In contrast to the existing Gaussian smoothing process with varying window size, an iterative Gaussian convolution with constant window size is proposed. The iterative process is shown to converge as the norm of the convolution matrix is less than unity. For a closed digital curve the number of iterations is shown to be related to the number of points on the curve. The Gaussian filter coefficients that are used to smooth the curve are shown to enjoy the scale-space property. A scale-space map showing the location of the maxima of absolute curvature over iterations is proposed. The map is converted into a tree organization on the basis of an analysis of the scale-space behavior of different corner models such as Γ models, END models and STAIR models. Corners are detected in a process of interpreting the tree. The corner detector has been applied successfully on different digital curves even in presence of additive white Gaussian noise and at varying orientations. © 1995.