基于小波变换的图像多尺度数据融合

现有的图像数据融合方法对目标检测并不十分满意，为了提高目标检测的分辨率，抑制每个传感器的检测噪声，提出一种基于小波谱换的图像数据融合新方法，在图像分解的高域风，选择多源图像绝对值较大的系数作为重要小波系数，在低频域内，新的逼近系统通过对多源图像的逼近系数进行加权平均得到，然后利用重要小波系数和加权逼近系数进行小波反变换，即可得到融合之后的图像，实验结果表明，基于小波变换的图像数据融合方法具有良好的效果，并用于广泛的研究领域。     

Interactive Multiresolution Editing and Display of Large Terrains

In recent years, many systems have been developed for the real‐time display of very large terrains. While many of these techniques combine high‐quality rendering with impressive performance, most make the fundamental assumption that the terrain is represented by a fixed height map that cannot be altered at run time. Such systems frequently rely on extensive preprocessing of the raw terrain data. They are mostly designed for maximum performance. Consequently, these techniques are ill‐suited for the many applications such as geological simulations and games in which terrain surfaces must be altered interactively. We present a two‐component system that can achieve real‐time view‐dependent rendering while allowing on‐line multiresolution alterations of a large terrain. Our fundamental height map representation is a wavelet quadtree hierarchy, allowing one to easily apply arbitrary multiresolution edits to the terrain. Our display algorithm extracts a view‐dependent approximation of the terrain from the wavelet quadtree in real time. The algorithm dynamically alters this approximation based on any ongoing edits. To allow for flexibility and to limit performance loss, the two components of this system have been designed to be as independent as possible.     

互为Hilbert变换对的双正交小波构造

证明了两个双正交小波滤波器组构成Hilbert变换对的充要条件,并从理论上说明了两个线性相位双正交小波系统构成Hilbert变换对的必要条件是它们的长度分别为奇数和偶数．在此基础上通过选择合适的小波消失矩和优化过程中的目标函数,提出了一种构造这类Hilbert变换对的新算法．采用该算法不但可以得到系数对称的线性相位小波滤波器组,而且在性能基本相当的条件下,滤波器长度较已有算法大幅度减小（以13／19和12／16小波为例,可以降到约为原来的1／2）．通过适当调整设计参数,还可以得到全为有理系数的小波滤波器,从而进一步减少计算代价．实验表明上述构造得到的Hilbert变换在用于复数小波进行图像去噪时,处理时间可以降低为原来的2／3左右．     

Hardness and approximation of minimum maximal matchings

In this paper, we consider the minimum maximal matching problem in some classes of graphs such as regular graphs. We show that the minimum maximal matching problem is NP-hard even in regular bipartite graphs, and a polynomial time exact algorithm is given for almost complete regular bipartite graphs. From the approximation point of view, it is well known that any maximal matching guarantees the approximation ratio of 2 but surprisingly very few improvements have been obtained. In this paper we give improved approximation ratios for several classes of graphs. For example any algorithm is shown to guarantee an approximation ratio of (2-o(1)) in graphs with high average degree. We also propose an algorithm guaranteeing for any graph of maximum degree Δ an approximation ratio of (2?1/Δ), which slightly improves the best known results. In addition, we analyse a natural linear-time greedy algorithm guaranteeing a ratio of (2?23/18k) in k-regular graphs admitting a perfect matching.     

Practical Product Importance Sampling for Direct Illumination

We present a practical algorithm for sampling the product of environment map lighting and surface reflectance. Our method builds on wavelet‐based importance sampling, but has a number of important advantages over previous methods. Most importantly, we avoid using precomputed reflectance functions by sampling the BRDF on‐the‐fly. Hence, all types of materials can be handled, including anisotropic and spatially varying BRDFs, as well as procedural shaders. This also opens up for using very high resolution, uncompressed, environment maps. Our results show that this gives a significant reduction of variance compared to using lower resolution approximations. In addition, we study the wavelet product, and present a faster algorithm geared for sampling purposes. For our application, the computations are reduced to a simple quadtree‐based multiplication. We build the BRDF approximation and evaluate the product in a single tree traversal, which makes the algorithm both faster and more flexible than previous methods.     

基于PSO算法的WNN大包线增益调参控制律设计

提出了一种基于粒子群优化算法的小波神经网络大包线调参控制律设计方法.该方法用小波函数代替了Sigmoid函数作为激活函数.由于结合了小波变换良好的高频域时间精度、低频域频率精度的性质和神经网络的自学习功能,因而具有较强逼近非线性函数的能力.为了克服局部极小值问题并进一步提高对非线性函数逼近能力,利用粒子群优化算法对小波神经网络进行参数训练,并利用该网络实现了大包线增益调参.飞行仿真结果表明,所设计的小波神经网络增益调参控制器具有优良的控制性能,不仅能够保证平衡状态下的控制效果,而且在未训练的平衡状态下依然具有良好的控制性能,并且在存在20%的建模误差时,最大超调量仅为6 m,仅是使用常规增益调参方法的18%.     

