agent-inf / mergepositionnormals

Matlab implementation of Nehab et al. 2005 "Efficiently combining positions and normals for precise 3D geometry"

MergePositionNormals

In 2005, Nehab et al. proposed a very efficient method for combining either a depth map or mesh with target surface normals:

Nehab, D., Rusinkiewicz, S., Davis, J. and Ramamoorthi, R., 2005. Efficiently combining positions and normals for precise 3D geometry. ACM transactions on graphics (TOG), 24(3), pp. 536-543.

The original paper came with a C implementation but this has become more difficult to compile over the years due to required dependencies. In this repository, we provide an efficient re-implementation of the Nehab method in Matlab.

mergeDepthNormals.m

This merges a perspective depth map and surface normal map.

Inputs:

1. Z - H x W perspective depth map
2. NM - H x W x 3 normal map in cameras coordinates
3. cx,cy,f - camera parameters
4. lambda - regularisation weight, larger means Z_merged is closer to Z
5. mask - H x W binary foreground mask (logical)

Outputs:

1. Z_merged - H x W refined depth map
2. mask - H x W mask (mask may need to be modified to compute finite differences)

mergeMeshNormals.m

This merges a mesh and per-vertex surface normals.

Inputs:

1. V - nverts x 3 matrix of vertex positions
2. F - nfaces x 3 matrix of triangle vertex indices
3. N - nverts x 3 matrix of per-vertex surface normals
4. lambda - regularisation weight, larger means Vnew is closer to V

Outputs:

1. Vnew - nverts x 3 refined vertex positions

Citation

This implementation was developed for the following paper:

Ye Yu and William A. P. Smith. Depth estimation meets inverse rendering for single image novel view synthesis. In Proc. CVMP, 2019.

in which we show how to write the depth/normal merging in terms of finite difference matrices and also include the centre of projection. If you use our implementation, you may also like to cite our paper.