A comparison between two edge maps based on the Non-decimated Haar Wavel

E. RUFEIL FIORI; J. GIMENEZ; A. G. FLESIA

Córdoba

Congreso; IV Congreso Latinoamericano de Matemáticos CLAM 2012; 2012

Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba.

Edge detection has always played an important role in digital image processing. Lately, wavelet based edge maps have been derived as a way of extracting structural information for image quality measures. In this paper, we propose a comparison between two wavelet based edge detection methods. We implemented a deterministic thresholding scheme over the non-decimated Haar wavelet transform, and a probabilistic method based on a one dimensional Hidden Markov model of the same wavelet coefficients. The hidden states are modeled with a Laplacian and a Gaussian distribution to model the information of the edge state and the non-edge state respectively. The model is trained with the EM algorithm,and one finds the hidden state of each coefficient by using the Viterbi algorithm, according to MAP estimation. We observe that the quality of edges detected by the two methods are visually different, and we quantify these differences with an index that penalizes differently edge hits than background hits. We show a detailed study of a natural image with different levels of noise added.