RPCC: Rectified Pearson Correlation Coefficient for Radiance Fields Optimization

Neural radiance fields (NeRF) and its variants have achieved remarkable success for novel view synthesis. Most existing radiance field models utilize the mean squared error (MSE) as the photometric loss, which is prone to resulting in blurriness and geometry inaccuracy, especially for sparse views. Instead of the pixel-wise loss, we introduce the Pearson correlation coefficient (PCC) for constructing a new photometric loss from the perspective of linear correlation. Due to the relativeness of PCC, we rectify PCC to absolutize it. To be specific, we relax the denominator of PCC based on the inequality of arithmetic and geometric means to enforce unit scale, and add an extra modulation factor to further enforce zero location. The experimental results show the proposed loss is significantly better than the MSE loss, e.g. the peak signal-to-noise ratio (PSNR) increasing by 186% for TensoRF on Replica dataset, and 3 $\sim$ 5 dB for DVGO at scenes from Tanks and Temples dataset with sparse views setting.