Cross-Atlas Convolution for Parameterization Invariant Learning on Textured Mesh Surface

We present a convolutional network architecture for direct feature learning on mesh surfaces through their atlases of texture maps. The texture map encodes the parameterization from 3D to 2D domain, rendering not only RGB values but also rasterized geometric features if necessary. Since the parameterization of texture map is not pre-determined, and depends on the surface topologies, we therefore introduce a novel cross-atlas convolution to recover the original mesh geodesic neighborhood, so as to achieve the invariance property to arbitrary parameterization. The proposed module is integrated into classification and segmentation architectures, which takes the input texture map of a mesh, and infers the output predictions. Our method not only shows competitive performances on classification and segmentation public benchmarks, but also paves the way for the broad mesh surfaces learning.