SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels

TL;DR

SplineCNN introduces a novel B-spline based convolution operator for geometric deep learning, enabling fast, domain-independent processing of irregular structures like graphs and meshes with end-to-end trainability.

Contribution

The paper proposes a continuous B-spline kernel convolution operator that is computationally efficient and generalizes traditional CNNs for irregular geometric data.

Findings

Outperforms state-of-the-art methods in graph and shape tasks

Faster computation due to local support of B-splines

Supports end-to-end training with minimal handcrafted features

Abstract

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence.