From unordered point cloud to weighted B-spline: a novel PCA-based method

Authors:
Rocco Furferi;Lapo Governi;Matteo Palai;Yary Volpe
Affiliations:
Department of Mechanics and Industrial Technologies, Università degli Studi di Firenze, Firenze, Italy;Department of Mechanics and Industrial Technologies, Università degli Studi di Firenze, Firenze, Italy;Department of Mechanics and Industrial Technologies, Università degli Studi di Firenze, Firenze, Italy;Department of Mechanics and Industrial Technologies, Università degli Studi di Firenze, Firenze, Italy
Venue:
AMERICAN-MATH'11/CEA'11 Proceedings of the 2011 American conference on applied mathematics and the 5th WSEAS international conference on Computer engineering and applications
Year:
2011

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Abstract

Digital applications such as CG, CAD and GIS are based on vectorial data since all the information about shape, size, topology etc. are provided in such kind of data representation rather than raster one. Turning raster images into vector ones is a key issue which has been addressed by a number of authors but still far to be exhaustively worked out. Especially in the case of 2D images representing technical drawings, fitting analytical curves to point clouds (pixel sets) is a critical matter. The present paper provides a novel approach to fit unordered point cloud data. Such an approach integrates a PCA-based method, for detecting the main local directions of the point cloud and to order the points, with and a weighted approximation of a B-spline curve to the original data, based on pixel gray levels. The methodology, tested against alternative techniques based on Least Square (LS) B-spline approximation and on image thinning, proved to be effective in preserving the original shape according to human perception.