Polyline Simplification Research Articles

Polyline simplification using a region proposal network integrating raster and vector features

ABSTRACT Polyline simplification is crucial for cartography and spatial database management. In recent decades, various rule-based algorithms for vector polyline simplification have been proposed. However, most existing algorithms lack parameter self-adaptive capabilities and require repeated manual parameter adjustments when applied to different polylines. While deep-learning-based methods have recently been introduced for raster polyline image simplification, they cannot achieve end-to-end simplification when the input data and output results are vector polylines. This paper proposes a new deep-learning-based method for vector polyline simplification by integrating both the vector and raster features of the polyline. Specifically, a deep separable convolutional residual neural network was first used to extract the convolutional features of each image. Then, the region proposal network was modified to generate proposal boxes using vector coordinates, and these proposal boxes were used to locate the convolutional feature maps of bends. Finally, convolutional feature maps were fed into a binary classification network to identify unimportant vertices that should be omitted for vector polyline simplification. The experimental results indicated that the proposed method can exploit raster and vector features to achieve automatic and effective polyline simplification without prior map generalization knowledge and manual settings of rules and parameters. The polyline simplification results of the proposed method have a higher compression ratio of coordinate points and lower shape deformation and deviation than the results generated by the classic Wang and Müller (WM) algorithm and Support Vector Machine (SVM) based algorithm, which shows the potential of the proposed method for future applications in map generalization.

Rapid prediction of wildfire spread using ensemble Kalman filter and polyline simplification

This paper proposes a new method for rapid prediction of wildfire spread, which employs computational wildfire simulations by FARSITE and assimilates the simulation results with actual observation data by means of an ensemble Kalman filter. To expedite data assimilation, the wildfire perimeter is represented by a two-dimensional polyline simplification algorithm. In addition, to facilitate the data assimilation, a new process is developed to relate the prediction results with the actual observation data. The proposed method is tested and demonstrated by an example wildfire spread scenario generated based on actual climate, topography, and vegetation. The results confirm that the polyline simplification algorithm can drastically reduce the computational time required for data assimilation while maintaining the accuracy of predictions. The proposed method is expected to serve as a core algorithm for near-real-time prediction and data-driven updating of wildfire spread.

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

AbstractAutomatic 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.

LOOPS: LOcally Optimized Polygon Simplification

AbstractDisplaying polygonal vector data is essential in various application scenarios such as geometry visualization, vector graphics rendering, CAD drawing and in particular geographic, or cartographic visualization. Dealing with static polygonal datasets that has a large scale and are highly detailed poses several challenges to the efficient and adaptive display of polygons in interactive geographic visualization applications. For linear vector data, only recently a GPU‐based level‐of‐detail (LOD) polyline simplification and rendering approach has been presented which can perform locally‐adaptive LOD visualization of large‐scale line datasets interactively. However, locally optimized LOD simplification and interactive display of large‐scale polygon data, consisting of filled vector line loops, remains still a challenge, specifically in 3D geographic visualizations where varying LOD over a scene is necessary. Our solution to this challenge is a novel technique for locally‐optimized simplification and visualization of 2D polygons over a 3D terrain which features a parallelized point‐inside‐polygon testing mechanism. Our approach is capable of employing any simplification algorithm that sequentially removes vertices such as Douglas‐Peucker and Wang‐Müller. Moreover, we generalized our technique to also visualizing polylines in order to have a unified method for displaying both data types. The results and performance analysis show that our new algorithm can handle large datasets containing polygons composed of millions of segments in real time, and has a lower memory demand and higher performance in comparison to prior methods of line simplification and visualization.

Polyline simplification based on the artificial neural network with constraints of generalization knowledge

ABSTRACT The present paper presents techniques for polyline simplification based on an artificial neural network within the constraints of generalization knowledge. The proposed method measures polyline shape characteristics that influence polyline simplification using abstracted descriptors and then introduces these descriptors into the artificial neural network as input properties. In total, 18 descriptors categorized into three types are presented in detail. In a second approach, map simplification principles are abstracted as controllers, imposed after the output layer of the trained artificial neural network to make the polyline simplification comply with these principles. This study worked with three controllers – a basic controller and two knowledge-based controllers. These descriptors and controllers abstracted from generalization knowledge were tested in experiments to determine their efficacy in polyline simplification based on the artificial neural network. The experimental results show that the utilization of abstracted descriptors and controllers can constrain the artificial neural network-based polyline simplification according to polyline shape characteristics and simplification principles.

