Assessing Data Regularity in Complex Wavelet Domain: Application to Mammography Image Classification

• Activity Number: 341
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Seonghye Jeon*+ and Seonghye Jeon and Brani Vidakovic
• Companies: Georgia Institute of Technology and Georgia Institute of Technology and Georgia Institute of Technology
• Keywords: image classification ; regularity index ; complex wavelets ; mammography image

Abstract

A wide range of complex structures in nature exhibits irregular behavior in both time and scale. Although irregular, the phenomena can be well modeled by multifractal processes that are quantified by statistical similarity of patterns at different scales. Wavelet transform is a powerful tool for analyzing the complex structures of the data and assessing the regularity of the multifractal processes.

Complex wavelets have been advocated as solutions to some of the limitations of the real-valued wavelet transforms. Apart from the Haar wavelet, complex wavelets are only compactly supported orthogonal wavelets which are symmetric. Another advantage of the complex wavelets is the complementary phase information that describes the coherent structure of the image.

Although complex wavelet transform has been used in various areas, ours are the first to explore the comprehensive regularity indices. We extend the wavelet spectrum and multifractal spectrum to the complex wavelet domain and propose new regularity descriptors including phase information and coherence function. This study is motivated and illustrated by mammography image classification.