一种新颖的求解离散Gabor展开对偶窗的方法

本文给出了一种新颖的简捷的求解离散Gabor展开最佳对偶窗的方法．首先推导了离散Gabor展开的公式，给出了连续Gabor展开和离散Gabor展开间的关系．最后利用连续展开和离散展开间的关系给出了一求解离散Gabor展开最佳对偶窗的表达式及实例．     

Gabor feature based classification using the enhanced fisher lineardiscriminant model for face recognition

This paper introduces a novel Gabor-Fisher (1936) classifier (GFC) for face recognition. The GFC method, which is robust to changes in illumination and facial expression, applies the enhanced Fisher linear discriminant model (EFM) to an augmented Gabor feature vector derived from the Gabor wavelet representation of face images. The novelty of this paper comes from (1) the derivation of an augmented Gabor feature vector, whose dimensionality is further reduced using the EFM by considering both data compression and recognition (generalization) performance; (2) the development of a Gabor-Fisher classifier for multi-class problems; and (3) extensive performance evaluation studies. In particular, we performed comparative studies of different similarity measures applied to various classifiers. We also performed comparative experimental studies of various face recognition schemes, including our novel GFC method, the Gabor wavelet method, the eigenfaces method, the Fisherfaces method, the EFM method, the combination of Gabor and the eigenfaces method, and the combination of Gabor and the Fisherfaces method. The feasibility of the new GFC method has been successfully tested on face recognition using 600 FERET frontal face images corresponding to 200 subjects, which were acquired under variable illumination and facial expressions. The novel GFC method achieves 100% accuracy on face recognition using only 62 features.     

An introduction to discrete finite frames

The frame concept was first introduced by Duffin and Schaeffer (1952), and it is widely used today to describe the behavior of vectors for signal representation. The Gabor (1946) expansion and wavelet transform are two special well-known cases. The goal of this article is to describe the frame theory and introduce a simple tutorial method to find discrete finite frame operators and their frame bounds. An easily implementable method for finding the discrete finite frame and subframe operators has been presented by Kaiser (1994). We introduce the method of Kaiser to compute the discrete finite frame operator. Using subframe operators, the biorthogonal basis and projection vectors in a subspace can be easily calculated. Gabor and wavelet analysis are two popular tools for signal processing, and they can reveal time-frequency distribution for a nonstationary signal. Both schemes can be regarded as signal decompositions onto a set of basis functions, and their basis functions are derived from a single prototype function through simple operations. Therefore, the basis functions used in Gabor and wavelet analysis can be regarded as special frames. For completeness we also make some simple introductions on the results of special frames such as discrete Gabor and wavelet analysis     

Note on B-splines, wavelet scaling functions, and Gabor frames

Let g be a continuous, compactly supported function on such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g,a,b), with window g and time-shift and frequency-shift parameters a,b>0 has no lower frame bound larger than 0 if b=2,3,... and a>0. In particular, (g,a,b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b=2,3,... and a>0. We give an example for our result for the case that g=B/sub 1/, the triangle function supported by [-1,1], by showing pictures of the canonical dual corresponding to (g,a,b) where ab=1/4 and b crosses the lines N=2,3,.     

Face Recognition Using Dual-Tree Complex Wavelet Features

We propose a novel facial representation based on the dual-tree complex wavelet transform for face recognition. It is effective and efficient to represent the geometrical structures in facial image with low redundancy. Moreover, we experimentally verify that the proposed method is more powerful to extract facial features robust against the variations of shift and illumination than the discrete wavelet transform and Gabor wavelet transform.     

log Gabor函数在人类视觉系统特性研究中的应用

本文对Gabor函数与log Gabor函数进行比较。构造了log Gabor小波,从人类视觉系统认知特性的角度分析了log Gabor小波的性能,并与Gabor小波进行比较,讨论了log Gabor小波的优良性能。最后将log Gabor小波应用于图像特征检测,证明用log　Gabor小波不但可以提高特征定位精度,而且在相同检测效果的情况下,可以比Gabor小波节省大约一半的计算量。     

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions—the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of ${rm L}^2({BBR})$ by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of ${rm L}^2({BBR}^2)$, we then discuss a methodology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT—the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient fast Fourier transform (FFT)-based filterbank algorithm for implementing the associated complex wavelet transform.      

