MESHGRID - a compact, multi-scalable and animation-friendly surface representation

Abstract

Abstract-MESHGRID is a novel, compact, multiscalable and animation-friendly surface representation method, which has been introduced in MPEG-4 [1]. The MESHGRID representation attaches a description of the "global connectivity" between the vertices on the object's surface (i.e., the 3-D connectivity wireframe) to a regular 3-D grid of points (i.e., the reference grid). MESHGRID efficiently encodes the 3-D connectivity wireframe by using a new type of 3-D extension of Freeman chain-code. MESHGRID does not explicitly store the polygons of the surface, since the 3-D connectivity wireframe has particular connectivity properties allowing for the unambiguous derivation of the triangulation. The reference grid is a smooth vector field defined on a regular discrete 3-D space. This grid is efficiently compressed by using an embedded 3-D wavelet-based multiresolution intra-band coding algorithm. MESHGRID can be efficiently exploited for QoS since it allows for three types of scalability in both view-dependent and view-independent scenarios, including: 1) resolution scalability, i.e., the adaptation of the number of transmitted vertices; 2) shape precision, i.e., the adaptive reconstruction of the reference grid positions; and 3) vertex position scalability, i.e., the change of the precision of known vertex positions with respect to the reference grid. Furthermore, in addition to the classical vertex-based animation, MESHGRID also supports specific animation capabilities, such as: 1) rippling effects by changing the position of the vertices relative to corresponding reference grid points and 2) reshaping on a hierarchical basis of the regular reference grid and its attached vertices.

Efficient error control in 3D mesh coding

“…Relation (1) can be written as It is important to highlight the terminology difference between the L-p norm, defined by (2), and the L-p distortion, given by the L-p norm to the power p. We point out that in the remainder of this work, unless it is clearly stated, we systematically refer to the L-p distortion instead of the L-p norm.…”

“…The sources can be independent spatial regions, if we consider a spatial partitioning of the input mesh, such as [3][4][5], or wavelet subbands, if we consider a waveletbased coding approach, such as MESHGRID [2] and WSS [6,7]. The classical approach in lossy compression consists in optimizing the compression scheme so as to maximize the overall compression ratio for a given reconstruction error.…”

“…In this survey paper we give an overview of our L-infinite estimators recently introduced in [1] and investigate how the L-infinite distortion metric performs compared to the L-2 distortion metric, when both are instantiated for the MESHGRID coding system [2].…”

“…With this respect, [1] proposes a scalable L-infinite mesh coding approach, simultaneously performing local error control and providing scalability in L-infinite sense. The L-infinite coding approach is instantiated by using the MESHGRID coding system [2]. Additionally, an L-infinite distortion estimator is proposed [1], expressing the L-infinite distortion in the spatial domain as a function of quantization errors occurring in the wavelet domain.…”

MESHGRID—A Compact, Multiscalable and Animation-Friendly Surface Representation

“…18 are the overall rates for the entire MeshGrid model. Notice that for this particular type of quadrilateral mesh there are similarities between the MESHGRID and wavelet subdivision surfaces (WSS) [22] representations. The connectivity wireframe is encoded at the lowest resolution level, which corresponds to the encoding of the base mesh in WSS, while the wavelet-based encoding of the coordinates of the reference grid corresponds to the wavelet-based encoding of the coordinates of the vertices in WSS.…”