Fast space-scale filtering of the wavelet-transform of medical ultrasound images
Preben Graaberg Ness
Department of Mathematical Sciences, Norwegian University of Science and Technology
given at strobl07 (..)
The purpose of our investigation is to construct an efficient multi-scale edge-detector for medical ultrasound images using the continuous wavelet-transform. Typically such detectors require that the wavelet-transform is computed at several scales, merely in order to decide which information should be combined across scales. Our focus has been if/how one can determine which modulus-maxima are connected by a maxima-line if computing the wavelet-transform at only a few scales. We propose an algorithm which (when applied to medical ultrasound images) uses as few scales as possible.
The theoretical part of the investigation has focused on how the mutual amplitude and position of step-edges in a signal will influence the position and amplitude of the modulus-maxima across scales. This has been used to find bounds for which scales one has to compute the wavelet-transform, in order to ensure that one is able to determine which modulus-maxima are connected by a maxima-line.
Numerical investigation of the algorithm applied to rays in medical ultrasound images of brain-tumors, indicates that for such type of signals our algorithm is close to optimal if using scales s=2^j, and still good when using scales s=2^2j.