The local accumulative histogram gives us the statistic characteristics about the image more flexibly and precisely than the whole histogram of the image. We use the intrinsic structure of the edge region alternated with steep rising and stable rising to detect the edge information, which is the key feature in the local accumulative histogram. Then we refine the edge image to one-pixel wide edge image by the threshold obtained from the local accumulative histogram. The experimental results show that not only the algorithm can give us a good edge detecting result, but also it has the ability of antinoise. And some definitions of the one-pixel wide edge are given out in accordance with the people's intuition more directly and simply than other definitions before.