Generalized multichannel image-filtering structures

Recent works in multispectral image processing advocate the employment of vector approaches for this class of signals. Vector processing operators that involve the minimization of a suitable error criterion have been proposed and shown appropriate for this task. In this framework, two main classes of vector processing filters have been reported in the literature. Astola et al. (1990) introduce the well-known class of vector median filters (VMF), which are derived as maximum likelihood (ML) estimates from exponential distributions. Trahanias et al. (see ibid., vol.2, no.4, p.528-34, 1993 and vol.5, no.6, p.868-80, 1996) study the processing of color image data using directional information, considering the class of vector directional filters (VDF). We introduce a new filter structure, the directional-distance filters (DDF), which combine both VDF and VMF in a novel way. We show that DDF are robust signal estimators under various noise distributions, they have the property of chromaticity preservation and, finally, compare favorably to other multichannel image processing filters.     

彩色形态滤波器分析

形态滤波属于非线性信号变换处理,它利用信号的局部特征对信号进行修正。最近的研究表明形态滤波器能有效地滤除二值图像及灰度图像中的噪声,本文引入了建立在ＲＧＢ彩色空间上的彩色形态变换,针数字形态学理论从灰度空间扩展到彩色空间,对基本彩色形态滤波器（即彩色形态闭、开）及以它们为基础所构造出一些复杂的彩色形态滤波器进行了研究,并对它们选用不同结构元素的情况进行了分析,实验表明彩色形态滤波器能直接有效地消除     

An orthogonal wavelet representation of multivalued images

A new orthogonal wavelet representation of multivalued images is presented. The idea for this representation is based on the concept of maximal gradient of multivalued images. This concept is generalized from gradients toward linear vector operators in the image plane with equal components along rows and columns. Using this generalization, the pyramidal dyadic wavelet transform algorithm using quadrature mirror filters is modified to be applied to multivalued images. This results in a representation of a single image, containing multiscale detail information from all component images involved. This representation leads to multiple applications ranging from multispectral image fusion to color and multivalued image enhancement, denoising and segmentation. In this paper, the representation is applied for fusion of images. More in particular, we introduce a scheme to merge high spatial resolution greylevel images with low spatial resolution multivalued images to improve spatial resolution of the latter while preserving spectral resolution. Two applications are studied: demosaicing of color images and merging of multispectral remote sensing images.     

Adaptive and vector directional processing applied to video colour images

The adapted K-nearest neighbour and adaptive vector median filters together with vector directional processing to filter 3D images are presented. Vector median, median and adaptive vector median filters have been modified and proved to suppress impulsive noise in the video sequences.     

Directional lapped orthogonal transform: theory and design

This paper proposes a directional design method of 2-D nonseparable linear-phase paraunitary filter banks. The proposed method is based on a lattice structure consisting of the 2-D separable DCT block and nonseparable support extension processes. Because of the nonseparability, the bases are allowed to be directional with the critically fixed subsampling, overlapping, orthogonal, symmetric, real-valued, and compact support properties. First, a novel vanishing moment (VM) condition is introduced as a suitable directional constraint, where the moment is referred to as the trend VM. The condition forces wavelet filters, i.e., high-pass and bandpass filters, to annihilate trend-surface components. Second, some theoretical properties of TVMs are discussed for general 2-D paraunitary systems, and then, the properties are applied to the lattice parameters. In order to verify the significance, several design examples are shown, the trend-surface annihilation properties are numerically confirmed, and the denoising capability is evaluated for images through shrinkage. It is shown that our proposed transforms yield perceptually preferable results.     

Vector median filters

Two nonlinear algorithms for processing vector-valued signals are introduced. The algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum-likelihood-estimate approach. The underlying probability densities are exponential, and the resulting operations have properties very similar to those of the median filter. In the vector median approach, the samples of the vector-valued input signal are processed as vectors. The operation inherently utilizes the correlation between the signal components, giving the filters some desirable properties. General properties as well as the root signals of the vector median filters are studied. The vector median operation is combined with linear filtering, resulting in filters with improved noise attenuation and filters with very good edge response. An efficient algorithm for implementing long vector median filters is presented. The noise attenuation of the filters is discussed, and an application to velocity filtering is shown     

基于张量滤波器的多波段红外目标辨识

红外多光谱成像在面对红外干扰和红外隐身时具有全色红外成像手段无法比拟的优势,通过目标在不同波段响应的差异,能有效地克服干扰和检测隐身目标.但传统基于向量的方法在处理多波段图像时没有有效地利用光谱和空间之间的相关性,通过在张量框架下设计辨识方法时,可以综合利用多光谱图像的光谱和空间特性.在设计张量辨识方法时,多光谱图像被...     

