The morphing for continuous generalization of linear features based on Dynamic Time Warping distance

Abstract

Shape morphing has been used to generate arbitrary scale maps in the field of continuous generalization in recent years. The morphing approach consists of two main steps: shape characteristic matching and trajectory interpolation. Most of the shape characteristic matching methods are difficult to consider the local and global characteristics of spatial data at the same time, which will result in distortion of interpolation results. This paper proposes a Dynamic Time Warping (DTW) distance-based morphing method for continuous generalization of linear features. In this method, the DTW distance is employed as shape similarity distance to find the optimal correspondence by minimizing the total cost between each pair of vertices, which considers both the local and global structure of two linear features. Firstly, we build a matrix to record the distance between vertices in two linear features at two different scales. Then we use the DTW algorithm to find the optimal warping path to establish the corresponding relationship between the vertices of two linear features. Finally, the linear interpolation method is used to dynamically generate the geometric shape at any intermediate scale. Experiment results demonstrate that the proposed method can generate continuous and smooth geometric shapes with a gradual transformation effect, and can be used for the continuous generalization of linear features. The generalization results are consistent with map representation rules and human cognition.