)和Powell算法相结合的多分辨率医学图像配准方法,其不仅可以克服Powell算法依赖初始点的缺点,还可以降低陷入局部极值的几率。首先,对源图像进行多分辨处理,获得包括源图像在内的三层图像;然后,在低分辨率图像上使用自适应DE算法进行全局变换参数的搜索,获得的变换参数作为Powell算法的初始点;最后,在高分辨率图像及源图像上使用Powell算法进行配准。与传统实验相比,该方法具有更高的精确度,能够有效避免局部收敛问题。     

On sequential estimation of the parameters of continuous-time trigonometric regression

Consideration was given to the problem of estimating the parameters of a trigonometric regression with the Gaussian Ornstein–Uhlenbeck noise. One-step sequential estimation procedure with a special stopping time defined by a sample Fischer information matrix was proposed. It ensures a given mean square accuracy of estimates uniformly over some parametric region. The results of Monte Carlo simulation of the sequential procedure were presented and compared with the maximum likelihood estimates.     

Performance-optimized applied identification of separabledistributed-parameter processes

Studies practical algorithms for parametric identification of cross-directional processes from input/output data. Instead of working directly with the original two-dimensional array of the high-resolution profile scans, the proposed algorithms use separation properties of the problem. It is demonstrated that by estimating and identifying in turn cross directional and time responses of the process, it is possible to obtain unbiased least-square error estimates of the model parameters. At each step, a single data sequence is used for identification which ensures high computational performance of the proposed algorithm. A theoretical proof of algorithm convergence is presented. The discussed algorithms are implemented in an industrial identification tool and the note includes a real-life example using paper machine data