A quasi-Euclidean norm to speed up vector median filtering

For reducing impulsive noise without degrading image contours, median filtering is a powerful tool. In multiband images, as for example color images or vector fields obtained by optic flow computation, a vector median filter can be used. Vector median filters are defined on the basis of a suitable distance, the best performing distance being the Euclidean. Euclidean distance is evaluated by using the Euclidean norm which is quite demanding from the point of view of computation given that a square root is required. In this paper an optimal piece-wise linear approximation of the Euclidean norm is presented which is applied to vector median filtering.     

Application of partition-based median type filters for suppressingnoise in images

An adaptive median based filter is proposed for removing noise from images. Specifically, the observed sample vector at each pixel location is classified into one of M mutually exclusive partitions, each of which has a particular filtering operation. The observation signal space is partitioned based an the differences defined between the current pixel value and the outputs of CWM (center weighted median) filters with variable center weights. The estimate at each location is formed as a linear combination of the outputs of those CWM filters and the current pixel value. To control the dynamic range of filter outputs, a location-invariance constraint is imposed upon each weighting vector. The weights are optimized using the constrained LMS (least mean square) algorithm. Recursive implementation of the new filter is then addressed. The new technique consistently outperforms other median based filters in suppressing both random-valued and fixed-valued impulses, and it also works satisfactorily in reducing Gaussian noise as well as mixed Gaussian and impulse noise     

基于多级引导滤波器的图像区域融合算法

为了提高多光谱图像与全色图像的融合质量,研究了多种滤波器和融合算法,提出了基于多级引导滤波器的区域融合方法。采用该方法对多光谱图像进行插值,利用改进的分水岭算法对全色图像进行区域划分,并将划分结果映射至每个多光谱图像,然后将多光谱图像与全色图像利用多级引导滤波器分别进行滤波,得到各自的细节信息,最后根据每个区域中全色图像和多光谱图像的关系指标局部相关系数与4阶相关系数的大小,对细节信息进行区域融合,得到融合后的多光谱图像。结果表明,该算法充分保留了多光谱图像的光谱信息,并尽可能多地注入了全色图像的细节信息,成功地提高了多光谱图像的融合效果。     

Feature predictive vector quantization of multispectral images

A compression method for multispectral data sets is proposed where a small subset of image bands is initially vector quantized. The remaining bands are predicted from the quantized images. Two different types of predictors are examined, an affine predictor and a new nonlinear predictor. The residual (error) images are encoded at a second stage based on the magnitude of the errors. This scheme simultaneously exploits both spatial and spectral correlation inherent in multispectral images. Simulation results on an image set from the Thematic Mapper with seven spectral bands provide a comparison of the affine predictor with the nonlinear predictor. It is shown that the nonlinear predictor provides significantly improved performance compared to the affine predictor. Image compression ratios between 15 and 25 are achieved with remarkably good image quality     

Multispectral code excited linear prediction coding and itsapplication in magnetic resonance images

This paper reports a multispectral code excited linear prediction (MCELP) method for the compression of multispectral images. Different linear prediction models and adaptation schemes have been compared. The method that uses a forward adaptive autoregressive (AR) model has been proven to achieve a good compromise between performance, complexity, and robustness. This approach is referred to as the MFCELP method. Given a set of multispectral images, the linear predictive coefficients are updated over nonoverlapping three-dimensional (3-D) macroblocks. Each macroblock is further divided into several 3-D micro-blocks, and the best excitation signal for each microblock is determined through an analysis-by-synthesis procedure. The MFCELP method has been applied to multispectral magnetic resonance (MR) images. To satisfy the high quality requirement for medical images, the error between the original image set and the synthesized one is further specified using a vector quantizer. This method has been applied to images from 26 clinical MR neuro studies (20 slices/study, three spectral bands/slice, 256x256 pixels/band, 12 b/pixel). The MFCELP method provides a significant visual improvement over the discrete cosine transform (DCT) based Joint Photographers Expert Group (JPEG) method, the wavelet transform based embedded zero-tree wavelet (EZW) coding method, and the vector tree (VT) coding method, as well as the multispectral segmented autoregressive moving average (MSARMA) method we developed previously.     

A new approach to vector median filtering based on space fillingcurves

The availability of a wide set of multidimensional information sources in different application fields (e.g., color cameras, multispectral remote sensing imagery devices, etc.) is the basis for the interest of image processing research on extensions of scalar nonlinear filtering approaches to multidimensional data filtering. A new approach to multidimensional median filtering is presented. The method is structured into two steps. Absolute sorting of the vectorial space based on Peano space filling curves is proposed as a preliminary step in order to map vectorial data onto an appropriate one-dimensional (1-D) space. Then, a scalar median filtering operation is applied. The main advantage of the proposed approach is the computational efficiency of the absolute sorting step, which makes the method globally faster than existing median filtering techniques. This is particularly important when dealing with a large amount of data (e.g., image sequences). Presented results also show that the filtering performances of the proposed approach are comparable with those of vector median filters presented in the literature.     

