Entropy-based image registration method using the curvelet transform

Registration is a prerequisite for fusion of geometrically distorted images. Traditionally, intensity-based image registration methods are preferred to feature-based ones due to higher accuracy of the former than that of the latter. To reduce computational load, image registration is often carried out using the approximate-level coefficients of a wavelet-like transform. Directional selectivity of the transform and the objective function used for the coefficients play vital roles in the alignment process of images. This paper introduces an image registration algorithm that uses the approximate-level coefficients of the curvelet transform, directional selectivity of which is better than many wavelet-like transforms. A conditional entropy-based objective function is developed for registration using a suitable probabilistic model of the curvelet coefficients of images. Suitability of the probability distribution of the coefficients is validated using a standard method to assess goodness of fit. To align the distorted images, the affine transformation that possesses parameters related to the translation, rotation, scaling, and shearing is used. Extensive experimentations are carried out to test the performance of the proposed registration method considering that the images are synthetically or naturally distorted. Experimental results show that performance of the proposed registration method is superior to existing methods in terms of commonly used performance metrics.     

The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a; trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement.     

Gray and color image contrast enhancement by the curvelet transform

We present a new method for contrast enhancement based on the curvelet transform. The curvelet transform represents edges better than wavelets, and is therefore well-suited for multiscale edge enhancement. We compare this approach with enhancement based on the wavelet transform, and the multiscale retinex. In a range of examples, we use edge detection and segmentation, among other processing applications, to provide for quantitative comparative evaluation. Our findings are that curvelet based enhancement out-performs other enhancement methods on noisy images, but on noiseless or near noiseless images curvelet based enhancement is not remarkably better than wavelet based enhancement.     

探地雷达直达波衰减的Curvelet变换方法

针对探地雷达信号处理中直达波衰减问题,提出了一种基于Curvelet变换的直达波衰减方法.该方法首先将原始信号变换到Curvelet域,通过直达波在Curvelet域的分布特点,得到其Curvelet系数,并对其进行重构,最后在总信号中减去重构的直达波信号得到有效信号.在处理过程中,利用Curvelet域分尺度阈值处理方法同时可以滤除随机噪声.通过对实测数据的处理和分析,验证了该方法的可行性和有效性,并且证实了该方法与2-D连续小波变换方法相比具有占有存储少和计算速度快的特点.     

基于小波变换的图像重构算法研究

小波变换是当前图像处理、应用数学和工程学科中一个迅速发展的领域,它具有多分辨率分析的特性,同时又在变换域有表征信号局部特征的能力,能有效地从信号中提取信息。本课题以MATLAB作为平台,研究小波变换的mallet算法,对一维离散采样信号进行滤波和重采样,并扩展到多维信号中。根据算法结果,对图像进行小波分解,重构其近似信...     

Three-dimensional reconstruction using homocentric spherical spatiotemporal image analysis

This paper presents a new algorithm for reconstructing a scene of three-dimensional structures from an image sequence. Three-dimensional reconstruction using an image sequence, called the spatiotemporal image method, is robust against image noises. But in this method, camera motion is limited to only one direction translation. Our algorithm makes allowances for camera rotation in spatiotemporal image analysis. With this technique, the whole spatiotemporal image is transformed to spherical projection and three-dimensional structures are determined robustly using the Hough transformation. We call the technique Homocentric Spherical Spatiotemporal Image (HSSI) analysis. With HSSI, it is possible to distinguish objects with a rotating camera from a longer baseline and to measure them with much greater accuracy than previously possible. This algorithm is demonstrated through simulations and experiments with real images from a translating and rotating camera, and the three-dimensional structures in a static scene are reconstructed.     

A Hankel transform approach to tomographic image reconstruction

A relatively unexplored algorithm is developed for reconstructing a two-dimensional image from a finite set of its sampled projections. The algorithm, referred to as the Hankel-transform-reconstruction (HTR) algorithm, is polar-coordinate based. The algorithm expands the polar-form Fourier transform F(r,theta) of an image into a Fourier series in theta calculates the appropriately ordered Hankel transform of the coefficients of this series, giving the coefficients for the Fourier series of the polar-form image f(p,phi); resolves this series, giving a polar-form reconstruction; and interpolates this reconstruction to a rectilinear grid. The HTR algorithm is outlined, and it is shown that its performance compares favorably to the popular convolution-backprojection algorithm.     

