Image multi-scale edge detection using 3-D Hidden Markov Model based on the non-decimated wavelet

Edge detection plays an important role in digital image processing. Based on the non-decimated wavelet which is shift-invariant, in this paper, we develop a new edge detecting technique using 3-D Hidden Markov Model. Our proposed model can not only capture the relationship of the wavelet coefficients inter-scale, but also consider the intra-scale dependence. A computationally efficient maximum likelihood (ML) estimation algorithm is employed to compute parameters and the hidden state of each coefficient is revealed by maximum a posteriori (MAP) estimation. Experimental results of natural images are provided to evaluate the algorithm. In addition, the proposed model has the potential to be an efficient multi-scale statistical modeling tool for other image or video processing tasks.