Morphological Pyramids in Multiresolution MIP Rendering of Large Volume Data: Survey and New Results

We survey and extend nonlinear signal decompositions based on morphological pyramids, and their application to multiresolution maximum intensity projection (MIP) volume rendering with progressive refinement and perfect reconstruction. The structure of the resulting multiresolution rendering algorithm is very similar to wavelet splatting. Several existing classes of pyramids are discussed, and their limitations indicated. To enhance the approximation quality of visualizations from reduced data (higher levels of the pyramid), two approaches are explored. First, a new class of morphological pyramids, involving connectivity enhancing operators, is considered. In the pyramidal analysis phase, a conditional dilation operator is used, with a given number n of iterations. The corresponding pyramids for n = 0 and n = 1 are known as the adjunction pyramid and Sun-Maragos pyramid, respectively. We show that the approximation quality when rendering from higher levels of the pyramid does increase as a function of the number of iterations n of the conditional dilation operator, but the improvement for n > 1 is limited. The second new approach, called streaming MIP-splatting, again starts from the adjunction pyramid. The new element is that detail coefficients of all levels are considered simultaneously and are resorted with respect to decreasing magnitude of a suitable error measure. All resorted coefficients are projected successively, until a desired accuracy of the resulting MIP image is obtained. We show that this method outperforms the previous methods based on morphological pyramids, both with respect to image quality with a fixed amount of detail data, and in terms of flexibility of controlling approximation error or computation time.Jos B.T.M. Roerdink received his M.Sc. (1979) in theoretical physics from the University of Nijmegen, the Netherlands. Following his Ph.D. (1983) from the University of Utrecht and a two-year position (1983–1985) as a Postdoctoral Fellow at the University of California, San Diego, both in the area of stochastic processes, he joined the Centre for Mathematics and Computer Science in Amsterdam. There he worked from 1986–1992 on image processing and tomographic reconstruction. He was appointed associate professor (1992) and full professor (2003), respectively, at the Institute for Mathematics and Computing Science of the University of Groningen, where he currently holds a chair in Scientific Visualization and Computer Graphics. His current research interests include morphological image processing, biomedical visualization, neuroimaging and bioinformatics.     

Nonlinear black-box models in system identification: Mathematical foundations

We discuss several aspects of the mathematical foundations of the nonlinear black-box identification problem. We shall see that the quality of the identification procedure is always a result of a certain trade-off between the expressive power of the model we try to identify (the larger the number of parameters used to describe the model, the more flexible is the approximation), and the stochastic error (which is proportional to the number of parameters). A consequence of this trade-off is the simple fact that a good approximation technique can be the basis of a good identification algorithm. From this point of view, we consider different approximation methods, and pay special attention to spatially adaptive approximants. We introduce wavelet and ‘neuron’ approximations, and show that they are spatially adaptive. Then we apply the acquired approximation experience to estimation problems. Finally, we consider some implications of these theoretical developments for the practically implemented versions of the ‘spatially adaptive’ algorithms.     

Wavelet basis function neural networks for sequential learning.

In this letter, we develop the wavelet basis function neural networks (WBFNNs). It is analogous to radial basis function neural networks (RBFNNs) and to wavelet neural networks (WNNs). In WBFNNs, both the scaling function and the wavelet function of a multiresolution approximation (MRA) are adopted as the basis for approximating functions. A sequential learning algorithm for WBFNNs is presented and compared to the sequential learning algorithm of RBFNNs. Experimental results show that WBFNNs have better generalization property and require shorter training time than RBFNNs.     

基于狼群算法的短时高速交通流量预测仿真

由于传统的短时高速交通流量预测算法的受到函数逼近能力影响,极易陷入局部极值的问题,提出基于狼群算法的短时高速交通流量预测算法。构造型前馈小波神经网络算法在多维空间内对短时高速交通流量预测,需通过构造型前馈小波神经网络算法分析随机相关多维样本逼近能力,利用改进狼群算法的全局寻优能力,提升算法搜索精度,并完成目标的搜索,根据搜索结果获取优质的函数逼近值最优解,提升构造型前馈小波神经网络算法函数的逼近能力,获取最佳短时高速交通流量预测值。仿真结果显示,上述算法的短时高速交通流量预测效果显著优于小波神经网络预测算法,且本文算法的预测精度较高,具有较高的稳定性。     

