构造径向基函数的一般方法及其在图象处理中的应用

gi．引言对于函数J：＊”＋R如果存在函数h：B＋R使得对VxE＊”;都有人对二周卜DD）,其中卜D为X的欧几里得范数,则称函数人X）为一个径向函数．径向函数具有本质上的一维性,它可以将任意高继问题映射为一维问题处理．当一个径向函数的平移和伸缩能够构成某函数空间的基底时,利用该基底的线性组合便可以设计径向基函数网络．径向基函数网络的降维特性为多层前馈网络的学习提供了一条新颖而简捷的途径山,现已广泛应用于非线性函数逼近、信号及图象处理等领域［‘,‘,‘］．它不仅具有良好的推广能力,而且避免了象反传算法那样繁…     

Parallel computation of the Euclidean distance transform on a three-dimensional image array

In a two- or three-dimensional image array, the computation of Euclidean distance transform (EDT) is an important task. With the increasing application of 3D voxel images, it is useful to consider the distance transform of a 3D digital image array. Because the EDT computation is a global operation, it is prohibitively time consuming when performing the EDT for image processing. In order to provide the efficient transform computations, parallelism is employed. We first derive several important geometry relations and properties among parallel planes. We then, develop a parallel algorithm for the three-dimensional Euclidean distance transform (3D-EDT) on the EREW PRAM computation model. The time complexity of our parallel algorithm is O(log/sup 2/ N) for an N/spl times/N/spl times/N image array and this is currently the best known result. A generalized parallel algorithm for the 3D-EDT is also proposed. We implement the proposed algorithms sequentially, the performance of which exceeds the existing algorithms (proposed by Yamada, 1984). Finally, we develop the corresponding parallel programs on both the emulated EREW PRAM model computer and the IBM SP2 to verify the speed-up properties of the proposed algorithms.     

使用二分图邻接矩阵的压缩传感图像快速重建

针对压缩传感中高维投影计算采用稀疏性较差的普通随机测量矩阵,从而导致计算复杂度高,重构性能不佳这一难题,提出一种基于二分图邻接矩阵的压缩传感图像快速重建算法。该算法在满足测量矩阵的RIP条件下,充分利用二分图邻接矩阵的稀疏性与二值性,将时间复杂度由传统算法的O(N·logN)降低至O(N)。实验结果表明,算法在保证图像重构质量情况下大大提高了运算性能,尤其对于色彩(灰度)变化平缓图像,该算法性能更加优越。     

Fast parallel algorithm for distance transform

We present an O((log log N)/sup 2/) -time algorithm for computing the distance transform of an N /spl times/ N binary image. Our algorithm is designed for the common concurrent read concurrent write parallel random access machine (CRCW PRAM) and requires O(N/sup 2+/spl epsi///log log N) processors, for any /spl epsi/ such that 0 < /spl epsi/ < 1. Our algorithm is based on a novel deterministic sampling scheme and can be used for computing distance transforms for a very general class of distance functions. We also present a scalable version of our algorithm when the number of processors is available p/sup 2+/spl epsi///log log p for some p < N. In this case, our algorithm runs in O((N/sup 2//p/sup 2/)+(N/p) log log p + (log log p)/sup 2/) time. This scalable algorithm is more practical since usually the number of available processors is much less than the size of the image.     

Optimal ℒ1 approximation of the Gaussian kernelwith application to scale-space construction

Scale-space construction based on Gaussian filtering requires convolving signals with a large bank of Gaussian filters with different widths. We propose an efficient way for this purpose by ℒ₁ optimal approximation of the Gaussian kernel in terms of linear combinations of a small number of basis functions. Exploring total positivity of the Gaussian kernel, the method has the following properties: 1) the optimal basis functions are still Gaussian and can be obtained analytically; 2) scale-spaces for a continuum of scales can be computed easily; 3) a significant reduction in computation and storage costs is possible. Moreover, this work sheds light on some issues related to use of Gaussian models for multiscale image processing     

Progressive refinement of 3-d images using coded binary trees: algorithms and architecture

An encoding/decoding technique and a computer architecture for progressive refinement of 3-D images is suggested. The method is based on a binary tree representation of grey-level images. A scheme to transform an N × N × N image array into a sequence of at most N × N × N elements is given. As more elements of the sequence are scanned finer resolution representations of the image are obtained. The proposed architecture, which is suitable for VLSI implementation, performs the transformations between the image and its encoding using O(log N) processors and in time and space proportional to the image size.     

Automatic Determination of the Gaussian Noise Level on Digital Images by High-Pass Filtering for Regions of Interest

A mathematical model, algorithm, and software are developed for automatic determination of the level of Gaussian nose on digital images by the method of high-pass filtering. The noise level is calculated for regions of interest of the image, selected by low-pass filtering. The optimal parameters of low-pass and high-pass filters are obtained. Processing a series of test images showed that the proposed method provides the less error of noise level determination than other analog methods do.     

