基于提升方案的高维形态小波构造

研究基于提升方案的高维形态小波构造方法.结合数学形态学和高维小波分析来构造 高维形态小波.提出高维多通道形态小波构造的一般性框架--高维多通道提升方案.采用最大 值(最小值)形态算子构造一维多通道Haar形态小波和高维多通道Haar形态小波.最后通过两 个例子说明形态小波变换的优点和可行性.     

A robust hit-or-miss transform for template matching applied to very noisy astronomical images

The morphological hit-or-miss transform (HMT) is a powerful tool for digital image analysis. Its recent extensions to grey level images have proven its ability to solve various template matching problems. In this paper we explore the capacity of various existing approaches to work in very noisy environments and discuss the generic methods used to improve their robustness to noise. We also propose a new formulation for a fuzzy morphological HMT which has been especially designed to deal with very noisy images. Our approach is validated through a pattern matching problem in astronomical images that consists of detecting very faint objects: low surface brightness galaxies. Despite their influence on the galactic evolution model, these objects remain mostly misunderstood by the astronomers. Due to their low signal to noise ratio, there is no automatic and reliable detection method yet. In this paper we introduce such a method based on the proposed hit-or-miss operator. The complete process is described starting from the building of a set of patterns until the reconstruction of a suitable map of detected objects. Implementation, running cost and optimisations are discussed. Outcomes have been examined by astronomers and compared to previous works. We have observed promising results in this difficult context for which mathematical morphology provides an original solution.     

Reconstruction of Patterns from Noisy Inputs Using Morphological Associative Memories

Morphological neural networks are based on a new paradigm for neural computing. Instead of adding the products of neural values and corresponding synaptic weights, the basic neural computation in a morphological neuron takes the maximum or minimum of the sums of neural values and their corresponding synaptic weights. By taking the maximum (or minimum) of sums instead of the sum of products, morphological neuron computation is nonlinear before thresholding. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. In this paper we restrict our attention to morphological associative memories. After a brief review of morphological neural computing and a short discussion about the properties of morphological associative memories, we present new methodologies and associated theorems for retrieving complete stored patterns from noisy or incomplete patterns using morphological associative memories. These methodologies are derived from the notions of morphological independence, strong independence, minimal representations of patterns vectors, and kernels. Several examples are provided in order to illuminate these novel concepts.     

噪声图像形态边缘检测的改进算法

研究了数学形态学在图像边缘检测中的具体应用，针对脉冲噪声污染的图像，深入分析了已有的抗噪型形态学差分算子的优缺点，结合对多方位形态学结构元素在边缘检测中应用的研究，提出了一种改进算法。实验表明，改进算法可以很好地去除噪声，同时较好地检测出图像边缘，改进效果明显。     

噪声图像形态边缘检测的改进算法

研究了数学形态学在图像边缘检测中的具体应用,针对脉冲噪声污染的图像,深入分析了已有的抗噪型形态学差分算子的优缺点,结合对多方位形态学结构元素在边缘检测中应用的研究,提出了一种改进算法。实验表明,改进算法可以很好地去除噪声,同时较好地检测出图像边缘,改进效果明显。     

DIMEX Runge–Kutta finite volume methods for multidimensional hyperbolic systems

We propose a class of finite volume methods for the discretization of time-dependent multidimensional hyperbolic systems in divergence form on unstructured grids. We discretize the divergence of the flux function by a cell-centered finite volume method whose spatial accuracy is provided by including into the scheme non-oscillatory piecewise polynomial reconstructions. We assume that the numerical flux function can be decomposed in a convective term and a non-convective term. The convective term, which may be source of numerical stiffness in high-speed flow regions, is treated implicitly, while the non-convective term is always discretized explicitly. To this purpose, we use the diagonally implicit–explicit Runge–Kutta (DIMEX-RK) time-marching formulation. We analyze the structural properties of the matrix operators that result from coupling finite volumes and DIMEX-RK time-stepping schemes by using M-matrix theory. Finally, we show the behavior of these methods by some numerical examples.     

Morphological Amoebas Are Self-snakes

This paper is concerned with amoeba median filtering, a structure-adaptive morphological image filter. It has been introduced by Lerallut et al. in a discrete formulation. Experimental evidence shows that iterated amoeba median filtering leads to segmentation-like results that are similar to those obtained by self-snakes, an image filter based on a partial differential equation. We establish this correspondence by analysing a space-continuous formulation of iterated amoeba median filtering. We prove that in the limit of vanishing radius of the structuring elements, iterated amoeba median filtering indeed approximates the partial differential equation of self-snakes. This result holds true under very general assumptions on the metric used to construct the amoebas. We present experiments with discrete iterated amoeba median filtering that confirm qualitative and quantitative predictions of our analysis.     

