23 September 2005 2-D wavelet with position controlled resolution
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Abstract
Wavelet transformation localizes all irregularities in the scene. It is most effective in the case when intensities in the scene have no sharp details. It is the case often present in a medical imaging. To identify the shape one has to extract it from the scene as typical irregularity. When the scene does not contain sharp changes then common differential filters are not efficient tool for a shape extraction. The new 2-D wavelet for such task has been proposed. Described wavelet transform is axially symmetric and has varied scale in dependence on the distance from the centre of the wavelet symmetry. The analytical form of the wavelet has been presented as well as its application for details extraction in the scene. Most important feature of the wavelet transform is that it gives a multi-scale transformation, and if zoom is on the wavelet selectivity varies proportionally to the zoom step. As a result, the extracted shape does not change during zoom operation. What is more the wavelet selectivity can be fit to the local intensity gradient properly to obtain best extraction of the irregularities.
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Andrzej Walczak, Andrzej Walczak, Leszek Puzio, Leszek Puzio, "2-D wavelet with position controlled resolution", Proc. SPIE 5959, Medical Imaging, 59590S (23 September 2005); doi: 10.1117/12.622783; https://doi.org/10.1117/12.622783
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