## Speeding Up the Douglas-Peucker Line-Simplification Algorithm (1992)

Venue: | Proc. 5th Intl. Symp. on Spatial Data Handling |

Citations: | 73 - 3 self |

### BibTeX

@INPROCEEDINGS{Hershberger92speedingup,

author = {John Hershberger and Jack Snoeyink},

title = {Speeding Up the Douglas-Peucker Line-Simplification Algorithm},

booktitle = {Proc. 5th Intl. Symp. on Spatial Data Handling},

year = {1992},

pages = {134--143}

}

### Years of Citing Articles

### OpenURL

### Abstract

We analyze the line simplification algorithm reported by Douglas and Peucker and show that its worst case is quadratic in n, the number of input points. Then we give a algorithm, based on path hulls, that uses the geometric structure of the problem to attain a worst-case running time proportional to n log 2 n, which is the best case of the Douglas algorithm. We give complete C code and compare the two algorithms theoretically, by operation counts, and practically, by machine timings.

### Citations

443 |
Algorithms for the reduction of the number of points required to represent a digitized line or its caricature
- Douglas, Peucker
- 1973
(Show Context)
Citation Context ...r that other measures of curve discrepancy are small. McMaster [9] gives a detailed study of mathematical similarity and discrepancy measures. He also ranks the method reported by Douglas and Peucker =-=[4] as "-=-mathematically superior." White [14] performed a study of three simplification algorithms, based on Marino's work [8] on critical points as a psychological measure of curve similarity. She showed... |

248 |
Seminumerical Algorithms
- Knuth
- 1998
(Show Context)
Citation Context ...f the algorithms---knowing what is the best and worst case data---then we can design better test sets and interpret the results of the tests more accurately. In the theoretical analysis of algorithms =-=[7]-=-, one counts the number of operations that the algorithm uses as a function of the number of input segments. (Those familiar with such analysis can safely skip the remainder of this section.) Because ... |

114 |
An iterative procedure for the polygonal approximation of plane curves
- Ramer
- 1972
(Show Context)
Citation Context ...ork of Jones and Abraham [6] on scale-independent cartographic databases. It should be no surprise that this method has been independently proposed in other contexts. Two examples are papers of Ramer =-=[12]-=- in image processing and Rote [13] in computational geometry. In this paper we analyze two algorithms that implement the Douglas-Peucker simplification method using different data structures. In the n... |

57 |
On-line construction of the convex hull of a simple polyline
- Melkman
- 1987
(Show Context)
Citation Context ...hus, after O(log 2 n) operations, we can report the farthest point from ` if we have CH (P ) available in an array. For the Build() operation, we use a modification of Melkman's convex hull algorithm =-=[3, 11]-=-. This algorithm (and therefore our algorithm as well) is valid only if the underlying path has no self intersections, which is usually the desired case in cartograpic and vision applications. Melkman... |

32 | An efficient algorithm for finding the CSG representation of a simple polygon
- Dobkin, Guibas, et al.
(Show Context)
Citation Context ...rding to lemma 4.1, only the vertices of CH (P ) need be considered as farthest points from `. So, our central task will be to maintain and search convex hulls of subchains efficiently. Dobkin et al. =-=[3]-=- developed the path hull data structure for a similar hull maintenance problem; here, we modify their structure slightly. We define the path hull of the chain from V i to V j to consist of a tag verte... |

25 |
Automated line generalization
- McMaster
(Show Context)
Citation Context ...ng them on a simple and readable map. As computers become increasingly involved in automated cartography, efficient algorithms are needed for the tasks of extraction and simplification. Cartographers =-=[1, 10]-=- have identified the line simplification problem as an important part of representing linear features. An ordered set of n + 1 points in the plane, fV 0 ; V 1 ; : : : ; V n g, forms a polygonal chain-... |

