A parallel algorithm for detecting dominant points on a digital closed curve is presented. The procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve. The procedure first determines the region of support for each point based on its local properties, then computes measures of relative significance (e.g., curvature) of each point, and finally detects dominant points by a process of nonmaxima suppression. This procedure leads to an important observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance, but mainly precise determination of the region of support. This solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms. The inherent nature of scale-space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point-detection algorithms, using a number of examples.