Applying Albedo Estimation and Implicit Neural Representations to Well-Posed Shape From Shading

We present a method that improves the accuracy of depth maps by combining albedo estimation and implicit neural representations to the well-posed shape from shading. Because the estimation of depth information from a single image is an under-constrained problem, we apply certain physical constrains to convert the ill-posed shape from shading problem to a well-posed problem. Subsequently, we construct an image irradiance equation wherein the surface parameter representing albedo is estimated using a learning-based encoder-decoder network. By solving the equation using implicit neural representations, we can obtain a depth map of the original image. The proposed method achieves an accuracy of depth estimation from a single image with the mean absolute error (MAE) of 0.1510 and root mean square error (RMSE) of 0.1768, indicating superior performance to that of existing methods. Both simulation and real experiments have been carried out to verify the effectiveness of the proposed method.