Practical considerations for 3-D image reconstruction using spherically symmetric volume elements

Spherically symmetric volume elements with smooth tapering of the values near their boundaries are alternatives to the more conventional voxels for the construction of volume images in the computer. Their use, instead of voxels, introduces additional parameters which enable the user to control the shape of the volume element (blob) and consequently to control the characteristics of the images produced by iterative methods for reconstruction from projection data. For images composed of blobs, efficient algorithms have been designed for the projection and discrete back-projection operations, which are the crucial parts of iterative reconstruction methods. The authors have investigated the relationship between the values of the blob parameters and the properties of images represented by the blobs. Experiments show that using blobs in iterative reconstruction methods leads to substantial improvement in the reconstruction performance, based on visual quality and on quantitative measures, in comparison with the voxel case. The images reconstructed using appropriately chosen blobs are characterized by less image noise for both noiseless data and noisy data, without loss of image resolution.     

基于小波变换和形态学的医学图像边缘检测

针对传统边缘检测算子对噪声敏感的缺点,结合小波阈值去噪和形态学边缘检测提出一种改进方法。首先对含高斯噪声的图像进行小波分解,然后再通过小波阈值法对高频系数进行处理,采用新设计的双结构形态学边缘检测算子对低频系数进行处理,最后用新系数重构出图像。实验结果表明:这种方法在去除噪声的同时较好地保留了边缘轮廓信息,是一种有效的边缘检测方法且具有实际参考价值。     

Digital image coding using legendre transform

Image coding can be implemented through DPCM, transform, hybrid, or segmentation coding techniques. Some transform coding techniques, such as cosine and Hadamard, have been exhaustively analyzed and evaluated, while others, such as Legendre, have not. This paper introduces the use of Legendre transform in image coding. The transform matrix for different block sizes is calculated, the fast algorithm is derived, and the performance is evaluated through both mean square error and subjective quality. The results obtained have indicated that the system performance is comparable with that of optimum KLT and cosine transforms; moreover, it is simpler in implementation.     

Image denoising by supervised adaptive fusion of decomposed images restored using wave atom,curvelet and wavelet transform

This paper presents an efficient image denoising method that adaptively combines the features of wavelets, wave atoms and curvelets. Wavelet shrinkage is used to denoise the smooth regions in the image while wave atoms are employed to denoise the textures, and the edges will take advantage of curvelet denoising. The received noisy image is firstly decomposed into a homogenous (smooth/cartoon) part and a textural part. The cartoon part of the noisy image is denoised using wavelet transform, and the texture part of the noisy image is denoised using wave atoms. The two denoised images are then fused adaptively. For adaptive fusion, different weights are chosen from the variance map of the denoised texture image. Further improvement in denoising results is achieved by denoising the edges through curvelet transform. The information about edge location is gathered from the variance map of denoised cartoon image. The denoised image results in perfect presentation of the smooth regions and efficient preservation of textures and edges in the image.     

Real-valued Hankel transform approach to image reconstruction from projections

A Hankel transform relation based on the real-valued Hartley transform and its application in image reconstuction from projections are proposed. In comparison with its counterpart based on the Fourier transform, the proposed method has evident advantages in computational and memory requirements because all operations are performed in the real-number space.<>     

Three-dimensional image reconstruction by digital tomo-synthesis using inverse filtering

Conventional X-ray tomosynthesis with film can provide a sagittal slice image with a single scan. This technique has the advantage of enabling reconstruction of a sagittal slice which is difficult to obtain from the X-ray CT system. However, only an image on the focal plane is obtained by a single scan. Furthermore, the image is degraded by superimpositions of the structures outside of the focal plane. A new three-dimensional image reconstruction method is proposed. This method utilizes a three-dimensional convolution process with an inverse filter function which is derived analytically by the point spread function of the projection and backprojection geometry. A digital tomosynthesis system has also been constructed for the purpose of evaluating the proposed method. This system was used in phantom experiments and clinical evaluations, and it was confirmed that the proposed method was able to reconstruct a better three-dimensional image with less artifacts from outside of the focused slice.     