Vector directional filters-a new class of multichannel imageprocessing filters

Vector directional filters (VDF) for multichannel image processing are introduced and studied. These filters separate the processing of vector-valued signals into directional processing and magnitude processing. This provides a link between single-channel image processing where only magnitude processing is essentially performed, and multichannel image processing where both the direction and the magnitude of the image vectors play an important role in the resulting (processed) image. VDF find applications in satellite image data processing, color image processing, and multispectral biomedical image processing. Results are presented here for the case of color images, as an important example of multichannel image processing. It is shown that VDF can achieve very good filtering results for various noise source models.     

Fuzzy scalar and vector median filters based on fuzzy distances

The fuzzy scalar median (FSM) is proposed, defined by using ordering of fuzzy numbers based on fuzzy minimum and maximum operations defined by using the extension principle. Alternatively, the FSM is defined from the minimization of a fuzzy distance measure, and the equivalence of the two definitions is proven. Then, the fuzzy vector median (FVM) is proposed as an extension of vector median, based on a novel distance definition of fuzzy vectors, which satisfy the property of angle decomposition. By defining properly the fuzziness of a value, the combination of the basic properties of the classical scalar and vector median (VM) filter with other desirable characteristics can be succeeded.     

A structure for adaptive order statistics filtering

In applications such as smoothing and enhancement of images, adaptive filtering techniques offer the flexibility needed for good performance with non-stationary observations. Many adaptive schemes can be based on the idea of determining the local statistics of the signal through appropriate tests on the data, to aid in the selection of a filtering procedure that is suited to the data. In the paper, the authors consider decision-directed or data-dependent adaptive filtering schemes that are based on order statistics. A general formulation for such a class of adaptive order statistics filters is presented. Approximate statistical performance analysis, especially in the presence of edges, may be carried out for this entire class of filters. The authors give examples of some existing filters that fit into this framework. The formulation also accommodates filters that employ multiple windows in their operation. To illustrate the potential of this class of multiple window (MW) filters, they construct and analyze simple filters, like the triple window median (TW-MED) and the triple window median of means (TW-MOM) filters, that are shown to yield useful performance. The class of mean-median hybrid (MMH) filters is also presented as a simple example which may be extended to give interesting performance.     

Partition-based weighted sum filters for image restoration

We develop the concept of partitioning the observation space to build a general class of filters referred to as partition-based weighted sum (PWS) filters. In the general framework, each observation vector is mapped to one of M partitions comprising the observation space, and each partition has an associated filtering function. We focus on partitioning the observation space utilizing vector quantization and restrict the filtering function within each partition to be linear. In this formulation, a weighted sum of the observation samples forms the estimate, where the weights are allowed to be unique within each partition. The partitions are selected and weights tuned by training on a representative set of data. It is shown that the proposed data adaptive processing allows for greater detail preservation when encountering nonstationarities in the data and yields superior results compared to several previously defined filters. Optimization of the PWS filters is addressed and experimental results are provided illustrating the performance of PWS filters in the restoration of images corrupted by Gaussian noise.     

Compression of multispectral images by three-dimensional SPIHTalgorithm

The authors carry out low bit-rate compression of multispectral images by means of the Said and Pearlman's SPIHT algorithm, suitably modified to take into account the interband dependencies. Two techniques are proposed: in the first, a three-dimensional (3D) transform is taken (wavelet in the spatial domain, Karhunen-Loeve in the spectral domain) and a simple 3D SPIHT is used; in the second, after taking a spatial wavelet transform, spectral vectors of pixels are vector quantized and a gain-driven SPIHT is used. Numerous experiments on two sample multispectral images show very good performance for both algorithms     

Nonlinear processing and analysis of angular signals

Physical quantities referring to angles, like vector direction, color hue, etc., exhibit an inherently periodic nature. Due to this periodicity, digital filters and edge operators proposed for data on the line cannot be applied on such data. We introduce filters for angular signals (circular mean, circular median, circular a-trimmed mean, circular modified trimmed mean). Particular emphasis is given to the circular median filter, for which some interesting properties are derived. We also use estimators of circular dispersion to introduce edge detectors for angular signals. Three variations for the extension of quasirange to circular data are proposed, and expressions for their output PDF are derived. These “circular” quasiranges have good and user-controlled properties as edge detectors in noisy angular signals. The performance of the proposed edge operators is evaluated on angular edges, using certain quantitative criteria. Finally, a series of experiments featuring one-dimensional (1-D) angular signals and hue images is used to illustrate the operation of the new filters and edge detectors