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

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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.