Accelerated Hough transform using rectangular image decomposition

A novel fast method for evaluating the Hough transform is proposed, which can be used to accelerate detection of prevalent linear formations in binary images. An image is decomposed using rectangular blocks and the contribution of each whole block to the Hough transform space is evaluated, rather than the contribution of each image point. The resulting acceleration in the calculation of the Hough transform field is demonstrated in two image processing experiments related to object axis identification and skew detection of digitised documents     

加强边缘保护的Curvelet图像去噪方法

提出了一种基于Curvelet变换的图像去噪方法。我们改进了Starck等所提出的Curvelet变换，去除了“环绕”现象，并将硬阈值去噪法与基于子带相关的图像去噪法相结合，在去除噪声的同时对图像的边缘特征予以保护。实验结果表明，用该方法去噪后的图像PSNR值更高，视觉效果也更好。     

基于小波变换和数学形态学的遥感图像边缘检测

由于遥感图像一般带有较大的噪声,通过实验表明,用传统的边缘检测方法效果不理想。采用小波方向性检测技术并结合数学形态学的方法,提出了一种基于小波变换和小尺度的数学形态学的遥感图像边缘检测方法。实验表明本算法计算有效,边缘定位准确,对噪声有一定的抑制作用,边缘检测效果明显。     

Colour image detection and matching using modified generalisedHough transform

A new approach to 2-dimensional (2D) colour-image detection and matching using a modified version of the generalised Hough transform (GHT) is proposed. In the conventional GHT, the useful colour information existing in the input image and the relationship between each pixel and its neighbourhood are not used. Furthermore, lighting changes in the image are not usually considered. Therefore, the conventional GHT is seldom applied to colour images. In the proposed approach, lighting are removed using normalised colour values. Next, certain critical pixels of an input colour image whose neighbourhoods have larger variances of normalised colour values are extracted. For each critical pixel, a feature vector, which includes the normalised colour values of the pixel as well as those of the pixel's neighbours, is then constructed. A modified voting rule for the GHT is therefore proposed which is based on a similarity-measure function of the feature vectors. High maximum peaks in the cell array are searched finally as the result. The proposed method is robust for colour-image detection and matching in noisy, occlusive, and lighting-change environments, as demonstrated by experimental results     

Signal and image approximation using interval wavelet transform.

In signal approximation, classical wavelet synthesis are known to produce Gibbs-like phenomenon around discontinuities when wavelet coefficients in the cone of influence of the discontinuities are quantized. By analyzing a function in a piecewise manner, filtering across discontinuities can be avoided. Using this principle, the interval wavelet transform can generate sparser representations in the vicinity of discontinuities than classical wavelet transforms. This work introduces two new constructions of interval wavelets and shows how they can be used for image compression and upscaling.     

Urban object reconstruction using airborne laser elevation image and aerial image

Creating three-dimensional (3-D) models of real urban objects is an important goal in a wide variety of applications. This paper describes a method that utilizes airborne laser elevation images and aerial images for the 3-D reconstruction of urban objects. Our modeling approach uses the vertical geometric pattern analysis of elevation images. These patterns correspond to object contours and, thus, enable the extraction of the object. In addition, to provide realistic textured details, textures are cut from aerial images and mapped onto 3-D models. Our texture-mapping approach can avoid geometry mismatching and enable the automatic registration to determine the most reliable correspondence between projected outlines of 3-D models and contours of real objects shown in aerial images. Edge pairs, which are matched with projected outlines, are detected from aerial images. In order to minimize mismatching, we apply the voting technique based on the generalized Hough transform. Experimental results show that 3-D reconstruction of urban objects is generally successful.