Interactive Procedure for Localized Monitoring and Control of Polyline Simplification

Interactive Procedure for Localized Monitoring and Control of Polyline Simplification

Polyline simplification has cubic complexity

$\DeclareMathOperator{\poly}{poly}$In the classic polyline simplification problem, given a polygonal curve~$P$ consisting of $n$ vertices and an error threshold $\delta \geq 0$, we want to replace $P$ by a subsequence~$Q$ of minimal size such that the distance between the polygonal curves $P$ and $Q$ is at most $\delta$. The distance between curves is usually measured using the Hausdorff or continuous Frechet distance. These distance measures can be applied globally, i.e., to the whole curves $P$ and $Q$, or locally, i.e., to each simplified subcurve and the line segment that it was replaced with separately (and then taking the maximum). This gives rise to four problem variants: Global-Hausdorff simplification (known to be NP-hard), Local-Hausdorff simplification (can be solved in time $O(n^3)$), Global-Frechet simplification (can be solved in time $O(k n^5)$, where $k$ is the size of the optimum simplification), and Local-Fr\'{e}chet simplification (can be solved in time $O(n^3)$).Our contribution is as follows:Cubic time for all variants:\ For Global-Frechet simplification, we design an algorithm running in time $O(n^3)$. This shows that all three problems (Local-Hausdorff, Local-Frechet, and Global-Frechet) can be solved in cubic time. All these algorithms work over a general metric space such as $(\mathbb{R}^d,L_p)$, but the hidden constant depends on $p$ and (linearly) on~$d$.Cubic conditional lower bound: We provide evidence that in high dimensions, cubic time is essentially optimal for all three problems (Local-Hausdorff, Local-Frechet, and Global-Frechet). Specifically, improving the cubic time to $O(n^{3-\epsilon} \poly(d))$ for polyline simplification over $(\mathbb{R}^d,L_p)$ for $p = 1$ would violate plausible conjectures. We obtain similar results for all $p \in [1,\infty), p \ne 2$.In total, in high dimensions and over general $L_p$-norms we resolve the complexity of polyline simplification with respect to Local-Hausdorff, Local-Frechet, and Global-Frechet, by a providing new algorithm and conditional lower bounds.

Simplification of polylines by segment collapse: minimizing areal displacement while preserving area

ABSTRACTThis paper reports on a new Area Preserving Segment Collapse (APSC) algorithm for simplifying polygonal boundaries while preserving the polygonal area at simplified target scales and minimizing areal displacement. A general segment collapse algorithm is defined by iteratively collapsing segments to Steiner points in priority order, guided by placement and displacement functions. The algorithm is specified by defining functions that minimize areal displacement under the constraint that the areas of adjoining polygons are preserved exactly. Self-intersections can be avoided by testing for intersections with two new line segments associated with each segment collapse operation. The paper demonstrates simplification results for a sample of 10 lakes formed from alpine, Karst, glacial and arid desert processes as well as artificial dams. APSC results are compared with three other simplification routines and evaluated for area preservation, linear and areal displacement, complexity and introduction of boundary self-intersections. Results confirm that the APSC algorithm preserves area exactly and indicate that it outperforms the other tested algorithms for minimizing areal displacement while producing reasonably low measures of linear displacement. Self-intersections can occur more commonly with APSC than other algorithms but are avoided with the proposed topology check. The APSC algorithm additionally preserves polygon complexity better than other tested algorithms.

Encryption Algorithm using Polyline Simplification for GIS Vector Map

Recently, vector map has developed, used in many domains, and in most cases vector map data contains confidential information which must be kept away from unauthorized users. Moreover, the manufacturing process of a vector map is complex and the maintenance of a digital map requires substantial monetary and human resources. This paper presents the selective encryption scheme based on polyline simplification methods for GIS vector map data protection to store, transmit or distribute to authorized users. Main advantages of our algorithm are random vertices and transformation processes but it still meets requirements of security by random processes, and this algorithm can be implement to many types of vector map formats.

