Efficient generation of simple polygons for characterizing the shape of a set of points in the plane

Duckham, Matt; Kulik, Lars; Worboys, Mike; Galton, Antony

doi:10.1016/j.patcog.2008.03.023

Cited by 199 publications

(117 citation statements)

References 20 publications

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“…As the network contracts it is 'snagged' at the outer nodes and the stable pattern reveals the convex hull. The concave hull is related to the convex hull and is commonly defined as the minimum region (or footprint, Galton and Duckham 2006) occupied by a set of points, which cannot, in some cases, be represented correctly by the convex hull (Duckham et al 2008) (for example, a set of points arranged to form the capital letter 'C' would not be correctly represented by the convex hull because the gap in the letter would be closed). The virtual plasmodium approximates the concave hull when all of the particles are within the region of the data source nodes.…”

Section: Spatially Represented Geometry Problems and The Virtual Plasmentioning

confidence: 99%

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

Jones

2010

Nat Comput

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Section: Spatially Represented Geometry Problems and The Virtual Plasmentioning

confidence: 99%

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

Jones

2010

Nat Comput

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“…An efficient concave boundary algorithm for datasets can be found in [37]. We use the MATLAB boundary command [38] to determine the boundary points of two-dimensional data.…”

Section: Design Stage 2: Determine the Actual Boudnaries Of Data Andmentioning

confidence: 99%

“…The check errors in (36) and (37) to stop the loops were e min lb = 0 and e min ub = 0, respectively. Figure 10 shows performance in this test case.…”

Section: Test Case 2: Estimating the Output Power Of Solar Pv Arraysmentioning

confidence: 99%

An Improved Interval Fuzzy Modeling Method: Applications to the Estimation of Photovoltaic/Wind/Battery Power in Renewable Energy Systems

Thao

Uchida

2018

Energies

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This paper proposes an improved interval fuzzy modeling (imIFML) technique based on modified linear programming and actual boundary points of data. The imIFML technique comprises four design stages. The first stage is based on conventional interval fuzzy modeling (coIFML) with first-order model and linear programming. The second stage defines reference lower and upper bounds of data using MATLAB. The third stage initially adjusts scaling parameters in the modified linear programming. The last stage automatically fine-tunes parameters in the modified linear programming to realize the best possible model. Lower and upper bounds approximated by the imIFML technique are closely fitted to the reference lower and upper bounds, respectively. The proposed imIFML is thus significantly less conservative in cases of large variation in data, while robustness is inherited from the coIFML. Design flowcharts, equations, and sample MATLAB code are presented for reference in future experiments. Performance and efficacy of the introduced imIFML are evaluated to estimate solar photovoltaic, wind and battery power in a demonstrative renewable energy system under large data changes. The effectiveness of the proposed imIFML technique is also compared with the coIFML technique.

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“…The aligned planar segment is denoted as P t . Afterwards, the boundary points of P t are extracted as an α-shape [21,22]. We denote the boundary as a concave hull H of the planar segment, which is an ordered list of vertices describing a polygon for which ∀p ∈ P t and p / ∈ H, p is inside the polygon.…”

Section: Preprocessingmentioning

confidence: 99%

Incremental and batch planar simplification of dense point cloud maps

Whelan

Bondarev

et al. 2015

Robotics and Autonomous Systems

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Dense RGB-D SLAM techniques and high-fidelity LIDAR scanners are examples from an abundant set of systems capable of providing multi-million point datasets. These datasets quickly become difficult to process due to the sheer volume of data, typically containing significant redundant information, such as the representation of planar surfaces with millions of points. In order to exploit the richness of information provided by dense methods in real-time robotics, techniques are required to reduce the inherent redundancy of the data. In this paper we present a method for incremental planar segmentation of a gradually expanding point cloud map and a method for efficient triangulation and texturing of planar surface segments. Experimental results show that our incremental segmentation method is capable of running in real-time while producing a segmentation faithful to what would be achieved using a batch segmentation method. Our results also show that the proposed planar simplification and triangulation algorithm removes more than 90% of the input planar points, leading to a triangulation with only 10% of the original quantity of triangles per planar segment. Additionally, our texture generation algorithm preserves all colour information contained within planar segments, resulting in a visually appealing and geometrically accurate simplified representation.

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Efficient generation of simple polygons for characterizing the shape of a set of points in the plane

Cited by 199 publications

References 20 publications

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

An Improved Interval Fuzzy Modeling Method: Applications to the Estimation of Photovoltaic/Wind/Battery Power in Renewable Energy Systems

Incremental and batch planar simplification of dense point cloud maps

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