卷积形态滤波与图像去噪

本文提出的卷积形态变换是一种新的形态变换形式,具有线性卷积的结构和形态变换的性质。这种新的形态变换以乘性结构元素为特征,它不同于具有加性结构元素的普通形态变换,对于它们的性质和结构的研究也是本文的主要工作之一。另一方面的工作是针对卷积形态核提出了一种结构化的自动生成算法。研究表明,卷积形态滤波与卷积积分变换一样,对于图像具有去噪和平滑作用,且在实验效果上具有较通常的形态滤波和线性卷积变换更优的去噪和平滑功能。     

Piece wise Laplacian‐based Projection for Interactive Data Exploration and Organization

Multidimensional projection has emerged as an important visualization tool in applications involving the visual analysis of high‐dimensional data. However, high precision projection methods are either computationally expensive or not flexible enough to enable feedback from user interaction into the projection process. A built‐in mechanism that dynamically adapts the projection based on direct user intervention would make the technique more useful for a larger range of applications and data sets. In this paper we propose the Piecewise Laplacian‐based Projection (PLP), a novel multidimensional projection technique, that, due to the local nature of its formulation, enables a versatile mechanism to interact with projected data and to allow interactive changes to alter the projection map dynamically, a capability unique of this technique. We exploit the flexibility provided by PLP in two interactive projection‐based applications, one designed to organize pictures visually and another to build music playlists. These applications illustrate the usefulness of PLP in handling high‐dimensional data in a flexible and highly visual way. We also compare PLP with the currently most promising projections in terms of precision and speed, showing that it performs very well also according to these quality criteria.     

Generalizing Operations of Binary Autoassociative Morphological Memories Using Fuzzy Set Theory

Morphological neural networks (MNNs) are a class of artificial neural networks whose operations can be expressed in the mathematical theory of minimax algebra. In a morphological neural net, the usual sum of weighted inputs is replaced by a maximum or minimum of weighted inputs (in this context, the weighting is performed by summing the weight and the input). We speak of a max product, a min product respectively.In recent years, a number of different MNN models and applications have emerged. The emphasis of this paper is on morphological associative memories (MAMs), in particular on binary autoassociative morphological memories (AMMs). We give a new set theoretic interpretation of recording and recall in binary AMMs and provide a generalization using fuzzy set theory.     

去除心磁信号基线漂移的形态学滤波器

本文针对去除心磁信号的基线漂移的问题,采用形态学滤波方法,构造了两种结构元素,通过开闭和闭开的平均组合实现了两种有效的数学形态滤波器。数值仿真和信号分析的结果表明：该方法能够很好地保留心磁信号中的T波成分,并能去除心磁信号的基线漂移。     

Novel Neural Network Models for Computing Homothetic Invariances: An Image Algebra Notation

In this paper we propose a theoretical approach toinvariant perception. Invariant perception is an importantaspect in both natural and artificial perception systems, and itremains an important unsolved problem in heuristically basedpattern recognition. Our approach is based on a general theoryof neural networks and studies of invariant perception by thecortex. The neural structures that we propose uphold both thearchitecture and functionality of the cortex as currentlyunderstood.The formulation of the proposed neural structuresis in the language of image algebra, a mathematical environmentfor expressing image processing algorithms. Thus, an additionalbenefit of our study is the implication that image algebraprovides an excellent environment for expressing and developingartificial perception systems.The focus of our study is oninvariances that are expressible in terms of affinetransformations, specifically, homothetic transformations. Ourdiscussion will include both one-dimensional andtwo-dimensional signal patterns. The main contribution of thispaper is the formulation of several novel morphological neuralnetworks that compute homothetic auditory and visualinvariances. With respect to the latter, we employ the theoryand trends of currently popular artificial vision systems.     

柔性形态滤波和遗传规划在电机轴承故障诊断的应用

针对电机轴承故障振动信号的强噪声背景.以及电机轴承故障是一个内圈故障、外圈故障和滚动体故障多级分类问题的情况,提出了一种基于柔性形态滤波和遗传规划的电机轴承故障诊断方法.该方法首先对电机轴承故障原始信号进行柔性形态滤波,然后提取滤波后信号的故障特征频率的归一化能量以及时域统计特征量作为遗传规划中的终止符,通过复制、交叉、突变以及适应度计算等操作,使个体逐渐逼近问题的最优解,得到电机轴承故障模式分类的最优模型,试验结果表明了该方法的有效性.     

