RTF2Mesh: Restricted Tangent Face Based Mesh Compression With Neural Displacement Fields.

In recent years, encoding explicit mesh surfaces into compact neural representations has emerged as a prominent research direction. Compression ratio and representation accuracy present a fundamental trade-off for evaluating such algorithms. Traditional approaches typically decompose the input mesh into two components: a simplified base mesh and a neural displacement field. However, this paradigm faces inherent limitations. First, employing triangles or quadrilaterals as geometric primitives necessitates the explicit storage of vertex connectivity, incurring substantial memory overhead. Second, existing approaches typically treat base mesh generation as a decoupled preprocessing step, failing to fully leverage automatic differentiation frameworks to optimize the distribution of the base mesh. To address these issues, we propose RTF2Mesh, a method that achieves compact representation using only unstructured point clouds with feature vectors and network parameters. At its core, our approach leverages a meshless vertex-normal representation derived from the Restricted Tangent Face (RTF). Furthermore, we employ the Kolmogorov-Arnold Network (KAN) to encode both the displacement information and the normals of the vertex-normal representation. The KAN is chosen for its superior parameter efficiency compared to traditional Multi-Layer Perceptrons (MLPs). These two improvements enable RTF2Mesh to achieve a more compact neural representation while eliminating the need for explicit storage of vertex connectivity. During decoding, surface normals are reconstructed from the input point cloud using the KAN's learned weights to generate a base surface. The KAN-based network then predicts the displacements of the subdivided base surface, producing a high-resolution triangle mesh. Compared to current state-of-the-art (SOTA) methods, RTF2Mesh achieves highly competitive performance at equivalent compression rates.