A new method for detecting dominant points is presented. It does not require any input parameter, and the dominant points obtained by this method remain relatively the same even when the object curve is scaled or rotated. In this method, for each boundary point, a support region is assigned to the point based on its local properties. Each point is then smoothed by a Gaussian filter with a width proportional to its determined support region. A significance measure for each point is then compared. Dominant points are finally obtained through nonmaximum suppression. Unlike other dominant point detection algorithms which are sensitive to scaling and rotation of the object curve, the new method will overcome this difficulty. Furthermore, it is robust in the presence of noise. The proposed new method is compared to a well-known dominant point detection algorithm in terms of the computational complexity and the approximation errors.