A multi-scale representation model of polyline based on head/tail breaks

Liu, Pengcheng; Xiao, Tianyuan; Xiao, Jia; Ai, Tinghua

doi:10.1080/13658816.2020.1753203

Cited by 13 publications

(13 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most of the existing studies are developed by setting certain rules, which are hard to adapt to different contexts. Recently, Liu et al (2015Liu et al ( , 2020 proposed to transform the polylines from the spatial domain to the frequency domain by Fourier series, that is, to represent a polyline as a series of Fourier descriptors. Based on Shannon's information entropy and radical law of cartography, the Fourier descriptors are used to reconstruct polylines of different scales.…”

Section: Rel Ated Workmentioning

confidence: 99%

Data‐driven polyline simplification using a stacked autoencoder‐based deep neural network

Chen

2022

Transactions in GIS

View full text Add to dashboard Cite

Automatic simplification of polylines is an important issue in spatial database and mapping. Traditional rule‐based methods are usually limited in performance, especially when the man‐made rules have to be adapted to different polylines with different shapes and structures. Compared to the existing neural network methods focusing only on the output layer or the code layers for classification or regression, our proposed method generates multi‐level abstractions of polylines by extracting features from multiple hidden layers. Specifically, we first organize the cartographic polylines into the form of feature vectors acceptable to the neural network model. Then, a stacked autoencoder‐based deep neural network model is trained to learn the pattern features of polyline bends and omit unimportant details layer by layer. Finally, the multi‐level abstractions of input polylines are generated from different hidden layers of a single model. The experimental results demonstrate that, compared with the classic Douglas–Peucker and Wang and Muller algorithms, the proposed method is able to properly simplify the polylines while representing their essential shapes smoothly and reducing areal displacement.

show abstract

Section: Rel Ated Workmentioning

confidence: 99%

Data‐driven polyline simplification using a stacked autoencoder‐based deep neural network

Chen

2022

Transactions in GIS

View full text Add to dashboard Cite

show abstract

“…Multi-scale spatial representation has a wide range of applications, such as zooming in/out, and is among the most common operators in geographic information and online mapping systems [1][2][3][4]. Rendering spatial data at different scales also improves our understanding and analysis of spatial data, thereby meeting the continuous visual needs of modern map users.…”

Section: Introductionmentioning

confidence: 99%

“…As essential geomorphic elements, contour lines are among the most often used data for describing the geographic information of the Earth's surface [5][6][7]. A simplification of these contour lines provides different levels of detail for linear features, which is an effective operator for maintaining essential shapes in multi-scale terrain maps [1,8,9]. Although contour simplification methods have been investigated for a long time, studies on the continuous multi-scale representation of contour lines still face considerable limitations.…”

Section: Introductionmentioning

confidence: 99%

“…This method has advantages in area preservation during the multi-scale representation. Liu et al [1] proposed a Fourier-based method using head/tail breaks that simplifies polylines via a Fourier approximation according to the global shape. These scale-driven simplification methods have advantages over the two aforementioned strategies (i.e., point set reduction and bending simplification).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Global Continuous Multi-Scale Terrain Contour Simplification Method Based on the Level Set

et al. 2021

View full text Add to dashboard Cite

Multi-scale spatial representation has been widely used in geographic information and online mapping systems. Terrain contour, which provides a reference for understanding and monitoring the Earth’s surface, is an important data category. For the multi-scale representation of contour lines, simplification is a fundamental step in providing different levels of detail for linear features. However, achieving a global continuous multi-scale simplification of contours remains a challenge. Therefore, based on the concept of level set, a novel contour simplification method labeled the continuous changing surface model (CCSM) was proposed in this paper. The CCSM was built by using a non-uniform rational B-spline constrained with characteristics and was then intersected with a set of horizontal planes with progressive height values. The generated intersection lines are considered continuous multi-scale simplified contours. Experiments were conducted on a 1:50,000 real contour dataset to verify the effectiveness of CCSM. Results showed that the changes in the shape of the simplified contours generated by CCSM are more natural and progressive than those generated by two other significant simplification methods. CCSM can also effectively balance local and global structures and has potential applications in obtaining a continuous multi-scale representation of terrain contours.

show abstract

“…Based on a series of previous studies, mapping practices, or map generalization in particular, can be considered to be head/tail breaks processes applied to geographic features or data. These kinds of thinking have received increased attention in the literature (e.g., [28][29][30][31][32]). However, given that fractal geometric thinking, especially linking with a map feature's own scaling hierarchy, is still relatively new for map generalization, the practical difficulty is the lack of a tool to facilitate the computation of related fractal metrics that can guide the map generalization process.…”

Section: Introductionmentioning

confidence: 99%

PolySimp: A Tool for Polygon Simplification Based on the Underlying Scaling Hierarchy

Zhao

Zheng

et al. 2020

IJGI

View full text Add to dashboard Cite

Map generalization is a process of reducing the contents of a map or data to properly show a geographic feature(s) at a smaller extent. Over the past few years, the fractal way of thinking has emerged as a new paradigm for map generalization. A geographic feature can be deemed as a fractal given the perspective of scaling, as its rough, irregular, and unsmooth shape inherently holds a striking scaling hierarchy of far more small elements than large ones. The pattern of far more small things than large ones is a de facto heavy tailed distribution. In this paper, we apply the scaling hierarchy for map generalization to polygonal features. To do this, we firstly revisit the scaling hierarchy of a classic fractal: the Koch Snowflake. We then review previous work that used the Douglas–Peuker algorithm, which identifies characteristic points on a line to derive three types of measures that are long-tailed distributed: the baseline length (d), the perpendicular distance to the baseline (x), and the area formed by x and d (area). More importantly, we extend the usage of the three measures to other most popular cartographical generalization methods; i.e., the bend simplify method, Visvalingam–Whyatt method, and hierarchical decomposition method, each of which decomposes any polygon into a set of bends, triangles, or convex hulls as basic geometric units for simplification. The different levels of details of the polygon can then be derived by recursively selecting the head part of geometric units and omitting the tail part using head/tail breaks, which is a new classification scheme for data with a heavy-tailed distribution. Since there are currently few tools with which to readily conduct the polygon simplification from such a fractal perspective, we have developed PolySimp, a tool that integrates the mentioned four algorithms for polygon simplification based on its underlying scaling hierarchy. The British coastline was selected to demonstrate the tool’s usefulness. The developed tool can be expected to showcase the applicability of fractal way of thinking and contribute to the development of map generalization.

show abstract

A multi-scale representation model of polyline based on head/tail breaks

Cited by 13 publications

References 22 publications

Data‐driven polyline simplification using a stacked autoencoder‐based deep neural network

Data‐driven polyline simplification using a stacked autoencoder‐based deep neural network

A Global Continuous Multi-Scale Terrain Contour Simplification Method Based on the Level Set

PolySimp: A Tool for Polygon Simplification Based on the Underlying Scaling Hierarchy

Contact Info

Product

Resources

About