In this paper a novel non-parametric method of detecting dominant points on a digital curve is proposed. The proposed method estimates the curvature at every point on the curve by computing the reciprocal of the angle made at that point due to the left and right arms of the point. The points that bear local maxima curvature are selected as true dominant points. A novel method for determining a region of support of a point useful for its curvature estimation is also presented. Unlike other methods, the proposed method determines a region of support which is not necessarily symmetric. A finite automaton is devised to determine an adaptive region of support of a point. An extensive experiment has been conducted to reveal the robustness of the proposed method on various shapes with different parameters and is shown to be superior to several other existing methods