Date of Award
Level of Access Assigned by Author
Master of Science (MS)
Second Committee Member
Third Committee Member
The Two-Dimensional Wavelet Transform Modulus Maxima (2D WTMM) sliding window methodology has proven to be a robust approach, in particular for the extraction of the Hurst (H) roughness exponent from grayscale mammograms. The power spectrum is a computational analysis based on the Fourier transform that can be used to estimate the roughness of a scale-invariant image or region via the calculation of H. We aim to examine how the calculation of H in fractional Brownian motion (fBm) images and mammograms can be improved. fBm images are generated for H ∈ [0.00,1.00] for testing through the previous 2D WTMM sliding window analysis using the Gaussian smoothing function, the second-order derivative of the Gaussian smoothing function, the Mexican hat, and the power spectrum analysis. The power spectrum is shown to provide a more accurate calculation of H for Htheo < 0.45 (RMSE = 0.01), while the 2D WTMM analysis with the Mexican hat smoothing function provides this for H ≥ 0.45 (RMSE = 0.058) in fBm images. Through the previous implementation of the 2D WTMM sliding window analysis, we have categorized mammographic subregions into three categories: Fatty (H < 0.45), risky dense (0.45 ≤ H ≤ 0.55), and healthy dense mammographic tissue (H > 0.55). The power spectrum and the 2D WTMM analysis are further tested on the CompuMAINE Laboratory’s acquired de-identified Perm and Maine mammographic datasets. From this analysis, it can be concluded that the power spectrum analysis cannot accurately distinguish fatty from dense tissue in grayscale mammograms. The implementation of the Mexican hat smoothing function provides a decrease in the number of mammographic subregions rejected during our analysis. In addition, the Mexican hat smoothing function indicates a greater difference in risky dense mammographic tissue between cancerous and normal patients compared to the previously adapted 2D WTMM analysis with the Gaussian smoothing function. The presence of noise in the Perm mammographic dataset indicates a larger minimum size for the range of wavelet scales a (MinADelta = 3.0) should be used in the calculation of H using the Mexican hat smoothing function in the 2D WTMM sliding window analysis. Higher quality (16-bit) mammograms in the Maine mammographic dataset indicate a similar minimum range of wavelet scales used in previous studies (MinADelta = 1.0) should be used to calculate H with the Mexican hat smoothing function. Through extensive calibration and testing of the power spectrum and 2D WTMM methodologies, we conclude the implementation of the 2D WTMM methodology with the Mexican hat smoothing function provides the most accurate calculation of H ∈ [0.00,1.00] in fBm and mammographic images.
White, Basel, "Hybrid Power Spectral and Wavelet Image Roughness Analysis" (2023). Electronic Theses and Dissertations. 3757.