A distance transform function is superior to sequential dilations in obtaining the perimeter fractal dimensions of two-dimensional objects. Eight connected outlines of objects were distance-transformed and the frequency distribution of the resulting image then used to obtain fractal dimensions from Richardson plots. The measured dimensions of quadric and triadic islands were accurate. The method has three advantages over sequential dilations : (i) it is significantly faster, (ii) it generates more data points and (iii) it achieves a true radial dilation. The commonly-used 5 x 5 dilation element generates an octagonal dilation and half the data points of the distance transform. A minor correction is suggested to compensate for distortions that result from overlaying a truly radial dilation on an orthogonal grid.