24 |
A quantitative analysis of mathematical measures in linear simplification
- McMaster
- 1983
(Show Context)
Citation Context ...at C and C 0 are close in distance, that the area between C and C 0 is small, that the critical points of C are incorporated into C 0 , or that other measures of curve discrepancy are small. McMaster =-=[9] gives a d-=-etailed study of mathematical similarity and discrepancy measures. He also ranks the method reported by Douglas and Peucker [4] as "mathematically superior." White [14] performed a study of ... |

17 |
Assessment of line-generalization algorithms using characteristic points
- White
- 1985
(Show Context)
Citation Context ...cy are small. McMaster [9] gives a detailed study of mathematical similarity and discrepancy measures. He also ranks the method reported by Douglas and Peucker [4] as "mathematically superior.&qu=-=ot; White [14]-=- performed a study of three simplification algorithms, based on Marino's work [8] on critical points as a psychological measure of curve similarity. She showed that the Douglas-Peucker method was best... |

11 |
Treatment of the cartographic line
- Buttenfield
- 1985
(Show Context)
Citation Context ...ng them on a simple and readable map. As computers become increasingly involved in automated cartography, efficient algorithms are needed for the tasks of extraction and simplification. Cartographers =-=[1, 10]-=- have identified the line simplification problem as an important part of representing linear features. An ordered set of n + 1 points in the plane, fV 0 ; V 1 ; : : : ; V n g, forms a polygonal chain-... |

10 |
Hierarchical methods of line simplification
- Cromley
- 1991
(Show Context)
Citation Context ...s. First, it is easy to program; Whyatt and Wade [15] give complete FORTRAN code in their paper. Second, the simplification it produces has a hierarchical structure that has been exploited by Cromley =-=[2]-=-, following the work of Jones and Abraham [6] on scale-independent cartographic databases. It should be no surprise that this method has been independently proposed in other contexts. Two examples are... |

7 |
Identification of characteristic points along naturally occurring lines/an empirical study
- Marino
- 1979
(Show Context)
Citation Context ...iscrepancy measures. He also ranks the method reported by Douglas and Peucker [4] as "mathematically superior." White [14] performed a study of three simplification algorithms, based on Mari=-=no's work [8] on c-=-ritical points as a psychological measure of curve similarity. She showed that the Douglas-Peucker method was best at choosing critical points and also reports, "The generalizations produced by t... |

4 |
Line generalisation in a global cartographic database
- Jones, Abraham
- 1987
(Show Context)
Citation Context ...ade [15] give complete FORTRAN code in their paper. Second, the simplification it produces has a hierarchical structure that has been exploited by Cromley [2], following the work of Jones and Abraham =-=[6]-=- on scale-independent cartographic databases. It should be no surprise that this method has been independently proposed in other contexts. Two examples are papers of Ramer [12] in image processing and... |

3 |
Minimum link approximation of polygons and subdivisions
- Guibas, Hershberger, et al.
- 1991
(Show Context)
Citation Context ...often indicate errors in digitization [10]. Although we would like to require that the approximation C 0 should also be simple, there is some indication that it is computationally infeasible do to so =-=[5]. "Re-=-presenting well" has many possible meanings. For example, it may require that C and C 0 are close in distance, that the area between C and C 0 is small, that the critical points of C are incorpor... |

3 |
The convergence of the sandwich algorithm for approximating convex functions
- Rote
- 1992
(Show Context)
Citation Context ...ale-independent cartographic databases. It should be no surprise that this method has been independently proposed in other contexts. Two examples are papers of Ramer [12] in image processing and Rote =-=[13]-=- in computational geometry. In this paper we analyze two algorithms that implement the Douglas-Peucker simplification method using different data structures. In the next section we give the basic simp... |

3 |
The Douglas-Peucker line simplification algorithm
- Whyatt, Wade
- 1988
(Show Context)
Citation Context ...by 86 percent of all sample subjects---deemed the best perceptual representations of the original lines." 1 The Douglas method also has other advantages. First, it is easy to program; Whyatt and =-=Wade [15]-=- give complete FORTRAN code in their paper. Second, the simplification it produces has a hierarchical structure that has been exploited by Cromley [2], following the work of Jones and Abraham [6] on s... |