基于Gabor小波和支持向量机的人脸识别方法

基于Gabor小波在图像表征方面的优越性,提出了将Gabor小波和支持向量机(SVM)相结合用于人脸识别的方案。用Gabor小波对人脸图像进行特征提取,再利用SVM策略对特征向量进行分类识别,实验的仿真结果验证了本算法的有效性。     

Gabor wavelet representation for 3-D object recognition

This paper presents a model-based object recognition approach that uses a Gabor wavelet representation. The key idea is to use magnitude, phase, and frequency measures of the Gabor wavelet representation in an innovative flexible matching approach that can provide robust recognition. The Gabor grid, a topology-preserving map, efficiently encodes both signal energy and structural information of an object in a sparse multiresolution representation. The Gabor grid subsamples the Gabor wavelet decomposition of an object model and is deformed to allow the indexed object model match with similar representation obtained using image data. Flexible matching between the model and the image minimizes a cost function based on local similarity and geometric distortion of the Gabor grid. Grid erosion and repairing is performed whenever a collapsed grid, due to object occlusion, is detected. The results on infrared imagery are presented, where objects undergo rotation, translation, scale, occlusion, and aspect variations under changing environmental conditions.     

一种基于小波域的指纹图像增强算法

面对采集的指纹图像质量较差的问题,提出一种在小波域对指纹图像滤波增强算法。该算法在小波域进行Ga-bor滤波增强,通过Radon变换后的投影估计Gabor滤波的方向和频率,对滤波增强后的子图进行小波重构得到最后的结果,有效地抑制高频扰动对指纹图像质量的影响,提高运算速度和准确性。通过对FVC2000指纹库中的部分低质量指纹图像进行增强,表明该算法对指纹图像的增强效果明显,并且处理速度较快。     

线算子引导Gabor小波的视网膜血管分割

视网膜血管自动分割能辅助诊断某些眼底疾病和系统性血管疾病。为了提高血管自动分割的效率,因此提出了一种线算子引导Gabor小波的视网膜血管分割方法。利用线算子检测血管方向的最优匹配角,将其作为Gabor小波变换的旋转角构建4个不同尺度的Gabor小波,并提取4维Gabor小波特征,加上两个线强度和预处理后的图像灰度,构建7维特征向量,采用SVM进行分类。与其他基于Gabor小波的方法相比,本方法只需计算最优匹配角所对应方向的Gabor小波特征,大大降低了多尺度Gabor小波特征提取的计算量,此外线算子特征与Gabor小波特征的良好互补性,有利于提高血管与背景的辨别度。在DRIVE眼底数据库上进行实验,其平均准确率、灵敏度及特异性分别为0. 936 1、0. 823 8及0. 955 4,获得了不错的分割性能。     

Texture classification and discrimination for region-based image retrieval

In RBIR, texture features are crucial in determining the class a region belongs to since they can overcome the limitations of color and shape features. Two robust approaches to model texture features are Gabor and curvelet features. Although both features are close to human visual perception, sufficient information needs to be extracted from their sub-bands for effective texture classification. Moreover, shape irregularity can be a problem since Gabor and curvelet transforms can only be applied on the regular shapes. In this paper, we propose an approach that uses both the Gabor wavelet and the curvelet transforms on the transferred regular shapes of the image regions. We also apply a fitting method to encode the sub-bands’ information in the polynomial coefficients to create a texture feature vector with the maximum power of discrimination. Experiments on texture classification task with ImageCLEF and Outex databases demonstrate the effectiveness of the proposed approach.     