Image Approximation by Rectangular Wavelet Transform

We study image approximation by a separable wavelet basis and ϕ,ψ are elements of a standard biorthogonal wavelet basis in L₂(ℝ). Because k₁≠ k₂, the supports of the basis elements are rectangles, and the corresponding transform is known as the rectangular wavelet transform. We provide a self-contained proof that if one-dimensional wavelet basis has M dual vanishing moments then the rate of approximation by N coefficients of rectangular wavelet transform is for functions with mixed derivative of order M in each direction. These results are consistent with optimal approximation rates for such functions. The square wavelet transform yields the approximation rate is for functions with all derivatives of the total order M. Thus, the rectangular wavelet transform can outperform the square one if an image has a mixed derivative. We provide experimental comparison of image approximation which shows that rectangular wavelet transform outperform the square one. Vyacheslav Zavadsky got his M.Sc. (with distinction) in computer science and applied mathematics from Belarusian State University in 1994 and his Ph.D. in mathematics and statistics in 1998 from Belarusian Academy of Sciences and Belarusian State University. He worked at Institute of Mathematics of Belarusian Academy of sciences, and Belarusian center for medical technologies. He also held progressively responsible technical and research positions in the industry: at MZOR, eBusiness technologies, and Webmotion. At present, he is the principal software architect with Semiconductor insights. His research interests include mathematical and statistical methods in vision; machine learning, and structural data mining. Vyacheslav is author of more then ten peer reviewed papers and conference presentation, and 7 pending inventions.     

非线性小波变换在人脸识别中应用

文中提出非线性小波逼近在人脸识别中的应用，并将之与基于线性小波逼近的人脸识别算法进行比较，提出一种基于非线性小波逼近的高效算法，并且用实验证明本算法的具有很高识别率，同时证明本算法具有不会受到人脸姿态特征的影响的优点。     

On the Flattest Common Supersequence Method for Deadlock-Free Routing in Arbitrary Networks

In this paper we consider the problem of deadlock-free routing in arbitrary parallel and distributed computers. We focus on asynchronous routing algorithms which continuously receive new packets to route and which do not discard packets that encounter congestion. Specifically, we examine what we call the deadlock-free routing (DFR ) problem. The input to the DFR problem consists of an arbitrary network and an arbitrary set of paths in the network. The output consists of a routing algorithm, which is a list of the buffers used along each of the paths. The routing algorithm is required to be free from deadlock and the goal is to minimize the number of buffers required in any one node. We study the DFR problem by converting it into an equivalent problem which we call the flattest common supersequence (FCS ) problem. The input to the FCS problem consists of a set of sequences and the output consists of a single sequence that contains all of the input sequences as (possibly noncontiguous) subsequences. The goal of the FCS problem is to minimize the maximum frequency of any symbol in the output sequence. We present three main results. First, we prove that the decision version of the FCS problem is NP-complete, and has no polynomial-time approximation scheme unless P= NP . An alternative proof is presented which shows that unlike the shortest common supersequence (SCS) problem, the FCS problem is still NP-complete for two input sequences. This implies that approximation algorithms for FCS based on an exact pairwise merge are not possible. Next, we propose and experimentally evaluate a range of heuristics for FCS. Our experimental results show that one of these heuristics performs very well over a wide range of inputs. Lastly, we prove that this heuristic is in fact optimal for certain restricted classes of inputs. Online publication November 27, 2000.     

A Hierarchical Evolutionary Algorithm for Constructing and Training Wavelet Networks

The wavelet network has been introduced as a special feed-forward neural network supported by the wavelet theory, and has become a popular tool in the approximation and forecast fields. In this paper, an evolutionary algorithm is proposed for constructing and training the wavelet network for approximation and forecast. This evolutionary algorithm utilises the hierarchical chromosome to encode the structure and parameters of the wavelet network, and combines a genetic algorithm and evolutionary programming to construct and train the network simultaneously through evolution. The numerical examples are presented to show the efficiency and potential of the proposed algorithm with respect to function approximation, sunspot time series forecast and condition forecast for a hydroturbine machine, respectively. The study also indicates that the proposed method has the potential to solve a wide range of neural network construction and training problems in a systematic and robust way.     

Improving within-genus tree species discrimination using the discrete wavelet transform applied to airborne hyperspectral data

Discrete wavelet analysis was assessed for its utility in aiding discrimination of three pine species (Pinus spp.) using airborne hyperspectral data (AVIRIS). Two different sets of Haar wavelet features were compared to each other and to calibrated radiance, as follows: (1) all combinations of detail and final level approximation coefficients and (2) wavelet energy features rather than individual coefficients. We applied stepwise discriminant techniques to reduce data dimensionality, followed by discriminant techniques to determine separability. Leave-one-out cross validation was used to measure the classification accuracy. The most accurate (74.2%) classification used all combinations of detail and approximation coefficients, followed by the original radiance (66.7%) and wavelet energy features (55.1%). These results indicate that application of the discrete wavelet transform can improve species discrimination within the Pinus genus.     

