Although shape similarity is one fundamental element in coastline generalization quality, its related research is still inadequate. Consistent with the hierarchical pattern of shape recognition, the Dual-side Bend Forest Shape Representation Model is presented by reorganizing the coastline into bilateral bend forests, which are made of continuous root-bends based on Constrained Delaunay Triangulation and Convex Hull. Subsequently, the shape contribution ratio of each level in the model is expressed by its area distribution in the model. Then, the shape similarity assessment is conducted on the model in a top–down layer by layer pattern. Contrast experiments are conducted among the presented method and the Length Ratio, Hausdorff Distance and Turning Function, showing the improvements of the presented method over the others, including (1) the hierarchical shape representation model can distinguish shape features of different layers on dual-side effectively, which is consistent with shape recognition, (2) its usability and stability among coastlines and scales, and (3) it is sensitive to changes in main shape features caused by coastline generalization.

This study discusses a method for quantitative quality assessment for the simplification of linear features. Considering the multi-scale nature of linear features, this paper combines the improved Douglas–Peucker method without threshold and the multiway tree model to construct a weighted hierarchical linear feature representation model called the Douglas–Peucker Multiway Tree (DMC-tree). Subsequently, the uncertainty computation is conducted from the root of the DMC-Tree top-down level by level to obtain the quality indexes. Then, the quality index of the whole linear feature is obtained by combining the indexes of every layer together with their weights. The results of the presented method are compared with those of the length ratio method and the Hausdorff distance method. The results show the advantages of the presented method over the others, including (1) its sensitivity to feature points of multiple scales, (2) the quantitative characteristics of the indexes, and (3) the finer granularity in assessment.