A unified approach towards reconstruction of a planar point set

Methirumangalath, Subhasree; Parakkat, Amal Dev; Muthuganapathy, Ramanathan

doi:10.1016/j.cag.2015.05.025

Cited by 22 publications

(18 citation statements)

References 17 publications

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“…To assess the performance of the proposed algorithm, we perform an extensive comparison of our algorithm with various reconstruction algorithms viz. α‐shape [EKS83], crust [ABE98], nn‐crust [DK99], χ‐shape [DKWG08], simple‐shape [GDJ*11], de Goes et al [dGCSAD11], ec‐shape [MPM15] and wdm‐crust [PPM15]. It can be noted that our algorithm is non‐parametric, whereas many of the algorithms require tuning of at least one parameter.…”

Section: Resultsmentioning

confidence: 99%

“…There are quite a few approaches viz. [DKWG08, GDJ*11, PM15, MPM15] that can be classified as Delaunay sculpting methods which remove edges in a particular order. χ ‐shape [DKWG08] generates a simple polygon by successively removing Delaunay edges based on a user given parameter χ .…”

Section: Introductionmentioning

confidence: 99%

“…The ec ‐shape algorithm is a non‐parametric algorithm for reconstructing a simple polygon. In ec‐shape [MPM15], an exterior edge gets removed if it is longer than the local neighbouring edges.…”

Section: Introductionmentioning

confidence: 99%

“…The Shape hull algorithm [PM15] only works for specific case of curves called divergent‐concave shapes (please see [PM15] for more details). The ec ‐shape [MPM15] may fail to remove non‐boundary edges in some particular cases where all circles are empty and the edge is still not a part of the shape. χ ‐shape, simple shape, shape hull and ec‐shape algorithms have been designed such that the result will always be a single simple polygon and hence they cannot handle objects with holes, open curves, and multiple objects.…”

Section: Introductionmentioning

confidence: 99%

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Crawl through Neighbors: A Simple Curve Reconstruction Algorithm

Parakkat

Muthuganapathy

2016

Computer Graphics Forum

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Given a planar point set sampled from an object boundary, the process of approximating the original shape is called curve reconstruction. In this paper, a novel non‐parametric curve reconstruction algorithm based on Delaunay triangulation has been proposed and it has been theoretically proved that the proposed method reconstructs the original curve under ε‐sampling. Starting from an initial Delaunay seed edge, the algorithm proceeds by finding an appropriate neighbouring point and adding an edge between them. Experimental results show that the proposed algorithm is capable of reconstructing curves with different features like sharp corners, outliers, multiple objects, objects with holes, etc. The proposed method also works for open curves. Based on a study by a few users, the paper also discusses an application of the proposed algorithm for reconstructing hand drawn skip stroke sketches, which will be useful in various sketch based interfaces.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Crawl through Neighbors: A Simple Curve Reconstruction Algorithm

Parakkat

Muthuganapathy

2016

Computer Graphics Forum

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“…Despite two decades of research, curve reconstruction is still an active problem among the computational geometry and computer graphics research communities. Recent research trends target aspects such as improved sampling conditions [OMW16], reconstructing from fewer number of samples and curves with sharp corners [OM13], reconstruction from unstructured and noisy point cloud [OW18], unified frameworks for curve and shape reconstruction [MPM15], and applications of curve reconstruction to hand drawn sketches [PM16]. The proposed algorithm is a modified extension of the water flow‐based labelling algorithm proposed in [PPM15].…”

Section: Related Workmentioning

confidence: 99%

Incremental Labelling of Voronoi Vertices for Shape Reconstruction

Peethambaran

Parakkat

Tagliasacchi

et al. 2018

Computer Graphics Forum

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We present an incremental Voronoi vertex labelling algorithm for approximating contours, medial axes and dominant points (high curvature points) from 2D point sets. Though there exist many number of algorithms for reconstructing curves, medial axes or dominant points, a unified framework capable of approximating all the three in one place from points is missing in the literature. Our algorithm estimates the normals at each sample point through poles (farthest Voronoi vertices of a sample point) and uses the estimated normals and the corresponding tangents to determine the spatial locations (inner or outer) of the Voronoi vertices with respect to the original curve. The vertex classification helps to construct a piece‐wise linear approximation to the object boundary. We provide a theoretical analysis of the algorithm for points non‐uniformly (ε‐sampling) sampled from simple, closed, concave and smooth curves. The proposed framework has been thoroughly evaluated for its usefulness using various test data. Results indicate that even sparsely and non‐uniformly sampled curves with outliers or collection of curves are faithfully reconstructed by the proposed algorithm.

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Finding the polygon hull of a network without conditions on the starting vertex

Bounceur

Bezoui

Hammoudeh

et al. 2019

Trans Emerging Tel Tech

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Many real-life problems arising within the fields of wireless communication, image processing, combinatorial optimisation, etc., can be modeled by means of Euclidean graphs. In the case of Wireless Sensor Networks (WSN), the overall topology of the graph is not known, because sensor nodes are often randomly deployed. One of the significant problems in this field is the search for boundary nodes. This problem is important in cases such as the surveillance of an area of interest, image contour reconstruction, graph matching problems, routing or clustering data, etc. In the literature, many algorithms are proposed to solve this problem, a recent one of which is the LPCN algorithm and its distributed version D-LPCN which are both based on the concept of a polar angle visit. An inconvenience of these algorithms is the determination of the starting vertex. In effect, the point with the minimum x-coordinate is a possible starting point but it has to be known at the beginning which considerably increases the algorithms' complexity. In this article, we propose a new method called RRLPCN (Reset and Restart with Least Polar-angle Connected Node) which is based on the LPCN algorithm to find the boundary vertices of a Euclidean graph. The main idea is to start the LPCN algorithm from an arbitrary vertex and, whenever it finds a vertex with an x-coordinate smaller than that of the starting one, LPCN is reset and restarted from this new vertex. The algorithm stops as soon as it visits the

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A unified approach towards reconstruction of a planar point set

Cited by 22 publications

References 17 publications

Crawl through Neighbors: A Simple Curve Reconstruction Algorithm

Crawl through Neighbors: A Simple Curve Reconstruction Algorithm

Incremental Labelling of Voronoi Vertices for Shape Reconstruction

Finding the polygon hull of a network without conditions on the starting vertex

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