We have proposed a boundary extraction algorithm for cross-sectional critical dimension (CD) measurements of the scanning electron microscope (SEM) images in machine/computer vision. Noisy SEM images have the image discontinuity of roof edge with peak. A task is to extract a low contrast boundary or edge with about one pixel width in a noisy cross sectional SEM image. Also CD measurements require that the algorithm locate a boundary or an edge at the correct position. Our policy is to detect the edges with high degree of confidence at first, and then to extract the edges with the high probabilities of edge that are calculated by using gray levels of neighboring pixels. Our proposed algorithm integrates the Gaussian pyramid to suppress noise, morphological operations to detect the edges with high degree of confidence, the relaxation method to recover the gaps in the detected edges, and the hierarchical approach. Application of the proposed algorithm to cross sectional SEM images of DRAMs shows its validity.