Design of Multi-dimensional variable Digital Filters and Their Application to Image and Video Processing

本课题研究具有较高幅度响应调谐精度的多维数字滤波器的设计及其在图像和视频处理中的应用。1.本课题提出了系数更新计算量较小的二维可变IIR数字滤波器结构。该实现方法以可分离分母二维滤波器衍生的二维并行全通结构作为二维可变数字滤波器的原型结构。为了减少运算量，所有冗余的一阶复全通部分通过变结构的模块化合并。2.根据状态空间方程，提出了二维数字滤波器的频率变换。为了推导出频率变换的二维状态空间公式，我们将Mullis和Roberts的一维频率变换的状态空间公式推广到二维情况。所提出的频率变换非常适合于变换后的滤波器的状态空间分析，因为所得到的公式由矩阵加法、乘法、逆等简单的代数运算组成。3本项目评估了由上述方法得到的多维可变数字滤波器的变频特性的理论和实际性能。4.本项目提出了一种基于仅相位相关的旧胶片的帧位移估计方法。对于亚像素位移量的估计，提出了二次曲线拟合法。该方法基于用正弦函数逼近两幅图像的纯相位相关。并将该方法应用于老胶片的帧位移估计中。结果表明，该方法可以准确估计旧胶片的帧位移，并对其进行校正。目测结果表明，该方法能显著减小车架位移。

This project studies design of multi-dimensional digital filters which have high tuning accuracy of amplitude response and their application to image and video processing.1.This project proposes 2-D variable IIR digital filter structures with a small amount of calculations for coefficient update. The proposed realization method uses the 2-D parallel allpass structure derived from the separable denominator 2-D filter as the prototype structure for 2-D variable digital filters. In order to reduce the amount of calculations, all the redundant first-order complex allpass sections are combined by modularization of the variable structure.2.This project proposes frequency transformation for two-dimensional (2-D) digital filters in terms of the state-space equations. In order to derive the 2-D state-space formulation of the frequency transformation, we extend Mullis and Roberts' state-space formulation of one-dimensional frequency transformation to 2-D case. The proposed frequency transformation is very suitable for state-space analysis of the transformed filters since the resultant formulation consists of simple algebraic operations such as matrix addition, multiplication, inverse and so on.3 This project evaluates the theoretical and practical performance of variable frequency properties of multi-dimensional variable digital filters obtained by the above method.4.This project proposes an estimation method of frame displacement for old films using phase-only correlation. For the estimation of the subpixel displacement, the quadratic curve fitting method is proposed. This method is based on approximating the phase-only correlation of two images by a sinc function. Moreover, the method is applied to the frame displacement estimation for old films. It is shown that frame displacement of old films can be estimated accurately and then corrected. Visual inspection confirms that the proposed method can reduce the frame displacement significantly.