Textural filters based on the texture spectrum

Conventional digital filtering techniques, based on classical Fourier analysis (that is, low-pass, high-pass and band-pass), are widely used in digital image processing. Unsatisfaction may be encountered when applying these filters to texture analysis of images, where one needs some specific spatial filters which are able to transform an image in the sense of texture rather than the spectral properties. Such textural filters can be designed in the texture spectrum domain and they are of interest for texture analysis. An example is given in this paper, and has been applied to four of Brodatz's natural images. The result shows a promising potential of the texture spectrum for designing textural filters.     

基于二维FFT的图像滤波方法及实现

二维快速傅立叶变换(FFT)在一个传统概念的处理机上实现时,需要芯片具有更多的逻辑资源。本文给出了基于FPGA的自定义处理机(CCM)的二维FFT算法和实现。在CCM的Splash-2平台上实现了二维FFT,计算速度达到180Mflops,最快速度超过Sparc-10工作站的23倍。同时,对于一个N×N图像,这种实现方法可以满足二维FFT所需要的O(N2log2N)次的浮点算术运算。     

A fast digital Radon transform—An efficient means for evaluating the Hough transform

A fast digital Radon transform based on recursively defined digital straight lines is described, which has the sequential complexity of N² log N additions for an N × N image. This transform can be used to evaluate the Hough transform to detect straight lines in a digital image. Whilst a parallel implementation of the Hough transform algorithm is difficult because of global memory access requirements, the fast digital Radon transform is vectorizable and therefore well suited for parallel computation. The structure of the fast algorithm is shown to be quite similar to the FFT algorithm for decimation in frequency. It is demonstrated that even for sequential computation the fast Radon transform is an attractive alternative to the classical Hough transform algorithm.     

L2 vector median filters on arrays with reconfigurableoptical buses

In spite of their good filtering characteristics for vector-valued image processing, the usability of vector median filters is limited by their high computational complexity. Given an N × N image and a W × W window, the computational complexity of vector median filter is O(W⁴N²). In this paper, we design three fast and efficient parallel algorithms for vector median filtering based on the 2-norm (L₂) on the arrays with reconfigurable optical buses (AROB). For 1 ⩽ p ⩽ W ⩽ q ⩽ N, our algorithms run in O(W⁴ log W/p⁴), O(W²N²/p ⁴q² log W) and O(1) times using p⁴N² / log W, p⁴q² / log W, and W⁴N² log N processors, respectively. In the sense of the product of time and the number of processors used, the first two results are cost optimal and the last one is time optimal     

海量遥感图像频域编辑器软件的设计与实现

针对图像增强和图像复原中变换算法的问题,该文设计和实现了海量遥感图像频率域信息编辑的软件构架。采用该软件,不仅能高效地显示图像的频率信息,而且同时提供了Barlett低通滤波器、Gaussian高通滤波器等基本滤波工具,使得可视化交互式滤波器设计成为可能,从而达到对频率信息进行编辑修改的目的。利用这一工具,设计和实现了TM影像周期条带噪声去除的滤波器。实验结果证实了该软件构架的可行性。     

On the location error of curved edges in low-pass filtered 2-D and3-D images

The authors study the location error of curved edges in two- and three-dimensional images after analog and digital low-pass filtering. The zero crossing of a second derivative filter is a well-known edge localization criterion. The second derivative in gradient direction (SDGD) produces a predictable bias in edge location towards the centers of curvature while the linear Laplace filter produces a shift in the opposite direction. Their sum called PLUS (PLUS=Laplace+SDGD) leads to an edge detector that finds curved edges one order more accurately than its constituents. This argument holds irrespective of the dimension. The influence of commonly used low-pass filters (such as the PSF originating from diffraction limited optics using incoherent light (2-D), the Gaussian filter with variable cutoff point (D-D), and the isotropic uniform filter (D-D)) is studied     

基于图像纹理和小波变换的聚类分割方法

针对纹理图像,本文提出了一种基于图像纹理特征的非学习分割方法。采用小波变换和快速k-means聚类分割算法,减少了整个处理过程的运算量。为了保证分类算法的精确性,运用了总体流量变化最小（Total Variation Flow）[1]非线性去噪方法对图像进行预处理,从而将减小图像噪声污染带来的分割误差。在图像特征的提取上,运用Gabor滤波器原理生成滤波空间,并让图像通过滤波空间而生成特征向量空间。通过制定一个快速寻优策略,从而达到分割图像的目的。     

Low complexity, and high fidelity image compression using fixed threshold method

This paper deals with the design and implementation of an image coding algorithm based on fixed threshold method. Threshold is the Peak Absolute Error (PAE) allowed in the reconstructed image. It has been shown that lossless edges with near-lossless/lossless filled area give a high fidelity images. Results are compared with Set Partitioning In Hierarchical Tree (SPIHT) [A. Said, W.A. Pearlman, A new, fast, and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circ. Syst. Video Technol. 12 (1996) 243-250] method. Experimented results show that the proposed method provides high fidelity images, and it has been shown that these images are visually better than images reconstructed using SPIHT algorithm for the same compression ratio. The execution time of the algorithm is almost half compared to that of the SPIHT algorithm which requires wavelet transform of an image.     

