Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)
Lingyu Liang, LianWen Jin, Yong Xu
Graph neural network (GNN) has powerful representation ability, but optimal configurations of GNN are non-trivial to obtain due to diversity of graph structure and cascaded nonlinearities. This paper aims to understand some properties of GNN from a computer vision (CV) perspective. In mathematical analysis, we propose an adaptive GNN model by recursive definition, and derive its relation with two basic operations in CV: filtering and propagation operations. The proposed GNN model is formulated as a label propagation system with guided map, graph Laplacian and node weight. It reveals that 1) the guided map and node weight determine whether a GNN leads to filtering or propagation diffusion, and 2) the kernel of graph Laplacian controls diffusion pattern. In practical verification, we design a new regularization structure with guided feature to produce GNN-based filtering and propagation diffusion to tackle the ill-posed inverse problems of quotient image analysis (QIA), which recovers the reflectance ratio as a signature for image analysis or adjustment. A flexible QIA-GNN framework is constructed to achieve various image-based editing tasks, like face illumination synthesis and low-light image enhancement. Experiments show the effectiveness of the QIA-GNN, and provide new insights of GNN for image analysis and editing.