Crawl through Neighbors: A Simple Curve Reconstruction Algorithm

Abstract

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.

Incremental Labelling of Voronoi Vertices for Shape Reconstruction

“…A few data sets were generated from the corresponding images using mesecina software [MGP07]. We compared our algorithm with other Delaunay/Voronoi‐based algorithms such as crust [ABE98], nearest neighbour crust [DK99], ec‐shape [MPM15], shape‐hull [PM15b] and the recent algorithms in [PM16] and [PMM18]. We also evaluate our method using simplification algorithms such as optimal transport‐based algorithm [dGCSAD11].…”

“… Outlier experiment : All the stages of outlier injection, dove shape reconstructed by the proposed algorithm, preserve fine details as compared to a simplified reconstruction by deGoes et al. [dGCSAD11] and the reconstruction with curve artefacts in [PM16] and [PMM18]. Outliers were generated using the software by deGoes et al.…”

“…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].…”

“…So, we label all such EVVs as inner. All the remaining Voronoi vertices [dGCSAD11] and the reconstruction with curve artefacts in [PM16] and [PMM18]. Outliers were generated using the software by deGoes et al [dGCSAD11].…”

FitConnect: Connecting Noisy 2D Samples by Fitted Neighbourhoods

“…Starting by requiring uniform sampling density [EKS83, KR85, FMG94, Att97, DT14, DT15, Ste08, ST09], Amenta et al . [ABE98] introduced the ε‐sampling condition based on the lfs which spurred further development [Gol99, DK99, Alt01, Len06, PM16], extending it to handle open curves [DMR99], sharp corners [DW02, FR01] and modifying the sampling condition to get tighter bounds [OM13, OMW16].…”