P2Voxel: Pyramid Pivot Voxelization for 3D Mesh Tokenization

Triangle meshes provide explicit and accurate surface geometry, yet their irregular topology connectivity makes 3D mesh tokenization a geometric sampling problem: how to sample and organize geometric evidence into compact, structured and learnable tokens. Beyond field-centric volumetric sampling and edge-intersection surface sampling, we retarget mesh tokenization as local surface evidence sampling: identifying the minimal geometric evidence inside each active voxel that is sufficient for deterministic surface recovery. To this end, we introduce P2Voxel, a pyramid pivot voxelization framework for compact and reconstruction-aware mesh tokenization. P2Voxel is built on three key innovations. Under the Local Planarity assumption, Pivot Voxelization represents each active voxel with a surface pivot and an orientation sign, providing minimal local evidence that can induce the corner values required for deterministic reconstruction. Under the Spatial Complexity assumption, Pyramid Pivot Voxelization exploits the spatial non-uniformity of real surfaces by allocating finer pivot tokens to geometrically complex regions while keeping smooth regions coarse and compact. Under the Block Reconstructability assumption, a Pyramid VAE learns compact multi-resolution latent codes over locally reconstructable pivot blocks, avoiding the need to model the entire high-resolution voxelized shape as a dense global field. Together, these designs convert meshes into compact, structured, and learnable pyramid pivot tokens, enabling efficient mesh reconstruction for downstream 3D tasks.