Shape from Shading by Model Inclusive Learning Method with Simultaneous Estimation of Parameters

The problem of recovering shape from shading is important in computer vision and robotics. It is essentially an ill-posed problem and several studies have been done. In this paper, we present a versatile method of solving the problem by neural networks. The proposed method introduces the concept of the model inclusive learning with simultaneous estimation of unknown parameters. In the method a mathematical model, which we call ‘image-formation model’, expressing the process that the image is formed from an object surface, is introduced and is included in the learning loop of a neural network. The neural network is trained so as to recover the shape with simultaneously estimating unknown parameters in the image-formation model. The performance of the proposed method is demonstrated through experiments.