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.

中文翻译：

---

基于头尾断裂的折线多尺度表示模型

摘要本文提出了一种基于迭代头/尾中断来量化折线的多尺度表示的模型。折线首先被转换为相应的傅里叶描述符，该描述符由归一化的傅里叶级数展开系数组成。然后，傅里叶描述符的最重要的有限分量被选择并排序以构成折线约束傅里叶描述符。使用香农的信息论，定义了受约束的傅立叶描述符组件的信息内容。接下来，引入头/尾中断，根据信息内容的重尾分布将约束傅立叶描述符迭代划分为头和尾分量。因此，使用从头/尾断裂生成的有序头重建简化的折线。最后，通过量化每条简化折线的比例，引入了激进法则并将其应用于建模多尺度折线表示。设计并进行了三个实验来评估所提出的模型。结果表明，所提出的模型对于量化多尺度折线表示是有效且高效的。