  3D surface reconstruction from multi-view images is essential for scene
understanding and interaction. However, complex indoor scenes pose challenges
such as ambiguity due to limited observations. Recent implicit surface
representations, such as Neural Radiance Fields (NeRFs) and signed distance
functions (SDFs), employ various geometric priors to resolve the lack of
observed information. Nevertheless, their performance heavily depends on the
quality of the pre-trained geometry estimation models. To ease such dependence,
we propose regularizing the geometric modeling by explicitly encouraging the
mutual information among surface normals of highly correlated scene points. In
this way, the geometry learning process is modulated by the second-order
correlations from noisy (first-order) geometric priors, thus eliminating the
bias due to poor generalization. Additionally, we introduce a simple yet
effective scheme that utilizes semantic and geometric features to identify
correlated points, enhancing their mutual information accordingly. The proposed
technique can serve as a plugin for SDF-based neural surface representations.
Our experiments demonstrate the effectiveness of the proposed in improving the
surface reconstruction quality of major states of the arts. Our code is
available at: \url{https://github.com/Muliphein/InfoNorm}.
