A multi-scale representation model of polyline based on head/tail breaks. Issue 11 (1st November 2020) - Liu, Pengcheng; Xiao, Tianyuan; Xiao, Jia; Ai, Tinghua
ABSTRACT: This paper proposes a model to quantify the multiscale representation of a polyline based on iterative head/tail breaks. A polyline is first transformed into a corresponding Fourier descriptor consisting of normalized Fourier-series-expansion coefficients. Then, the most significant finite components of the Fourier descriptor are selected and ranked to constitute the polyline constrained Fourier descriptor. Using Shannon's information theory, information content of the constrained Fourier-descriptor components is defined. Next, head/tail breaks are introduced to iteratively divide the constrained Fourier descriptor into head and tail components according to the heavy-tailed distribution of information contents. Thus, simplified polylines are reconstructed using ordered heads generated from head/tail breaks. Finally, the radical law is introduced and applied to model multiscale polyline representation by quantifying the scale of each simplified polyline. Three experiments are designed and conducted to evaluate the proposed model. The results demonstrate that the proposed model is valid and efficient for quantifying multiscale polyline representation.