Position-dependent partial convolutions for supervised spatial interpolation

Acquiring continuous spatial data, e.g., spatial ground motion is essential to assess the damaged area and appropriately assign rescue and medical teams. To this purpose, spatial interpolation methods have been developed to estimate the value of unobserved points linearly from neighbor observed values, i.e., inverse distance weighting and Kriging. Recently, realistic spatial continuous environmental data with various scenarios can be generated by 3D finite difference methods with a high-resolution structure model. It enables us to collect supervised data even for unobserved points. Along this line, we propose a framework of supervised spatial interpolation and apply highly advanced deep inpainting methods where we treat spatially distributed observed points as a masked image and non-linearly expand them through convolutional encoder-decoder networks. However, the property of translation invariance would avoid locally fine-grained interpolation since the relation between the target and surrounding observation points varies over regions due to its topography and subsurface structure. To overcome this problem, we propose introducing position-dependent convolution where kernel weights are adjusted depending on their position on an image based on the trainable position-feature map. We show the effectiveness of our proposed method, called, PoDIM (Position-dependent Deep Inpainting Method), through experiments using simulated ground-motion data.