The digital image can be distorted by a noise for a transmission or other elements of system. It happen to be vague of a boundary side in the division of an image object, especially, boundary side of an input image is very important because it can be determined to the division and detection element in pattern recognition. Therefore it is proposed an edge detection method of optimal to divide and detect exactly a boundary part. In this paper, it detected the optimal edge with applying this image to Meyer wavelet-CNN algorithm, after it does level up a boundary side of an image by using the adaptive morphology as the threshold of an input image. It confirmed that the proposed algorithm is more superior to the conventional methods and the conventional Sobel method which is an image edge detection algorithm. Especially, it is confirmed by simulation that the proposed algorithm can be got the better result edge at the place of closing to each edges and having smoothly curved line.