Envelope generation and simplification of polylines using Delaunay triangulation

ABSTRACTAs a basic and significant operator in map generalization, polyline simplification needs to work across scales. Perkal’s ε-circle rolling approach, in which a circle with diameter ε is rolled on both sides of the polyline so that the small bend features can be detected and removed, is considered as one of the few scale-driven solutions. However, the envelope computation, which is a key part of this method, has been difficult to implement. Here, we present a computational method that implements Perkal’s proposal. To simulate the effects of a rolling circle, Delaunay triangulation is used to detect bend features and further to construct the envelope structure around a polyline. Then, different connection methods within the enveloping area are provided to output the abstracted result, and a strategy to determine the best connection method is explored. Experiments with real land-use polygon data are implemented, and comparison with other algorithms is discussed. In addition to the scale-specificity inherited from Perkal’s proposal, the results show that the proposed algorithm can preserve the main shape of the polyline and meet the area-maintaining constraint during large-scale change. This algorithm is also free from self-intersection.

Contextual Douglas-Peucker Simplification

In this paper, we develop a constrained Douglas-Peucker algorithm using a polyline to be simplified and other geometries as contextual constraints. We develop a contextual model that incrementally rewinds to the original polyline with relevant characteristic vertices to resolve contextual conflicts. Constraints cov ered in this paper are topology and direction. Our implementation shows a consistent representation and a technique to accelerate multi-scale simplification of polylines.

Robust line simplification on the surface of the sphere

Polyline simplification is an important task in map generalization. Several solutions have been developed in order to perform this task automatically, but the vast majority of them consider that the objective line to simplify is lying on the plane. One of the most widely used methods is the so-called Douglas–Peucker algorithm, which is fast and in most cases produces good results. However, the Douglas–Peucker method was defined in its original form in order to be applied to polylines contained in the Euclidean 2D space, and it can lead to inconsistent results such as self-intersections. In this work, a robust (results without self-intersections) variation of the Douglas–Peucker for polylines on the surface of the sphere is presented. It produces correct results regardless of the morphology of the original line and the tolerance parameter size.The algorithm is coded in standard C99 and it can be compiled for serial or parallel execution via OpenMP. Both, the algorithm itself and a program implementing it are distributed as free software. The solution validity was tested using the GSHHG geography database, which can be obtained free through the Web. Results about output accuracy, execution speed, and parallel implementation scalability are presented.

GIS 벡터맵 데이터 압축을 위한 혼합형 폴리라인 단순화

본 논문은 혼합형 폴리라인 단순화와 공간 에너지 집중을 이용한 GIS 벡터맵 데이터 압축을 제안한다. 제안한 방법에서는 GIS 벡터맵에서 폴리라인 속성을 가지는 레이어들에 대해, 최소 면적 오차 기반의 혼합형 폴리라인 단순화 및 공간 에너지 집중에 의하여 선택된 레이어 내의 폴리라인 데이터들을 압축한다. 제안한 단순화 및 공간 에너지 집중는 폴리라인의 형상을 유지하면서 데이터 압축 효과를 향상시킨다. 가시적 화질과 압축률을 통한 평가 결과로부터 제안한 방법이 기존 방법보다 우수한 화질과 높은 압축률을 보임을 확인하였다. This paper presents a GIS vector map data compression scheme based on hybrid polyline simplification method and SEC(spatial energy compaction). The proposed method extracts all layers which contain polylines in the GIS vector map and compress all polylines in extracted layers by the hybrid polyline simplification and SEC based on MAE(minimum area error) for each segment in the line. The proposed simplification and SEC increase the compression ratio while preserving the shape quality. We analyze the visual aspects and compression efficiency between the original GIS vector map and the compressed map. From experimental results, we verify that our method has the higher compression efficiency and visual quality than conventional methods.

