Model-based coding is a new data compression scheme for very low bit rate image transmission. It consists of image analysis, parameter transmission, and image synthesis, in which edge detection based facial feature estimation is probably one of the most essential process. As many of the existing edge detection methods are not able to produce a satisfying and efficient result for this specific coding application, we are proposing herewith a new wavelet -based facial edge detection approach. Our approach applies the coarse-to-fine strategy using discrete wavelet transform for distinct facial edge feature detection, and extract the local modulus maxima of a continuous wavelet transform as the edge candidates by choosing a suitable continuous wavelet. In terms of speed and quality of the output when used for model-based coding, experiments show, our method outperforms many of the existing edge detection approaches, such as Prewitt's method, Canny's method, Marr-Hildreth's method, etc. It makes full use of the multiresolution properties of wavelet transform and can be used in conjunction with other methods for extremely low bit rate transmission of videophone pictures.