Greedy map generalization by iterative point removal
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This paper describes a map generalization program we submitted to the ACM SIGSPATIAL Cup 2014. In this competition, the goal is to remove as many points in a set of polygonal lines as quickly as possible with respect to two constraints. The topological relationships among the lines must not change, and the relationships between a set of control points and the lines must not change. Inspired by Visvalingam-Whyatt Algorithm, we iteratively examine successive triplets along each line, and remove the middle point if no control point or point of other lines is in the associated triangle. Based on the features of the training datasets, we further introduce many optimization techniques to speed up the computation.Keywords:
Line (geometry)
Line segment
In this paper, we propose a novel line segment detector, named as NETLines, which can produce a set of accurate line segments and a set of node-connected line-networks formed by connection of the line segments and the image boundary. Based on the line segments generated by other line segment detectors (e.g., EDLines [1]) on an edge map, the proposed algorithm efficiently makes use of the gradient map of the original image instead of its edge map to extend and refine the line segments. The line-networks are constructed with the extended and refined line segments and a set of nodes generated by connecting of the line segments. Furthermore, the line segments and line-networks are optimally supplemented and refined by linking and merging the line segments. Experimental results on a set of natural images illustrate the proposed NETLines produces more accurate and complete line segments compared with state-of-the-art line segments detectors.
Line segment
Line (geometry)
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Let $S$ and $D$ each be a set of orthogonal line segments in the plane. A line segment $s\in S$ \emph{stabs} a line segment $s'\in D$ if $s\cap s'\neq\emptyset$. It is known that the problem of stabbing the line segments in $D$ with the minimum number of line segments of $S$ is NP-hard. However, no better than $O(\log |S\cup D|)$-approximation is known for the problem. In this paper, we introduce a constrained version of this problem in which every horizontal line segment of $S\cup D$ intersects a common vertical line. We study several versions of the problem, depending on which line segments are used for stabbing and which line segments must be stabbed. We obtain several NP-hardness and constant approximation results for these versions. Our finding implies, the problem remains NP-hard even under the extra assumption on input, but small constant approximation algorithms can be designed.
Line segment
Line (geometry)
Constant (computer programming)
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Line segment
Line (geometry)
Contour line
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Let $S$ and $D$ each be a set of orthogonal line segments in the plane. A line segment $s\in S$ \emph{stabs} a line segment $s'\in D$ if $s\cap s'\neq\emptyset$. It is known that the problem of stabbing the line segments in $D$ with the minimum number of line segments of $S$ is NP-hard. However, no better than $O(\log |S\cup D|)$-approximation is known for the problem. In this paper, we introduce a constrained version of this problem in which every horizontal line segment of $S\cup D$ intersects a common vertical line. We study several versions of the problem, depending on which line segments are used for stabbing and which line segments must be stabbed. We obtain several NP-hardness and constant approximation results for these versions. Our finding implies, the problem remains NP-hard even under the extra assumption on input, but small constant approximation algorithms can be designed.
Line segment
Line (geometry)
Constant (computer programming)
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A fast line segment detection method is proposed based on edge linking.In digital image,digital lines consist of many line segment elements.The directions of these elements are same and are inhibited by the slope of digital line.Thus the detection of line segment can be carried out through extracting line segment elements and analyzing their connection.First,the edge is detected by ADM algorithm,and then rough line segments are extracted in four directions.In the end, the obtained results are testified and the line segments with same slope and intercept are merged,some shorter line segments are deleted.Experiments show that the proposed method can fast extract line segments in complex image,and is robust to noise.
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Line (geometry)
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The previous works on 3Dline segment reconstruction of building facades require known geometrical constraints in multi-image line matching,and the line segment reconstruction is affected by accumulated input error.An improved algorithm with non-geometry constraint is proposed.In line matching across multi-image,robust two-view line matching method is chosen, line-point invariants are taken as the foundation and matched-line-segment sets are formed via transitivity of matched line segments.Incompatible matches are eliminated and compatible matches are merged from those sets to form an accurate result.For this line segments reconstruction,3Dline segments corresponding to each matched-line-segment set are obtained in piecewise,and the length constraint and angle constraint are considered to remove the line segments which do not constitute building facades.The whole structure of building facades is thus effectively reconstructed with this algorithm.
Line segment
Line (geometry)
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For a given set S of line segments,finding a straight line intersecting with all the line segments in S is studied in this paper.If an intersection restriction is satisfied by the set,the algorithm presented is to answer whether there is a straight line intersecting with all the line segments in S.If the straight lines exist,the algorithm finds a maximum range,where every straight line located in the range intersects with all the line segments in S.The time complexity of the algorithm is O(n×log n).The algorithm can be used in pattern marching and so on.
Line segment
Line (geometry)
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A study is made of the capacity of fifty subjects to estimate the position of the point of intersection between a straight line and the visually extrapolated extension of a line segment at three different angles between the line and the segment: 30 degrees, 60 degrees and 90 degrees. The results show systematic deviations in the estimation of acute angles. The point of intersection of the straight line and the segment is misperceived to be shifted inwards in the angle between them. It is also shown that the set of imaginary extensions of a line segment with a given length, until its intersection with the given straight line, is determined only by the angle between the straight line and the segment and does not depend on the distance between them. Various possible mechanisms which could determine the solution of the task facing the subjects are discussed.
Line (geometry)
Line segment
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A real-time CNN-based method is proposed to detect line segments of a given image with a simple and compact pipeline, named as Center-based Line Segment Detector (CenterLine). A line segment is modeled by its center-point with two offsets along the x-axis and y-axis. Under that representation, the localization, direction and length of a line segment can be encoded simultaneously. The method uses keypoint estimation to find the center point of a line and regresses its offsets. Comprehensive experimental results on the Wireframe dataset and the YorkUrban dataset show that the proposed method achieves state-of-the-art performance with 49 FPS in inference speed, which is outperforming most of the existing line segment detectors. With good performance and rapidity, our method is applicable to practical systems with real-time requirements.
Line segment
Line (geometry)
Representation
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Most line segment detection methods suffer from over-segmentation. Therefore, we propose a line segment detector based on property similarity. It is composed of three steps. First, after the original line segments are generated, the competitive grouping method is used to group line segments with many same aligned endpoints, and a minimum bounding rectangle is adopted to enclose every group. In the second step, the line segments in the same group are verified whether they have similar positions and gradients. Finally, the center lines of the rectangles are the final line segments. We show that our method can significantly detect complete line segments and much less prone to over-segmentation while maintaining real-time performance. The experimental results illustrate that our method achieves a maximum F-score of approximately 27%, which about 5 % more than other leading methods when analyzing the images from the York urban line segments dataset.
Similarity (geometry)
Line (geometry)
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