An adaptive window mechanism for image smoothing

Image smoothing using adaptive windows whose shapes, sizes, and orientations vary with image structure is described. Window size is increased with decreasing gradient magnitude, and window shape and orientation are adjusted in such a way as to smooth most in the direction of least gradient. Rather than performing smoothing isotropically, smoothing is performed in preferred orientations to preserve region boundaries while reducing random noise within regions. Also, instead of performing smoothing uniformly, smoothing is performed more in homogeneous areas than in detailed areas. The proposed adaptive window mechanism is tested in the context of median, mean, and Gaussian filtering, and experimental results are presented using synthetic and real images and compared with a state-of-the-art method.     

A novel adaptive SVR based filter ASBF for image restoration

In this paper, a novel adaptive filter ASBF based on support vector regression (SVR) is proposed to preserve more image details and efficiently suppress impulse noise simultaneously. The main idea of the novel filter ASBF here is to employ a SVR based impulse detector to judge whether an input pixel is contaminated or not by impulse noise. If this case happens, a median filter is employed to remove the corresponding impulse noise. This judgment procedure is executed by regressing the filter window of an input pixel using SVR and then judging the input pixel by its regression distance. Huber loss function is used in SVR regression, due to its excellent robustness capability. The distinctive advantage of the filter ASBF over the latest Support Vector Classifier (SVC) based filter is that no training for the original noise-free image is required in our approach, which is well in accordance with our visual judgment way. Experimental results for benchmark images demonstrate that our filter ASBF here outperforms the extensively-used median-based filters and the SVC based filter.     

Graph spectral image smoothing using the heat kernel

A new method for smoothing both gray-scale and color images is presented that relies on the heat diffusion equation on a graph. We represent the image pixel lattice using a weighted undirected graph. The edge weights of the graph are determined by the Gaussian weighted distances between local neighboring windows. We then compute the associated Laplacian matrix (the degree matrix minus the adjacency matrix). Anisotropic diffusion across this weighted graph-structure with time is captured by the heat equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigensystem with time. Image smoothing is accomplished by convolving the heat kernel with the image, and its numerical implementation is realized by using the Krylov subspace technique. The method has the effect of smoothing within regions, but does not blur region boundaries. We also demonstrate the relationship between our method, standard diffusion-based PDEs, Fourier domain signal processing and spectral clustering. Experiments and comparisons on standard images illustrate the effectiveness of the method.     

Edge-preserving smoothing using a similarity measure in adaptive geodesic neighbourhoods

This paper introduces a novel image-dependent filtering approach derived from concepts known in mathematical morphology and aiming at edge-preserving smoothing of natural images. Like other adaptive methods, it assumes that the neighbourhood of a pixel contains the essential information required for the estimation of local features in the image. The proposed strategy essentially consists in a weighted averaging combining both spatial and tonal information. For that purpose, a twofold similarity measure is calculated from local geodesic time functions. This way, no prior operator definition is required since a weighting neighbourhood and a weighting kernel are determined automatically from the unfiltered input data for each pixel location. By designing relevant geodesic masks, two adaptive filtering algorithms are derived that are particularly efficient at smoothing heterogeneous areas while preserving relevant structures in greyscale and multichannel images.     

基于matlab的图像增强技术分析与实现

图像增强是图像处理的一个重要分支，是图像边缘提取、图像分割等的基础。由于图像在获取和传输过程中发生失真，影响了人和机器对图像的理解。文章主要介绍了常见的空域处理法。通过实验的对比，发现图像得到了很好的增强效果。     

基于matlab的图像增强技术分析与实现

图像增强是图像处理的一个重要分支,是图像边缘提取、图像分割等的基础。由于图像在获取和传输过程中发生失真,影响了人和机器对图像的理解。文章主要介绍了常见的空域处理法。通过实验的对比,发现图像得到了很好的增强效果。     

Predicting the Brazilian stock market through neural networks and adaptive exponential smoothing methods

The study of financial markets has been addressed in many works during the last years. Different methods have been used in order to capture the non-linear behavior which is characteristic of these complex systems. The development of profitable strategies has been associated with the predictive character of the market movement, and special attention has been devoted to forecast the trends of financial markets. This work performs a predictive study of the principal index of the Brazilian stock market through artificial neural networks and the adaptive exponential smoothing method, respectively. The objective is to compare the forecasting performance of both methods on this market index, and in particular, to evaluate the accuracy of both methods to predict the sign of the market returns. Also the influence on the results of some parameters associated to both methods is studied. Our results show that both methods produce similar results regarding the prediction of the index returns. On the contrary, the neural networks outperform the adaptive exponential smoothing method in the forecasting of the market movement, with relative hit rates similar to the ones found in other developed markets.     

