Error propagation control in Laplacian mesh compression

• Published in: Computer graphics forum Vol. 37; no. 5; pp. 61 - 70
• Main Authors: Váša, L., Dvořák, J.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2018
• Subjects: Algorithms; Anchors; Categories and Subject Descriptors (according to ACM CCS); Coding; Compression (Coding)—Approximate methods Computer Graphics [I.3.7]: Animation; Error analysis; Image Processing and Computer Vision [I.4.2]; Linear equations; Redundancy
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.13491

Laplacian mesh compression, also known as high‐pass mesh coding, is a popular technique for efficiently storing both static and dynamic triangle meshes that gained further recognition with the advent of perceptual mesh distortion evaluation metrics. Currently, the usual rule of thumb that drives the decision for a mesh compression algorithm is whether or not accuracy in absolute scale is required: Laplacian mesh encoding is chosen when perceptual quality is the main objective, while other techniques provide better results in terms of mechanistic error measures such as mean squared error. In this work, we present a modification of the Laplacian mesh encoding algorithm that preserves its benefits while it substantially reduces the resulting absolute error. Our approach is based on analyzing the reconstruction stage and modifying the quantization of differential coordinates, so that the decoded result stays close to the input even in areas that are distant from anchor points. In our approach, we avoid solving an overdetermined system of linear equations and thus reduce data redundancy, improve conditioning and achieve faster processing. Our approach can be directly applied to both static and dynamic mesh compression and we provide quantitative results comparing our approach with the state of the art methods.