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### Edge Detection of Noisy Images Using 2-D Discrete Wavelet Transform

 Title: Name(s): Edge Detection of Noisy Images Using 2-D Discrete Wavelet Transform. 214 views 95 downloads Chaganti, Venkata Ravikiran, authorFoo, Simon Y., professor directing thesisMeyer-Baese, Anke, committee memberRoberts, Rodney, committee member Department of Electrical and Computer Engineering, degree granting department Florida State University, degree granting institution text Text monographic 2005 Florida State University Tallahassee, Florida computeronline resource 1 online resource English Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. Wavelets are an extremely useful tool for coding images and other real signals. Because the wavelet transform is local in both time (space) and frequency, it localizes information very well compared to other transforms. Wavelets code transient phenomena, such as edges, efficiently, localizing them typically to just a few coefficients. This thesis deals with the different types of edge detection techniques, mainly concentrating on the two major categories Gradient and Laplacian. The gradient method detects the edges by looking for the maximum and minimum in the first derivative of the image. The Laplacian method searches for zerocrossings in the second derivative of the image to find edges. Given the wavelet transforms values wavelet analysis can be done in the wavelet domain by comparison of wavelet coefficients that account for the edges. The detection of the maxima or inflection points is generally a key factor for analyzing the characteristics of the non-stationary signals. The wavelet transformation has been proved to be a very promising technique for the multiscale edge detection applied both to 1-D and 2-D signals. The dyadic wavelet transforms at two adjacent scales are multiplied as a product function to magnify the edge structures and suppress the noise. Unlike many multiscale techniques that first form the edge maps at several scales and then synthesize them together, we determined the edges as the local maxima directly in the scale product after an efficient thresholding. It is shown that the scale multiplication achieves better results than either of the two scales, especially on the localization performance. The thesis deals with the comparison of edge detection of images using traditional edge detection operators (Prewitt, Sobel, Frei-chen and Laplacian of Gaussian) and Discrete Wavelet Transformation (DWT) using Haar, Daubechies, Coifman and Biorthogonal wavelets. It also deals with the edge detection of noisy images and the optimization of the wavelets for edge detection. FSU_migr_etd-3948 (IID) A Thesis submitted to the Department of Electrical Engineering in partial fulfillment of the requirements for the degree of Master of Science. Spring Semester, 2005. April 11, 2005. Coif, Haar, Db2, Bior, Edge Detection, Wavelets Includes bibliographical references. Simon Y. Foo, Professor Directing Thesis; Anke Meyer-Baese, Committee Member; Rodney Roberts, Committee Member. Electrical engineeringComputer engineering http://purl.flvc.org/fsu/fd/FSU_migr_etd-3948 FSU

Chaganti, V. R. (2005). Edge Detection of Noisy Images Using 2-D Discrete Wavelet Transform. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-3948