SCAN-BASED COMPRESSION OF 3D MESH SEQUENCES WITH GEOMETRY COMPENSATION Yasmine Boulfani and Marc Antonini Laboratoire I3S - UMR 6070 CNRS , Universit´ e de Nice - Sophia Antipolis Route des Lucioles - 06903 Sophia Antipolis FRANCE phone: +33 4 92 94 27 22, fax: +33 4 92 94 28 98, email: {boulfani,am}@i3s.unice.fr ABSTRACT We introduce in this paper a new compression process to en- code the geometry of 3D mesh sequences (with a fixed con- nectivity). The proposed method uses a scan-based wavelet transform with an original approach which consists to com- pensate the geometry displacements of the mesh sequence. The proposed coder is based on temporal lifting scheme and bit allocation using statistical models for the probability den- sities of the temporal wavelet coefficients. Then, scalar quan- tization and entropy coding are used to encode the quantized subbands and the geometry displacement vectors. The re- sulting compression scheme shows that good coding perfor- mances are obtained when the compensation of the geometry is done on the whole sequence, which requires large memory. Furthermore, we showed that when low memory scan-based compression is done, the performances of the encoder ap- proach the ones obtained when the whole sequence is known. Also, simulation results show that the proposed algorithm provides better compression performances than some state of the art coders. 1. INTRODUCTION The continuous development of the multimedia hardware and software causes an increasing interest for the use of 3D contents which permit a three-dimensional modeling of the real world. Although animated sequence of 3D meshes may be produced and represented in a variety of ways, they are of- ten stored and transmitted as series of consecutive triangular meshes generally called frames. Each frame is defined by the location of the vertices (geometry) and by a triangle/vertex incidence graph (connectivity). In general, the meshes are irregular, and the connectivity of the meshes may also evolve with time. Nevertheless, in this paper, we restrict our at- tention to a class of animations in which the connectivity is identical in all frames. Similarly to several techniques [1, 3, 4, 5], we propose an efficient way to compress animated sequences by consid- ering the sequence as geometric deformations of the geom- etry of the first frame. Among these techniques, Alexa and M¨ uller [1] , proposed a coding scheme based on the Principal Component Analysis (PCA). Karni and Gotsman improved this method by further exploiting the spatial and temporal co- herence and finally encode the principal components with a predictive coding scheme called LPC [5]. Also, Ibarria and Rossignac proposed a method which predicts the position of a vertex by using the already decoded vertices of its spatial neighbourhood and its position in previous frames[4]. Fi- nally, Guskov and Khodakovsky presented recently a com- pression algorithm based on a multiresolution analysis [3]. In their work the analysis is applied on the geometry of each frame to obtain a multiresolution representation. A predic- tive coding scheme is then applied on the resulting details of each frame. In this paper, we propose an alternative compression method using scan-based compression of 3D mesh sequences with geometry displacement compensation. More precisely, a scan-based estimation of the geometry displacement is done providing displacement vectors. These vectors are then used for the geometry displacement compensation before ap- plying the temporal wavelet transform. To reduce their cost, the displacement vectors are entropy coded. A scan-based temporal wavelet decomposition is applied on the compensated mesh sequence to get different temporal subbands which are encoded with a model-based bit alloca- tion proposed in [8]. This scan-based compression method requires low memory and allows to approach the coding per- formances when the whole sequence can be stored in mem- ory. The rest of this paper is organized as follows. Section 2 describes the structure of the proposed compression scheme. Section 3 deals with the scan-based wavelet transform using the geometry compensation. Section 4 presents the alloca- tion process included in the proposed coder. Experimental results are given and compared to results of several state of the art methods in Section 5. We finally conclude and pro- pose future works in section 6. 2. COMPRESSION SCHEME Figure 1 shows the global structure of the proposed compres- sion algorithm. The main steps of the algorithm are the following: • Compensation of the geometry and estimation of the displacement vectors: This is an essential step of the proposed coding scheme. Contrary to most of video coders, we do not have to use a motion estimation algo- rithm to match the current vertices with vertices of pre- vious frames before applying the temporal wavelet trans- form [2]. Here, the processed data are geometric posi- tions in space, and as the connectivity is the same for each frame involving a fixed number of vertices along the sequence, the motion of each vertex is implicit. The es- timation of the geometry displacement can then be com- puted analytically providing displacement vectors. This process is detailled in Section 3. • Temporal wavelet transform: A decomposition on sev- eral levels allows to get the low-frequency (LF) subband, which represents a coarse version of the compensated sequence, and sequences of wavelet coefficients which represent the high frequency (HF) details. The retained