The multirate processing of two-dimensional (2D) signals involves various types of sampling and matrices, due to different grid geometry. A more consistent theory is then needed in order to obtain better techniques and useful results in many areas, such as image and signal processing, biomedical, telecommunications, multimedia, remote sensing, optics. In this work, a 2-channel complementary filter banks theory, designed based on 2D multirate processing and complementary filters properties is presented with foundations for multiresolution levels methods modeling, for the processing of signals in two-dimensions, in nonseparable way. Signal analysis and synthesis using 2-channel complementary filter (CF) banks, the conditions under which the reconstruction of the 2D input signal is perfect and frequency division in the analysis part are developed. Since multiresolution decomposition of signals, wavelet representation and filter banks have a strong link, a relation of then with complementary filter banks is done. Other multiresolution levels methods can be derived from this theory and applications of them were found for compression, edge detection, 2D scaling and wavelets functions and digital TV systems.
Recently, new image processing techniques have been researched for application in many areas, such as biomedical, telecommunications, multimedia, remote sensing and optics. Multigrid and multirate processing of two-dimensional (2D) signals can be used in order to get a basis and consistent theory. Since it involves many types of lattices due to different grids geometry, they can be used as support of a consistent multirate processing theory for image applications. In this work, the concepts of lattice theory are used to make the rectangular, quincunx and hexagonal grid types modeling. The multirate processing of 2D signals involves also downsampling and upsampling and various types of sampling matrices and their formation are analyzed and grid types determined by them are shown.
Multiresolutional decomposition methods can have application in many areas such as in telecommunications, remote sensing, multimedia, signal and image processing. In this work, the two-dimensional (2D) nonseparable complementary filter (CF) banks and perfect reconstruction (PR) structures are presented. Developed for the processing of images, the 2D CF banks and PR structures were designed based on 2D multirate signal processing theory and complementary filters properties. The complementary filters were designed for an alias free decimation and interpolation. The perfect reconstruction conditions were studied for all types of sampling and filters, and although perfect reconstruction is achieved for quincunx sampling and filter, the analysis is aliasing free in all cases. The CF banks performance with images showed that the signal-to-noise ratio keeps high even for the cases where the reconstruction is not perfect. For PR structures, the reconstructed image is done perfectly, but at the cost of lower data compression. Examples of CF banks and PR structures analysis and synthesis with images are given.
In this paper, we present the 2D Complementary Filter (CF) Banks, a signal processing technique applied to information extraction by edge detection. Based on the 2D multirate signal processing theory and complementary filters properties, the CF Banks allow to consider different types of sampling and filters. Procedures to design 2D nonseparable quincunx, rectangular and circular complementary filters are developed for an alias free decimation and interpolation. The CF bank is related with wavelet theory. Perfect reconstruction is achieved when the CF bank is implemented with quincunx sampling and filters. Although perfect reconstruction is not reached in other cases, the analysis and synthesis are performed without aliasing, corresponding to a high signal-to-noise ratio and visual quality. New structures were designed to get a better data compression. Implementation of CF Banks analysis/synthesis with images and application in information extraction by edge detection are shown.
In this paper, the maximum-value composite of images procedure from Normalized Difference Vegetation Index is used to get a cloud free image mosaic. The image mosaic is used to identify vegetation targets such as tropical forest, savanna and caatinga as well to make the vegetation cover mapping of Minas Gerais state, Brazil.