A Morphological Tagger for Korean: Statistical Tagging Combined with Corpus-Based Morphological Rule Application

This paper describes a novel approach to morphological tagging for Korean, an agglutinative language with a very productive inflectional system. The tagger takes raw text as input and returns a lemmatized and morphologically disambiguated output for each word: the lemma is labeled with a part-of-speech (POS) tag and the inflections are labeled with inflectional tags. Unlike the standard approach to tagging for morphologically complex languages, in our proposed approach the tagging phase precedes the analysis phase. It comprises a trigram-based tagging component followed by a morphological rule application component, obtaining 95% precision and recall on unseen test data.     

基于形态学开闭运算和梯度优化的分水岭算法的目标检测方法*

提出了一种基于形态学开闭运算和梯度优化的分水岭算法的目标检测方法。该方法首先利用形态学开闭运算对原始图像进行平滑处理,再对梯度图像进行阈值优化,去除过多的区域极小值,然后利用分水岭分割算法检测目标,最后利用目标的面积和空间关系等特征去除少量误提目标。实验表明,新方法可以取得很好的效果。     

基于柔性形态变换的图像边缘检测

由于自然界中的噪声影响和图像模糊的边缘,这给图像的边缘检测和目标分割带来了一定的困难。柔性形态变换作为一种数学形态学的方法,既保留了标准形态变换的许多优良特性,又具有较好稳健性,为进行目标特征分析提供了可能。使用柔性形态变换构造边缘检测算子,对图像进行边缘检测。实验结果表明,与其他常用的边缘检测算子相比,基于柔性形态变换的边缘检测算子在有效去噪的同时,能较好地保留图像的细节信息,具有很强的实用性。     

Multiscale-stabilized solutions to one-dimensional systems of conservation laws

We present a variational multiscale formulation for the numerical solution of one-dimensional systems of conservation laws. The key idea of the proposed formulation, originally presented by Hughes [Comput. Methods Appl. Mech. Engrg., 127 (1995) 387–401], is a multiple-scale decomposition into resolved grid scales and unresolved subgrid scales. Incorporating the effect of the subgrid scales onto the coarse scale problem results in a finite element method with enhanced stability properties, capable of accurately representing the sharp features of the solution. In the formulation developed herein, the multiscale split is invoked prior to any linearization of the equations. Special attention is given to the choice of the matrix of stabilizing coefficients and the discontinuity-capturing diffusion. The methodology is applied to the one-dimensional simulation of three-phase flow in porous media, and the shallow water equations. These numerical simulations clearly show the potential and applicability of the formulation for solving highly nonlinear, nearly hyperbolic systems on very coarse grids. Application of the numerical formulation to multidimensional problems is presented in a forthcoming paper.     

基于形态学梯度重构和标记提取的分水岭图像分割

为了解决传统分水岭算法的过分割问题,提出一种使用形态学梯度重构和标记提取技术进行图像预处理的分水岭图像分割方法。该方法基于多尺度概念,进行梯度重构时采用了不同尺寸的结构元素,在对重构后的各梯度图像的区域极小值进行标记后,将各标记点的并集作为最终标记图像,用其修改梯度图像,然后进行分水岭变换,实现图像的区域分割。实验结果表明,该方法既能有效解决分水岭算法的过分割问题,又保留了各尺度下的重要目标,并且可以根据图像特点和具体的分割要求,调整分割过程中所选参数,得到满意的图像分割效果。     

形态学联想记忆的研究综述*

通过提炼出来的一个形态学联想记忆的研究框架,可以很清晰地概括出形态学联想记忆的研究成果,从而可以很合理地归纳出形态学联想记忆仍存在的问题以及今后的发展方向。此形态学联想记忆的研究框架对形态学联想记忆的进一步研究具有一定的指导意义。     

融合多结构滤波和多尺度重建的分水岭算法

为了解决传统分水岭算法中存在的过分割问题,提出一种结合多结构形态学开闭滤波和多尺度形态学开闭重建的新方法。该方法用12种不同结构的结构元对原始图像进行开闭滤波,接着对梯度图像应用多尺度开闭重建,通过加权融合不同的重建梯度为最终的梯度。在重建后的梯度上应用扩展最小变换技术（H-minima）以提取标记,用所得的标记修正原始梯度,在修改后的梯度上进行分水岭分割。实验结果表明：该方法不仅能有效抑制分水岭算法中的过分割,而且通过调节分割过程中的参数,还能防止欠分割的发生,对于不同的需求均可得到理想的分割效果。