Subdivision surface fitting for efficient compression and coding of 3D models

Guillaume Lavoué, Florent Dupont, Atilla Baskurt
2005 Visual Communications and Image Processing 2005  
In this paper we present a new framework, based on subdivision surface fitting, for high rate compression and coding of 3D models. Our algorithm fits the input 3D model, represented by a polygonal mesh, with a piecewise smooth subdivision surface represented by a coarse control polyhedron. Our fitting scheme, particularly suited for meshes issued from mechanical or CAD parts, aims at getting close to the optimality in terms of control points number, while remaining independent of the
more » ... y of the input mesh. The found subdivision control polyhedron is much more compact than the original mesh and visually represents the same shape after several subdivision steps, without artifacts or cracks, like traditional lossy compression schemes. This control polyhedron is then encoded specifically to give the final compressed stream. Experiments conducted on several 3D models have proven the coherency and the efficiency of our framework, compared with existing compression methods. ) 4 72 44 83 95, fax (33) 4 72 43 15 36, http://liris.cnrs.fr/guillaume.lavoue RELATED WORK Mesh compression A lot of work has been done about polygonal mesh compression. This representation contains two kinds of information: geometry and connectivity, the first describing coordinates of the vertices in the 3D space, and the later describing how to connect these positions. The connectivity graph is often encoded using a region growing approach based on faces 2 , edges 3 or vertices 1 . Others techniques consider progressive approaches which encode a base mesh and then vertex insertion operations 7 . Fewer efforts have been done about geometry compression which is often simply performed by predictive coding and quantization. Other researches have put more efforts on geometry driven mesh coding, using wavelets 4,5 or spectral compression 8 . On the whole, better mesh compression methods give between 1 and 2 bytes per vertex; although this represents an excellent result, the output bit stream remains large for complex objects because of the high number of vertices to encode. Moreover lossy compression schemes 4,5,7,8 often produce artifacts, visually damaging for smooth mechanical objects. That is why we have chosen to approximate input meshes with subdivision surfaces, of which control polyhedrons should contain much lesser faces to store or transmit, knowing that after several refinement steps, the subdivision surfaces will visually represent the shape of the original meshes (of which original connectivity will not be kept). Subdivision surface approximation Several methods already exist for subdivision surface fitting, most of them take as input a dense mesh, simplify it to obtain a base coarse control mesh 9,10 and then displace the control points (geometry optimization) to fit the target surface. These simplification based approaches allow to easily extract a control mesh with the same topology than the target object, however, the control mesh connectivity strongly depends on the input mesh and therefore can give quite bad results if the input mesh is very irregular, which is the case for our CAD models. Hence, in our algorithm, in order to remain independent of the original connectivity, we first decompose the object into surface patches, and then we use the boundaries of the patches and the curvature information to construct a control polyhedron having the same topology than the target object. Some algorithms 11,12 also remain independent of the target mesh, by iteratively subdividing and shrinking an initial control m esh toward the target surface. Unfortunately these methods fail to capture local characteristics for complex target surfaces. Once a coarse control mesh has been constructed, then the geometry has to be optimized by moving control points to match the subdivision surface with the target model. Lee et al. 9 and Hoppe et al. 13 sample a set of points from the original mesh and minimize a quadratic error to the subdivision surface. Suzuki et al. 11 propose a faster approach, also used in Ref. 12: the position of the control points is optimized, only by reducing the distances between their limit positions and the target surface. Hence only subsets of the surfaces are involved on the fitting procedure, thus results are not so precise and may produce oscillations. Ma et al. 10 consider the minimization of the distances from vertices of the subdivision surface after several refinements, to the target mesh; our algorithm follows this framework while using not a point to point distance minimization, but a point to surface minimization, by using the local quadratic approximants introduced by Pottmann and Leopoldseder 14 . This algorithm allows a more accurate and rapid convergence. To our knowledge, the optimality in terms of control points number and connectivity of the control polyhedron represents a minor problematic in the existing algorithms but seems particularly relevant for mechanical or CAD objects. Only Hoppe et al. 13 optimize the connectivity (but not the number of control points) by trying to collapse, split, or swap each edge of the control polyhedron. Their algorithm produces high quality models but need of course an extensive computing time. Our algorithm optimizes the connectivity of the control mesh by analyzing curvature directions of the target surface, which reflect the natural parameterization of the object. The number of control points is also optimized by enriching iteratively the control polyhedron according to the error distribution. Moreover our approach allows to directly control the approximation error, whereas simplification based methods 9,10 indirectly control the error by modifying the decimation level. OVERVIEW OF OUR ALGORITHM AND PRIOR WORK Overview Our framework for compression of 3D models is the following: Firstly the target 3D objects are segmented into surface patches (see Section 3.4), of which boundaries are extracted. Secondly, the network of boundaries is approximated with piecewise smooth subdivision curves (see Sections 3.3 and 3.5); this step provides a network of control polygons.
doi:10.1117/12.631641 fatcat:2qfa4ifuvfdctptf43hv64xnky