A method to shape reconstruction from planar point sets with Gestalt proximity and simplification principle

The widely used shape reconstruction algorithms based on Delaunay triangulation are far from sophisticated, and some problems are to be further addressed. First of all, the current methods involve a few of user-defined parameters, obstructing the effective use of them in practice. Secondly, the current methods cannot guarantee the perfect shape reconstruction if a planar point set follows a randomly distribution. To overcome these aforementioned problems, a method for planar point set shape reconstruction, namely SRGT (shape reconstruction based on Gestalt) based on Gestalt proximity and simplification is developed. On the one hand, based on the proximity theory, the gross error detection technique is used to identify and locate the extreme long edges in the Delaunay triangulation network, and then the inner and outer boundaries of the Delaunay are refined step by step. On the other hand, according to the simplification theory of Gestalt, the inner and outer holes are optimized by gross error detection technique again, and finally the small holes are removed from the list of inner boundary set. To validate the effectiveness of the proposed method, the SRGT was validated on several cases, and 4 widely used algorithms, i. e. α-shape, χ-shape, ∂RGG, and edge length ratios were selected for comparisons. The results demonstrate that SRGT can achieve the fine shape reconstruction from planar point sets in both uniform and random distribution. Moreover, the SRGT generally outperforms the other 4 methods in terms of the L2 measure. Finally, the shape reconstructions with the SRGT using two actual datasets corresponding to typical GIS applications were implemented to verify the effectiveness of the proposed method, and the results consistently suggest the superior ability of the SRGT. © 2020, Surveying and Mapping Press. All right reserved.