Multiresolution analysis of digital images using the continuous extension of discrete group transforms
Mickaël Germain, J. Patera · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2006
A new technique is presented for multiresolution analysis (MRA) of digital images. In 2D, it has four variants, two of which are applicable on square lattices; the Discrete Cosine Transform (DCT) is the simpler of the two. The remaining variants can be used in the same way on triangular lattices. The property of the Continuous Extension of the Discrete Group Transform (CEDGT) is used to analyse data for each level of decomposition. The MRA principle is obtained by increasing the data grid for each level of decomposition, and by using an adapted low filter to reduce some irregularities due to noise effect. Compared to some stationary wavelet transforms, the image analysis with a multiresolution CEDGT transform gives better results. In particular, a wavelet transform is capable of providing a local representation at multiple scales, but some local details disappear due to the use of the low pass filter and the reduction of the spatial resolution for a high level of decomposition. This problem is avoided with CEDGT. The smooth interpolation, used by the multiresolution CEDGT, gives interesting results for coarse-to-fine segmentation algorithm and others analysis processes.