In this paper, we develop a segmentation algorithm using configurations of singular points in the linear scale space. We define segment edges as a zero-crossing set in the linear scale space using the singular points. An image in the linear scale space is the convolution of the image and the Gaussian kernel. The Gaussian kernel of an appropriate variance is a typical presmoothing operator for segmentation. The variance is heuristically selected using statistics of images such as the noise distribution in images. The variance of the kernel is determined using the singular point configuration in the linear scale space, since singular points in the linear scale space allow the extraction of the dominant parts of an image. This scale selection strategy derives the hierarchical structure of the segments.