Image Edge Detection Using Hidden Markov Chain 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 hidden Markov chain (HMC) model. With this proposed model (NWHMC), each wavelet coefficient contains a hidden state, herein, we adopt Laplacian model and Gaussian model to represent the information of the state ldquobigrdquo and the state ldquosmall.rdquo The model can be trained by EM algorithm, and then we employ Viterbi algorithm to reveal the hidden state of each coefficient according to MAP estimation. The detecting results of several images are provided to evaluate the algorithm. In addition, the algorithm can be applied to noisy images efficiently.