  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. In
this release, we demonstrate the effectiveness of the proposed modules with
competitive segmentation results on S3DIS. The library will be made public
through https://github.com/hlei-ziyan/Picasso.
