The outline of an imaged object is usually obtained as a linked list of edge elements (`edgels'). When these edgels are connected, the resulting shape is hardly ever smooth. This is because even when edgels are detected with subpixel accuracy, the spatial and gray level quantization of the original image mans that consecutive edges show random fluctuations in position and orientation. Fluctuations may also occur as a result of noise or natural variation in the object's boundary. Hence to recognize an object it is necessary to represent the boundary at varying scales of resolution in order to extract the underlying shape. High frequencies may be discarded using smoothing filters or by thresholding wavelet transforms. In this paper these approaches are described and contrasted with an alternative approach of the authors' based on term rewriting. In the latter approach the object outline is represented by a sparse array of edgels. Between any two consecutive edgels the path of the object boundary can be reconstructed (by a contour completion algorithm) to within a tolerance given by the current value of the scale space parameter. As this parameter increases, the number of edgels required to define the outline decreases--hence the shape becomes simpler at the cost of increasing approximation.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.