NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction - Supplementary Material - A Derivation for Computing Opacity α

In this section we will derive the formula in Eqn. 13 of the paper for computing the discrete opacity It follows from Eqn. 12 of the paper that, α Eqn. 12 of the paper, we have α According to Eqn. 5 of the paper, the weight function w (t) is given by w (t) = T ( t) ρ (t), where ρ (t) = max null ( f ( p(t)) v) φ In this section we show that the weight function derived in naive solution is biased. According to Eqn. 8, the derivative of w (t) is given by: dw dt = T ( t) null dσ ( t) dt σ (t) Based on Eqn. 10 and Eqn. Therefore, the total number of sampled points for NeuS is 128. Figure 2: The section points and mid-points defined on a ray. E.1 Rendering Quality and Speed Besides the reconstructed surfaces, our method also renders high-quality images, as shown in Figure 4. Rendering an image in resolution of 1600x1200 costs about 320 seconds in the default In this experiment, we held out 10% of the images in the DTU dataset as the testing set and the others as the training set. As shown in Table 3, our method achieves comparable performance to NeRF.