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.

本文提出了用于不规则结构和几何输入的变体卷积神经网络 —— 基于样条的卷积神经网络，其创新之处在于基于 B 样条的卷积算子，使得计算时间不受卷积核大小的影响。作者在图像图形分类、形状对应和图节点分类等任务中验证了该方法的有效性。