## Picasso: A CUDA-based Library for Deep Learning over 3D Meshes

### Introduction

The Picasso Library is intended for complex real-world applications with large-scale surfaces, while it also performs impressively on the small-scale applications over synthetic shape manifolds. We have upgraded the point cloud modules of *SPH3D-GCN* from homogeneous to heterogeneous representations, and included the upgraded modules into this latest work as well. We are happy to announce that the work is accepted to IEEE CVPR2021.

We present Picasso, a CUDA-based library comprising novel modules for deep learning over complex real-world 3D meshes. Hierarchical neural architectures have proved effective in multi-scale feature extraction which signifies the need for fast mesh decimation. However, existing methods rely on CPU-based implementations to obtain multi-resolution meshes. We design GPU-accelerated mesh decimation to facilitate network resolution reduction efficiently on-the-fly. Pooling and unpooling modules are defined on the vertex clusters gathered during decimation. For feature learning over meshes, Picasso contains three types of novel convolutions namely, facet2vertex, vertex2facet, and facet2facet convolution. Hence, it treats a mesh as a geometric structure comprising vertices and facets, rather than a spatial graph with edges as previous methods do. Picasso also incorporates a fuzzy mechanism in its filters for robustness to mesh sampling (vertex density). It exploits Gaussian mixtures to define fuzzy coefficients for the facet2vertex convolution, and barycentric interpolation to define the coefficients for the remaining two convolutions.