Open AccessProgressive Compression of 3D Mesh Geometry Using Sparse Approximations from Redundant Frame Dictionaries
Author(s) -
Krivokuća Maja,
Abdulla Waleed Habib,
Wünsche Burkhard Claus
Publication year - 2017
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.17.0116.0509
Subject(s) - laplacian smoothing , matching pursuit , polygon mesh , algorithm , frame (networking) , computer science , laplace operator , matching (statistics) , compression (physics) , topology (electrical circuits) , eigenvalues and eigenvectors , manifold (fluid mechanics) , encoding (memory) , distortion (music) , mathematics , mesh generation , compressed sensing , geometry , artificial intelligence , finite element method , combinatorics , mathematical analysis , engineering , materials science , amplifier , computer network , structural engineering , bandwidth (computing) , composite material , telecommunications , quantum mechanics , statistics , mechanical engineering , physics
In this paper, we present a new approach for the progressive compression of three‐dimensional (3D) mesh geometry using redundant frame dictionaries and sparse approximation techniques. We construct the proposed frames from redundant linear combinations of the eigenvectors of a combinatorial mesh Laplacian matrix. We achieve a sparse synthesis of the mesh geometry by selecting atoms from a frame using matching pursuit. Experimental results show that the resulting rate‐distortion performance compares favorably with other progressive mesh compression algorithms in the same category, even when a very simple, sub‐optimal encoding strategy is used for the transmitted data. The proposed frames also have the desirable property of being able to be applied directly to a manifold mesh having arbitrary topology and connectivity types; thus, no initial remeshing is required and the original mesh connectivity is preserved.