剪切波构造方法研究及其在图像处理中的应用

发布时间：2018-08-13 11:24

【摘要】：小波变换是一种多分辨率分析方法,其变换过程类似于金字塔变换,已广泛应用于图像处理与信号处理等领域。运用小波变换能将图像分解成低频子带和水平、垂直和对角三个方向的高频子带,其中低频子带是源图像的近似,包含了源图像的主要能量,高频子带包含图像在不同尺度、不同方向上的细节信息,小波变换作为一种较新的数学工具,它具有良好的时频分析能力,对高频部分采用逐步精细的时域取样步长,“聚焦”到对象的任意细节,因此又被誉为“数学显微镜”。然而,传统的小波变换只能捕捉水平,垂直和对角三个方向的信息,并不能很好地表示图像的‘线奇异性’,在处理二维信号时有一定的局限性。本文运用傅立叶变换与时频分析方法,研究了有限离散剪切波的构造方法,通过构造若干个预备函数,提供了剪切波的一种新的构造方法,构造了锥面上和低频上的剪切波。有限离散剪切波变换具有良好的局部化特性与平移不变性。为了提高多聚焦图像和红外与可见光图像的融合精度,提出了一种基于有限离散剪切波变换(FD ST)的图像梯度信息相关性因子加权与对比度相结合的融合算法。首先,对严格配准后的图像进行FDST分解,得到低频子带系数和不同尺度不同方向的高频子带系数;然后对低频子带系数采用图像梯度信息相关性因子加权融合算法,高频子带系数则利用对比度将低频系数与高频系数联系起来并以对比度作为度量系数取舍的准则进行融合;最后,运用有限离散剪切波逆变换重构而得到融合图像,并对融合图像进行主观视觉和客观评价。实验结果表明,该算法在主观视觉效果和客观评价指标上优于其它融合算法。针对已有图像融合过程的不足之处,提出了四种不同的图像融合策略。为了说明本文融合策略的有效性和有限离散剪切波变换的优越性,对多聚焦图像和红外与可见光图像进行仿真实验。首先,比较不同变换域下同一融合策略的融合效果,这里用到的小波变换有离散小波变换(DWT),非下采样轮廓波变换(NSCT),非抽样双树复小波变换(UDTCWT),非下采样剪切波变换(NSST),有限离散剪切波变换(FDST)。其次,比较同一变换域下不同融合策略的融合效果。最后,对不同文献的图像融合算法进行比较。实验结果表明,与其它的图像融合算法相比较,本文算法不但有良好的主观视觉效果,而且各项客观指标均有所提高,充分说明了本文融合算法的有效性。
[Abstract]:Wavelet transform is a kind of multi-resolution analysis method. Its transformation process is similar to pyramid transform and has been widely used in image processing and signal processing. The main energy of the image, the high frequency subband contains the detailed information of the image in different scales and directions. As a new mathematical tool, wavelet transform has good time-frequency analysis ability. It uses step-by-step fine time-domain sampling step for the high frequency part and "focuses" on any detail of the object, so it is also known as "mathematical display". However, the traditional wavelet transform can only capture the horizontal, vertical and diagonal information, and can not well represent the "line singularity" of the image. It has certain limitations in processing two-dimensional signals. Several reserve functions provide a new method for constructing shear waves on cones and low frequencies. Finite discrete shear wave transform has good localization and translation invariance. In order to improve the fusion accuracy of multi-focus images and infrared and visible images, a finite discrete shear wave is proposed. Firstly, low-frequency subband coefficients and high-frequency subband coefficients of different scales and directions are obtained by FDST decomposition of the image after strict registration. Then, low-frequency subband coefficients are fused by weighted image gradient information correlation factor. The high-frequency sub-band coefficients are fused by the contrast between the low-frequency coefficients and the high-frequency coefficients, and the contrast is used as the criterion for the selection of the measurement coefficients. Finally, the fused image is reconstructed by inverse transform of finite discrete shear wave, and the fused image is evaluated subjectively and objectively. Four different image fusion strategies are proposed to overcome the shortcomings of the existing image fusion process. To illustrate the effectiveness of the fusion strategy and the advantages of the finite discrete shear wave transform, the multi-focus image and the infrared and visible image are simulated. Firstly, the fusion results of the same fusion strategy in different transform domains are compared. The wavelet transform used here includes discrete wavelet transform (DWT), non-downsampling contour wave transform (NSCT), non-sampling dual-tree complex wavelet transform (UDTCWT), non-downsampling shear wave transform (NSST), finite discrete shear wave transform (FDST). Secondly, the wavelet transform used in the same transform domain is compared. Finally, the fusion results of different fusion strategies are compared with those of other fusion algorithms. The experimental results show that the proposed algorithm not only has good subjective visual effects, but also improves the objective indicators, which fully demonstrates the effectiveness of the proposed fusion algorithm.
【学位授予单位】：西安建筑科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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