基于纹理分析的保细节平滑滤波器

平滑去噪是图象处理中一个重要课题,但是以往在处理平滑去噪问题上一直存在平滑和保细节的矛盾。为解决此问题,提出了一种基于纹理分析和保细节平滑滤波器,该滤波器采用了多尺度多方向的模板,并利用纹理分析等手段,同时根据图象各部分特性,通过自适应地选择模板来进行平滑滤波,该算法兼顾了降噪和保细节两方面要求。实验结果证明,该算法实现简单,计算速度快,且效果优于其他几种常用的保边界平滑算法。     

Easy recipes for cooperative smoothing

In this paper we suggest how several competing signal smoothers, differing in design parameters, or even in design principles, can be combined together to yield a better and more reliable smoothing algorithm. The proposed heuristic, but statistically well motivated, fusion mechanism allows one to combine practically all kinds of smoothers, from simple local averaging or order statistic filters, to parametric smoothers designed for different hypothetical signal and/or noise models. It also allows one to account for the distribution of measurement noise, and in particular to cope with heavy-tailed disturbances, such as Laplacian noise, and light-tailed disturbances, such as uniform noise.     

一种基于自适应阈值的保细节平滑滤波器

基于多尺度多方向的模板,提出一种自适应地的细节平滑算法.该算法一方面保持了模板在保留图像细节特征方面的优势,另一方面利用图像灰度梯度直方图的统计特征,将整幅图像分割成若干子图像,再根据各个子图像的特性,并结合全局梯度特征信息自适应地生成动态阈值,有效地解决了以往阈值选取的困难,提高了图像平滑的自动化程度.与现有的其他算法相比,该算法实现简单,计算速度快,在实际应用中取得了很好的效果.     

自适应图像复原模型梯度阈值选取研究

自适应图像复原模型,能满足中高噪声强度下进行图像复原的要求,但在选取图像梯度阈值时,通过交互迭代,运算量大,耗费时间长。本文基于对图像边缘灰度突变特性的考虑,通过引入图像梯度幅值直方图的方法,利用像素点梯度模值来区分边缘区和平滑区,开辟了在图像复原中选取梯度阈值参数的新途径,取得了很好的降噪复原效果,而且,选取梯度阈值的过程,耗时少,运算简单,选取过程直观快捷。     

自适应窗宽的均值迁移图像跟踪算法

针对传统均值迁移跟踪算法中核函数窗宽固定使之无法满足图像中运动目标尺寸变化需要的问题，在分析目标特征零阶矩特点基础上，以其变化比作为观测量，以目标面积的变化比作为状态量，利用卡尔曼滤波器对未来帧中目标面积的变化进行预测进而获得同目标尺度变化相适应的核函数窗宽。该算法通过窗宽自适应变化，提高了跟踪精度，增强了跟踪稳定性，同时仍保证了跟踪的实时性。实验结果证明了该方法的有效性。     

Adaptive application of feature detection operators based on image variance

It is well known that the strength of a feature in an image may depend on the scale at which the appropriate detection operator is applied. It is also the case that many features in images exist significantly over a limited range of scales, and, of particular interest here, that the most salient scale may vary spatially over the feature. Hence, when designing feature detection operators, it is necessary to consider the requirements for both the systematic development and adaptive application of such operators over scale- and image-domains. We present an overview to the design of scalable derivative edge detectors, based on the finite element method, that addresses the issues of method and scale-adaptability. The finite element approach allows us to formulate scalable image derivative operators that can be implemented using a combination of piecewise-polynomial and Gaussian basis functions. The general adaptive technique may be applied to a range of operators. Here we evaluate the approach using image gradient operators, and we present comparative qualitative and quantitative results for both first and second order derivative methods.     

灰度图像加权有向平滑滤波算法

为克服常用平滑滤波算法不能兼顾去噪和保持图像细节的不足,提出了加权有向平滑滤波算法.先根据相似者相容的原理得到待处理像素与各滤波模板的隶属关系,从而判断待处理像素是噪声点,是图像本身像素,还是图像背景像素,然后选用相应加权有向或无向平滑模板对待处理像素进行平滑处理.实验仿真结果表明,加权有向平滑滤波算法既能有效地滤除灰度图像中的噪声,又能很好保护图像的边缘和细节,弥补了常用空域平滑滤波算法不能兼顾去噪和保持图像细节的不足.     