An Extension of Fourier-Wavelet Volume Rendering by View Interpolation

This paper describes an extension to Fourier-wavelet volume rendering (FWVR), which is a Fourier domain implementation of the wavelet X-ray transform. This transform combines integration along the line of sight with a simultaneous 2-D wavelet transform in the view plane perpendicular to this line. During user interaction, only low resolution images are computed based on wavelet approximation coefficients. When user interaction ceases, the images are refined incrementally with the wavelet detail coefficients. The extension proposed in this paper is similar to a technique called view interpolation, which originates from the field of computer graphics. View interpolation is used to speed up rendering of complex scenes by precomputing images from a number of selected viewpoints. For intermediate viewpoints, rendering is performed by interpolating the precomputed images. In this paper, we show that for FWVR the speed of rendering low resolution images is increased by interpolation of precomputed sets of wavelet approximation coefficients in the Fourier domain. The differences with traditional view interpolation are that (i) interpolation is performed on the wavelet approximation coefficients in the Fourier domain and not on images, and (ii) interpolation is performed during user interaction only. When interaction ceases, ordinary FWVR progressively renders an image at high quality. Medical CT data are used to assess the accuracy and performance of the method. We use regular angular sampling of spherical coordinates which determine the viewing direction. The results show that angle increments as large as 10 degrees result in only a small degradation of image quality.     

Autostereoscopic Rendering of Multiple Light Fields

Light fields were introduced a decade ago as a new high‐dimensional graphics rendering model. However, they have not been thoroughly used because their applications are very specific and their storage requirements are too high. Recently, spatial imaging devices have been related to light fields. These devices allow several users to see three‐dimensional (3D) images without using glasses or other intrusive elements. This paper presents a light‐field model that can be rendered in an autostereoscopic spatial device. The model is viewpoint‐independent and supports continuous multiresolution, foveal rendering, and integrating multiple light fields and geometric models in the same scene. We also show that it is possible to examine interactively a scene composed of several light fields and geometric models. Visibility is taken care of by the algorithm. Our goal is to apply our models to 3D TV and spatial imaging.     

Searching in metric spaces by spatial approximation

We propose a new data structure to search in metric spaces. A metric space is formed by a collection of objects and a distance function defined among them which satisfies the triangle inequality. The goal is, given a set of objects and a query, retrieve those objects close enough to the query. The complexity measure is the number of distances computed to achieve this goal. Our data structure, called sa-tree (“spatial approximation tree”), is based on approaching the searched objects spatially, that is, getting closer and closer to them, rather than the classic divide-and-conquer approach of other data structures. We analyze our method and show that the number of distance evaluations to search among n objects is sublinear. We show experimentally that the sa-tree is the best existing technique when the metric space is hard to search or the query has low selectivity. These are the most important unsolved cases in real applications. As a practical advantage, our data structure is one of the few that does not need to tune parameters, which makes it appealing for use by non-experts. Edited by R. Sacks-Davis Received: 17 April 2001 / Accepted: 24 January 2002 / Published online: 14 May 2002     

The construction of wavelet network for speech signal processing

Wavelet decomposition reconstructs a signal by a series of scaled and translated wavelets. Incorporating discrete wavelet decomposition theory with neural network techniques, wavelet networks have recently emerged as a powerful tool for many applications in the field of signal processing, such as data compression and function approximation. In this paper, four contributions are claimed: (1) From the point of view of machine learning, we analyse and construct wavelet network to achieve the compact representation of a signal. (2) A new algorithm of constructing wavelet network is proposed. The orthogonal least square (OLS) is employed to prune the wavelet network. (3) Our experiments on speech signal processing results show that the wavelet network pruned by OLS achieves the best approximation and prediction capabilities among the representative speech processing techniques. (4) Our proposed methodology has been successfully applied to speech synthesis for a talking head to read web texts.     

A Randomized Approach for Patch-based Texture Synthesis using Wavelets

We present a wavelet‐based approach for selecting patches in patch‐based texture synthesis. We randomly select the first block that satisfies a minimum error criterion, computed from the wavelet coefficients (using 1D or 2D wavelets) for the overlapping region. We show that our wavelet‐based approach improves texture synthesis for samples where previous work fails, mainly textures with prominent aligned features. Also, it generates similar quality textures when compared against texture synthesis using feature maps with the advantage that our proposed method uses implicit edge information (since it is embedded in the wavelet coefficients) whereas feature maps rely explicitly on edge features. In previous work, the best patches are selected among all possible using a L2 norm on the RGB or grayscale pixel values of boundary zones. The L2 metric provides the raw pixel‐to‐pixel difference, disregarding relevant image structures — such as edges — that are relevant in the human visual system and therefore on synthesis of new textures.