Picasso: A CUDA-based Library for Deep Learning over 3D Meshes (2103.15076v1)

Abstract: 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.

• The paper introduces GPU-accelerated mesh simplification that is approximately 30 times faster than traditional quadric error metrics.
• It presents three innovative convolution operations—facet2vertex, vertex2facet, and facet2facet—that redefine feature extraction on 3D meshes.
• The Picasso library demonstrates competitive semantic segmentation performance, opening new avenues for efficient geometric deep learning.

An Analysis of Picasso: A CUDA-based Library for Deep Learning over 3D Meshes

The paper introduces Picasso, a CUDA-based library tailored to enhancing deep learning capabilities over 3D meshes. It tackles a challenging aspect of geometric deep learning by advancing efficient and specialized operations on 3D mesh data, diverging from conventional graph-based methods.

The authors foreground a GPU-accelerated mesh decimation technique fundamentally distinct from prior CPU-based methods, which often impeded real-time applications of multi-scale feature learning in 3D meshes. By leveraging GPU strengths, Picasso significantly reduces computational overhead. The analysis reveals an impressive speed advantage, with the proposed mesh simplification algorithm being approximately 30 times faster than the traditional quadric error metrics (QEM) method.

Central to Picasso's contributions are three novel convolutional operations designed for meshes: facet2vertex, vertex2facet, and facet2facet convolutions. These convolutions facilitate learning by treating meshes as geometric structures composed of vertices and facets, a departure from the traditional edge-focused graph-based treatment. Notably, the paper highlights the adaptability and robustness of facet2vertex convolution through a fuzzy mechanism, which employs Gaussian mixtures and barycentric interpolation to accommodate variations in vertex density and mesh sampling.

The practical implications of these contributions are demonstrated through competitive semantic segmentation results on the S3DIS dataset. PicassoNet, the library's reference network, showcases strong segmentation performance, comparable to and sometimes surpassing contemporary methods such as KPConv and DCM-Net. The network achieves high accuracy metrics, accentuating the effectiveness of the proposed confluent approach of mesh and point cloud-based module integration.

The implications of this work extend beyond immediate performance metrics. The introduction of GPU-accelerated operations points toward significant practical enhancements in processing speed and efficiency. Moreover, the methodological shift from edge-centric graphs to facet-vertex structures introduces a new avenue for conceptualizing 3D mesh data, which could influence future model architectures and the broader field of geometric deep learning. The Picasso library's open-source release further invites community engagement, suggesting potential refinements and expansions in its capabilities.

Future research directions could explore further optimization of these convolutional architectures, additional applications in 3D semantic segmentation, and integration with other 3D data types beyond meshes and point clouds. Moreover, expanding Picasso’s applicability across diverse domains such as robotics, autonomous navigation, and virtual reality would leverage its computational advantages across a range of real-world applications.