SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels
This work addresses the challenge of applying convolutional neural networks to irregular data structures like graphs and meshes, which is important for domains such as computer graphics and network analysis, representing a novel method for a known bottleneck rather than an incremental improvement.
The authors tackled the problem of performing deep learning on irregular geometric structures like graphs and meshes by introducing SplineCNN, a novel convolution operator based on B-splines that makes computation time independent of kernel size, resulting in state-of-the-art performance on tasks such as image graph classification and shape correspondence while being significantly faster.
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.