Physics Colloquium - Spring 2005 - Wavelets and Fractals: From Astrophysics to Bio-Medical Image Analysis
Dept of Physics & Astronomy
University of Maine, Orono, Maine
Presents
André Khalil
Post-Doc Associate
Institute for Molecular Biophysics,
University of Maine
The Jackson Laboratory
Wavelets and Fractals: From Astrophysics to Bio-Medical Image Analysis
Since the end of the 80's, the wavelet transform has been recognized as a tool to study fractal objects, providing a unified multifractal formalism for both functions and measures. In the first part, we present the 2D WTMM (Wavelet Transform Modulus Maxima) methodology, a wavelet-based multifractal formalism, and demonstrate its capabilities on synthetic surfaces.
In the second part, we use the 2D WTMM method to study the distribution of neutral hydrogen in the Galactic Plane of the Milky Way. The characterization of both the fractal properties and the anisotropic signatures (directional preferences) found in Galactic spiral arms and in the inter-arm regions will be discussed. In the context of digitized mammograms, we further illustrate the usefulness of the methodology in the study of texture segmentation of rough surfaces and the geometric characterization of clusters of microcalcifications, which are early signs of breast cancer.
Finally, we end with a presentation of the newly generalized WTMM method which provides a multifractal description of both 3D scalar and vector data fields.
Friday, February 18, 2005
3:10 pm
140 Bennett Hall
Refreshments will follow in Rm. 114, Bennett Hall
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