A vocabulary for a multiscale process description for fast transmission and continuous visualization of spatial data

With the increasing availability of small mobile computers there is also an increasing demand for visualizing spatial data on those devices. Prominent applications are location based services in general, and car and pedestrian navigation in particular. In order to be able to offer both detail and overview of a spatial situation, the devices have to provide flexible zooming in and out in real-time. The same demands arise from the increasing amounts of data available and accessible by web services through limited bandwidth channels. The presentation of spatial data sets in different zoom levels or resolutions is usually achieved using generalization operations. When larger scale steps have to be overcome, the shape of individual objects typically changes dramatically; also objects may disappear or merge with others to form new objects. As these steps typically are discrete in nature, this leads to visual ‘popping effects’ when going from one level of detail to the other. In this paper, we will present an approach to decompose generalization into simple geometric and topologic operations that allow describing the complete generalization chain to generate a multiscale object representation. The goal is to generate a representation without redundancy and to transmit only that information which is needed when scale changes occur. This representation scheme ultimately enables a continuous visualization, where the changes between the representations are visually indistinguishable. We identify elementary generalization operations and apply these concepts for polyline simplification, the generalization of building ground plans and for displacement.

Effects of polyline simplification of dynamic GPS data under forest canopy on area and perimeter estimations

The objectives of this study were to determine Global Positioning System (GPS) positional errors while moving under the forest canopy and to clarify the effects of polyline simplification on area and perimeter estimations. We used the Pathfinder Pro XR and GPSMAP 76S, which are categorized as “high-end mapping” and “general navigation” GPS receivers, respectively. The field tests were conducted in both natural and plantation forests. The results showed that the Pathfinder Pro XR, which has better multipath rejection technology, worked well, especially in the plantation forest under unfavorable conditions of higher stand density. We used analysis of variance to clarify the effects of the receiver type, positioning mode, stand type, and polyline simplification method on area and perimeter estimations. The receiver type and positioning mode were found to be significant factors that affected area estimation. The Pathfinder Pro XR estimated the area more accurately than the GPSMAP 76S, and differential GPS estimated the area more accurately than autonomous GPS. With respect to the perimeter, the receiver type, positioning mode, and polyline simplification method were found to be significant factors. The results showed that perimeter estimation was improved by using the velocity filter, and further improved by using the velocity filter and Douglas-Peucker algorithm, especially when the Pathfinder Pro XR was used. The GPSMAP 76S estimated the perimeter accurately without any filtering because its default speed filter worked well, even though the GPSMAP 76S is a general navigation GPS receiver.

Topologically Consistent Line Simplification with the Douglas-Peucker Algorithm

We examine key properties of the Douglas-Peucker polyline simplification algorithm which are shared with many similar "vertex sub-sampling" algorithms. We examine how the Douglas-Peucker algorithm and similar algorithms can fail to maintain consistent or correct topological relations among features. We then prove that a simple test added to the stopping condition of Douglas-Peucker-like algorithms can guarantee that the resulting simplified polyline is topologically consistent with itself and with all of its neighboring features, and is correctly situated topologically with respect to all other features. We describe how a dynamically updated convex hull data structure may be used to efficiently detect and remove potential topological conflicts of the polyline with itself and with other features in that polyline's neighborhood.

Automated Cartographic Generalization For Linear Features

An automated method is presented for the generalization of linear features that are already in a topologically structured computer-readable form. The method consists of three stages: feature elimination; feature simplification; and interference detection and resolution. The first stage is implemented using English-like rules to specify which map features are to be eliminated at the generalized map scale. The second stage consists of the simplification of linear map features, specifically in the form of polyline simplification and riverbank combination. The third stage deals with interference detection and resolution among linear map features. Due to the width of the symbol representing a feature, interference may occur when a simplified feature is added to the generalized map and it overlaps another feature already on the generalized map. If that occurs, one or both of the interfering features have to be displaced so as to eliminate the interference between them. This displacement may cause other features to be subsequently displaced in a process called feature displacement propagation. The algorithms used to detect feature interference and to perform the subsequent feature displacement propagation are described. A FORTRAN 77 computer program called MAPEX was written to perform automated generalization of linear map features. The intended scale range for MAPEX is 1:24 000 to 1: 250 000. The results of running MAPEX on two topologically structured test data files are given, along with some of the algorithmic details used in the implementation of the program.