WorDepth: Variational Language Prior for Monocular Depth Estimation
Authors: Ziyao Zeng, Daniel Wang, Fengyu Yang, Hyoungseob Park, Stefano Soatto, Dong Lao, Alex Wong

Three-dimensional (3D) reconstruction from a single image is an ill-posed problem with inherent ambiguities i.e. scale. Predicting a 3D scene from text description(s) is similarly ill-posed i.e. spatial arrangements of objects described. We investigate the question of whether two inherently ambiguous modalities can be used in conjunction to produce metric-scaled reconstructions. To test this we focus on monocular depth estimation the problem of predicting a dense depth map from a single image but with an additional text caption describing the scene. To this end we begin by encoding the text caption as a mean and standard deviation; using a variational framework we learn the distribution of the plausible metric reconstructions of 3D scenes corresponding to the text captions as a prior. To "select" a specific reconstruction or depth map we encode the given image through a conditional sampler that samples from the latent space of the variational text encoder which is then decoded to the output depth map. Our approach is trained alternatingly between the text and image branches: in one optimization step we predict the mean and standard deviation from the text description and sample from a standard Gaussian and in the other we sample using a (image) conditional sampler. Once trained we directly predict depth from the encoded text using the conditional sampler. We demonstrate our approach on indoor (NYUv2) and outdoor (KITTI) scenarios where we show that language can consistently improve performance in both. Code: https://github.com/Adonis-galaxy/WorDepth.