Enhancement of spatially adaptive smoothing splines via parameterization of smoothing parameters

This paper considers the problem of estimating curve and surface functions when the structures of an unknown function vary spatially. Classical approaches such as using smoothing splines, which are controlled by a single smoothing parameter, are inefficient in estimating the underlying function that consists of different spatial structures. In this paper, we propose a blockwise method of fitting smoothing splines wherein the smoothing parameter λ varies spatially, in order to accommodate possible spatial nonhomogeneity of the regression function. A key feature of the proposed blockwise method is the parameterization of a smoothing parameter function λ(x) that produces a continuous spatially adaptive fit over the entire range of design points. The proposed parameterization requires two important ingredients: (1) a blocking scheme that divides the data into several blocks according to the degree of spatial variation of the data; and (2) a method for choosing smoothing parameters of blocks. We propose a block selection approach that is based on the adaptive thinning algorithm and a choice of smoothing parameters that minimize a newly defined blockwise risk. The results obtained from numerical experiments validate the effectiveness of the proposed method.     

一种极值约束的边缘保持图像平滑算法

边缘保持的图像平滑在图像预处理以及许多图像编辑应用中都具有重要的意义。图像的边缘保持与细节平滑是一对矛盾。提出一种以极值为约束的边缘保持的图像平滑算法。该方法的基本思想是对处理后图像的极值进行约束,即要求其在给定位置处取得相应的极大(小)值来保持原图像的主边缘,同时平滑消除副边缘和信号小起伏。首先对原图像进行初步平滑,然后从中提取出极值点,再把这些极值点作为处理后图像的约束。在所有满足这些约束的函数中,取与原图像最接近的作为最终平滑结果。利用半二次技术和交替最小化得到了有效的数值求解方法。实验结果表明,提出的方法在一些基于边缘保持平滑的图像处理(如细节增强)中取得了更好的效果。     

A new design of robust filters for uncertain systems

In this paper, a structured polynomial parameter-dependent approach is proposed for robust H₂ filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with s vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust H₂ filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of s matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples.     

An adaptive image Euclidean distance

The image Euclidean distance (IMED) considers the spatial relationship between the pixels of different images and can easily be embedded in existing image recognition algorithms that are based on Euclidean distance. IMED uses the prior knowledge that pixels located near one another have little variance in gray scale values, and defines a metric matrix according to the spatial distance between pixels. In this paper, we propose an adaptive image Euclidean distance (AIMED), which considers not only the prior spatial knowledge, but also the prior gray level knowledge from images. The most important advantage of the proposed AIMED over IMED is that AIMED makes the metric matrix adaptive to the content of the concerned images. Two ways of using gray level information are proposed. One is based on gray level distances, and the other is based on cosine dissimilarity of gray levels. Experiments on two facial databases and a handwritten digital database show that AIMED achieves the highest classification accuracy when it is embedded in nearest neighbor classifiers, principal component analysis, and support vector machines.     

New Riemannian techniques for directional and tensorial image data

This paper develops new geometrical filtering and edge detection algorithms for processing non-Euclidean image data. We view image data as residing on a Riemannian manifold, and we work with a representation based on the exponential map for this manifold together with the Riemannian weighted mean of image data. We show how the weighted mean can be efficiently computed using Newton's method, which converges faster than the gradient descent method described elsewhere in the literature. Based on geodesic distances and the exponential map, we extend the classical median filter and the Perona-Malik anisotropic diffusion technique to smooth non-Euclidean image data. We then propose an anisotropic Gaussian kernel for image filtering, and we also show how both the median filter and the anisotropic Gaussian filter can be combined to develop a new edge preserving filter, which is effective at removing both Gaussian noise and impulse noise. By using the intrinsic metric of the feature manifold, we also generalise Di Zenzo's structure tensor to non-Euclidean images for edge detection. We demonstrate the applications of our Riemannian filtering and edge detection algorithms both on directional and tensor-valued images.     

基于改进ILAE算法的图像局部自适应增强研究

一些应用需要增强一幅图像的局部信息,而不改变图像的其它部分。为此,提出了图像局部自适应增强算法。采用改进的ILAE算法,根据局部统计信息找出一幅图像中所要增强的像素点,仅对这些像素点进行图像增强,然后利用自适应中值滤波方法对增强后的图像进行去噪。实验结果表明,经算法处理后的图像,不仅局部信息得到了增强而且还能取得很好的视觉效果。