Polygonal shape reconstruction in the plane

A unified approach towards reconstruction of a planar point set

“…The existing methods we considered are Crust [10], NN-crust [11], α-shape [5], simple-shape [3], RGG for directed boundary sample [4] and χ-shape [9].…”

“…One category of input consists of points sampled only from the boundary of the object, termed as boundary sample [3] or curve sample [4], as shown in Fig. 1(a).…”

“…Join and glue are the main topological operations performed in the algorithm which adds and deletes edges respectively. Simple shape algorithm [3] presents a non-Delaunay approach for reconstruction that can handle both dot patterns and boundary samples.…”

“…Almost all the approaches for reconstructing from either type of input depend on at least one input parameter which is difficult to identify. Moreover, most of the current approaches deal with only one of the input types and not both (except [3]). The approaches that work for RBS may not work for RDP and vice versa, illustrating the requirement of a unified approach.…”

“…The constraints imposed on removing an edge depend on Euclidean Minimum Spanning Tree and Extended Gabriel Hypergraph in [7]. In [15], decision on whether to insert an edge to the boundary is made using a pivoting ball whereas simple shape algorithm in [3] replaces a selected edge of initial convex hull with two new edges using a selection criteria value which depends upon edge length, closeness of points and angle formed by the two new edges. In [6] the sculpting strategy is based on the maximum distance in the sculpture.…”