Solving Well-posed Shape from Shading Problem Using Implicit Neural Representations

We propose a method for solving well-posed shape from shading problem by using implicit neural representations. We build an image irradiance equation and solve the equation by a sinusoidal representation network called SIREN, which is proposed by Sitzmann et al. in 2020. Object surface is expressed by Oren-Nayar model and a perspective projection model with light source located at the optical center is considered. Based on the above models, image irradiance equation is constructed, which is a partial differential equation (PDE). We introduce a neural network SIREN to solve this PDE, where implicit neural representations use the sine as a periodic activation function. Experiments are performed on three synthetic images and two real images. Results demonstrate that our proposed method performs with much higher accuracy.