Image compression and analysis using multiresolution representation

Multiresolution representation has been shown by many researchers to be an effective tool for image compression and analysis. We introduce several methods for the improved multiresolution representation of images. First, we introduce two algorithms for determining the optimal stack filters for the pyramidal decomposition of greyscale images under the minimum mean absolute error criterion. The first algorithm determines the optimal stack filter for interpolation, using linear programming. The other simultaneously determines the optimal stack filters for analysis and interpolation, using linear integer programming. Then, we introduce an algorithm for determining the optimal linear filters for the pyramidal decomposition of greyscale images under the minimum mean square error criterion. The algorithm iteratively determines the optimal analysis and interpolation filters by minimizing a quadratic cost function. Next, we introduce a multiresolution representation for the class of two-tone images described by their contours. Unlike previous multiscale representations of contours, the approximations are defined on successively decimated grids. Finally, we return to the pyramidal decomposition of greyscale images, introducing a new approach for the coding of the difference signals. Unlike most previous methods, which uniformly quantize the difference signals, this approach quantizes the difference signals based on their proximity to edges in the original image. The edges are efficiently represented using our multiresolution representation of contours. We show that improved rate-distortion can be achieved as compared to uniform quantization.U of I OnlyETDs are only available to UIUC Users without author permissio