Multiresolution analysis of digital images using the continuous extension of discrete group transforms

Mickaël Germain; Jiri Patera

doi:10.1117/12.650720

2 February 2006 Multiresolution analysis of digital images using the continuous extension of discrete group transforms

Mickaël Germain, Jiri Patera

Author Affiliations +

Proceedings Volume 6065, Computational Imaging IV; 606503 (2006) https://doi.org/10.1117/12.650720
Event: Electronic Imaging 2006, 2006, San Jose, California, United States

Abstract

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.

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Mickaël Germain and Jiri Patera "Multiresolution analysis of digital images using the continuous extension of discrete group transforms", Proc. SPIE 6065, Computational Imaging IV, 606503 (2 February 2006); https://doi.org/10.1117/12.650720

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