Self-similarity for accurate compression of point sampled surfaces

• Published in: Computer graphics forum Vol. 33; no. 2; pp. 155 - 164
• Main Authors: Digne, Julie, Chaine, Raphaëlle, Valette, Sébastien
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.05.2014; Wiley
• Subjects: Analysis; and object representations; Categories and Subject Descriptors (according to ACM CCS); Compressing; Computer graphics; Computer Science; Dictionaries; Engineering Sciences; Filtering; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; I.4.2 [ImageProcessing and Computer Vision]: Compression (Coding)-Approximate methods; Regularity; Representations; Scanners; Self-similarity; Signal and Image Processing; solid; Studies; surface; Three dimensional models; Topological manifolds; Images et Modèles; reseau_national; categ_st2i
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12305

Most surfaces, be it from a fine‐art artifact or a mechanical object, are characterized by a strong self‐similarity. This property finds its source in the natural structures of objects but also in the fabrication processes: regularity of the sculpting technique, or machine tool. In this paper, we propose to exploit the self‐similarity of the underlying shapes for compressing point cloud surfaces which can contain millions of points at a very high precision. Our approach locally resamples the point cloud in order to highlight the self‐similarity of the shape, while remaining consistent with the original shape and the scanner precision. It then uses this self‐similarity to create an ad hoc dictionary on which the local neighborhoods will be sparsely represented, thus allowing for a light‐weight representation of the total surface. We demonstrate the validity of our approach on several point clouds from fine‐arts and mechanical objects, as well as a urban scene. In addition, we show that our approach also achieves a filtering of noise whose magnitude is smaller than the scanner precision.