基于Gabor小波变换和PCA的人脸识别方法

基于Gabor小波在图像表征方面的优越性,阐述了将Gabor小波和主分量分析(PCA)相结合用于人脸识别的方案。对人脸图像进行Gabor小波变换,通过PCA(主分量分析)降维后,计算特征点之间的距离,最后进行人脸识别。     

基于Log Gabor小波相位一致不变量的目标识别

给出了一种基于Log Gabor小波的相位一致（PC）不变量的神经网络目标识别方法。针对Gabor小波存在的问题，分析了LogGabor小波优于Gabor小波的性能，给出了TPC不变量的定义，探讨了低层次图像不变量特征，运用LogGabor小波PC特征不变量公式进行了修正，提取了目标图像边缘特征。利用该方法进行了神经网络目标识别实验，仿真结果表明，该方法能够很好识别图像目标，识别率达到97％。     

基于Gabor小波特征的磨粒图像识别新方法

文章给出了一种基于Gabor小波纹理特征的磨粒图像识别新方法,主要是利用Gabor小波设计了一种多通道小波滤波器,对磨粒图像直接进行小波变换,用Gabor小波变换系数的模的平均值和其标准方差来表示抽取的图像特征。把获得的小波特征归一化后输入到改进的BP神经网络分类器进行分类识别。最后,对磨粒图像进行了一系列的仿真实验,结果表明,识别正确率在91%以上,并且识别速度很快。     

Fresnelets: new multiresolution wavelet bases for digital holography

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of L/sub 2/ to which we apply a unitary Fresnel transform. The transformed basis functions are shift-invariant on a level-by-level basis but their multiresolution properties are governed by the special form that the dilation operator takes in the Fresnel domain. We derive a Heisenberg-like uncertainty relation that relates the localization of Fresnelets with that of their associated wavelet basis. According to this criterion, the optimal functions for digital hologram processing turn out to be Gabor (1948) functions, bringing together two separate aspects of the holography inventor's work. We give the explicit expression of orthogonal and semi-orthogonal Fresnelet bases corresponding to polynomial spline wavelets. This special choice of Fresnelets is motivated by their near-optimal localization properties and their approximation characteristics. We then present an efficient multiresolution Fresnel transform algorithm, the Fresnelet transform. This algorithm allows for the reconstruction (backpropagation) of complex scalar waves at several user-defined, wavelength-independent resolutions. Furthermore, when reconstructing numerical holograms, the subband decomposition of the Fresnelet transform naturally separates the image to reconstruct from the unwanted zero-order and twin image terms. This greatly facilitates their suppression. We show results of experiments carried out on both synthetic (simulated) data sets as well as on digitally acquired holograms.     

基于Gabor小波与Memetic算法的人脸识别方法

提出一种基于Gabor小波与Memetic算法的人脸识别方法MA-Gabor(Memetic Algorithm-Gabor).算法使用一组特定的Gabor小波滤波器对人脸图像重要区域进行针对性的特征提取运算,可在较短处理时间内获得更具区分能力的识别数据.为提升识别性能,MA-Gabor引入Memetic算法用于Gabor小波滤波器组的优化设计.实验结果表明,Memetic算法可获得比传统优化方法更佳的设计效果.通过将优化设计的Gabor小波滤波器组用于人脸图像的特征提取,MA-Gabor算法可取得比现有人脸识别方法更高的识别率.     

Gabor feature-based face recognition using supervised locality preserving projection

This paper introduces a novel Gabor-based supervised locality preserving projection (GSLPP) method for face recognition. Locality preserving projection (LPP) is a recently proposed method for unsupervised linear dimensionality reduction. LPP seeks to preserve the local structure which is usually more significant than the global structure preserved by principal component analysis (PCA) and linear discriminant analysis (LDA). In this paper, we investigate its extension, called supervised locality preserving projection (SLPP), using class labels of data points to enhance its discriminant power in their mapping into a low-dimensional space. The GSLPP method, which is robust to variations of illumination and facial expression, applies the SLPP to an augmented Gabor feature vector derived from the Gabor wavelet representation of face images. We performed comparative experiments of various face recognition schemes, including the proposed GSLPP method, PCA method, LDA method, LPP method, the combination of Gabor and PCA method (GPCA) and the combination of Gabor and LDA method (GLDA). Experimental results on AR database and CMU PIE database show superior of the novel GSLPP method.     

变窗Gabor变换理论及其在图像处理中的应用

基于Ｇａｂｏｒ变换和小波变换提出了变窗Ｇａｂｏｒ变换，讨论了它它的若干优良特性。变窗Ｇａｂｒｏ变换包含了Ｆｏｕｒｉｅｒ变换，Ｇａｂｏｒ变换，波变换的一般化，基于上述变换对变窗Ｇａｂｏｒ变换提出了不同的快速算法。