基于高斯小波的多尺度积图像边缘检测算法

图像的边缘是图像最重要的特征之一。由于边缘和噪声都是图像的高频分量,提取的图像边缘总是受到噪声的污染。针对边缘检测中存在的噪声问题,本文根据Mallat快速小波变换算法的思想,提出用高斯函数和其一阶导数分别作为低通和高通滤波器对图像进行多尺度分析。为了精确定位图像边缘,对各尺度的低频、水平、垂直和对角分量不进行下采样。然后提取不同尺度上的系数,利用多尺度积对噪声严重的图像进行边缘检测。最后根据边缘点的梯度方向,采用改进的局部梯度极大值搜索方法获得图像的单像素边缘。实验结果表明本文所提出的方法,能在被噪声污染严重的图像中提取图像的单像素边缘,且边缘图像信噪比高。     

Optimal Sublogarithmic Time Parallel Algorithms on Rooted Forests

The problem of finding a sublogarithmic time optimal parallel algorithm for 3 -colouring rooted forests has been open for long. We settle this problem by obtaining an O(( log log n) log ^* ( log ^* n)) time optimal parallel algorithm on a TOLERANT Concurrent Read Concurrent Write (CRCW) Parallel Random Access Machine (PRAM). Furthermore, we show that if f(n) is the running time of the best known algorithm for 3 -colouring a rooted forest on a COMMON or TOLERANT CRCW PRAM, a fractional independent set of the rooted forest can be found in O(f(n)) time with the same number of processors, on the same model. Using these results, it is shown that decomposable top-down algebraic computation and, hence, depth computation (ranking), 2 -colouring and prefix summation on rooted forests can be done in O( log n) optimal time on a TOLERANT CRCW PRAM. These algorithms have been obtained by proving a result of independent interest, one concerning the self-simulation property of TOLERANT: an N -processor TOLERANT CRCW PRAM that uses an address space of size O(N) only, can be simulated on an n -processor TOLERANT PRAM in O(N/n) time, with no asymptotic increase in space or cost, when n=O(N/ log log N) . Received May 20, 1997; revised June 15, 1998.     

Fast image blending for high-quality panoramic images on mobile phones

This paper presents a fast image blending approach for combining a set of registered images into a composite mosaic with no visible seams and minimal texture distortion on mobile phones. A unique seam image is generated using two-pass nearest distance transform, which is independent on the order of input images and has good scalability. Each individual mask can be extracted from this seam image quickly. To promote blending speed and reduce memory usage in building high resolution image mosaics on mobile phones, the seam image and mask images are compressed using run-length encoding, and all the following mask operations are built on run-length encoding scheme. Moreover, single instruction multiple data instruction set is used in Gaussian and Laplacian pyramids construction to improve the blending speed further. The use of run-length encoding for masks processing leads to reduced memory requirements and a compact storage of the mask data, and the use of single instruction multiple data instruction set achieves better parallelism and faster execution speed on mobile phones.

     

Self-Invertible 2D Log-Gabor Wavelets

Orthogonal and biorthogonal wavelets became very popular image processing tools but exhibit major drawbacks, namely a poor resolution in orientation and the lack of translation invariance due to aliasing between subbands. Alternative multiresolution transforms which specifically solve these drawbacks have been proposed. These transforms are generally overcomplete and consequently offer large degrees of freedom in their design. At the same time their optimization gets a challenging task. We propose here the construction of log-Gabor wavelet transforms which allow exact reconstruction and strengthen the excellent mathematical properties of the Gabor filters. Two major improvements on the previous Gabor wavelet schemes are proposed: first the highest frequency bands are covered by narrowly localized oriented filters. Secondly, the set of filters cover uniformly the Fourier domain including the highest and lowest frequencies and thus exact reconstruction is achieved using the same filters in both the direct and the inverse transforms (which means that the transform is self-invertible). The present transform not only achieves important mathematical properties, it also follows as much as possible the knowledge on the receptive field properties of the simple cells of the Primary Visual Cortex (V1) and on the statistics of natural images. Compared to the state of the art, the log-Gabor wavelets show excellent ability to segregate the image information (e.g. the contrast edges) from spatially incoherent Gaussian noise by hard thresholding, and then to represent image features through a reduced set of large magnitude coefficients. Such characteristics make the transform a promising tool for processing natural images.