An Adaptive Screen-Space Meshing Approach for Normal Integration
This work addresses a key bottleneck in photometric stereo for researchers and practitioners by enabling faster and more efficient surface reconstruction, though it is an incremental improvement over existing methods.
The paper tackles the problem of reconstructing surfaces from normals in photometric stereo by introducing an adaptive screen-space meshing approach that uses curvature from normals to create sparse triangle meshes, resulting in 10 to 100 times fewer vertices than pixels and reducing runtime from hours to minutes for 64 MP normal maps.
Reconstructing surfaces from normals is a key component of photometric stereo. This work introduces an adaptive surface triangulation in the image domain and afterwards performs the normal integration on a triangle mesh. Our key insight is that surface curvature can be computed from normals. Based on the curvature, we identify flat areas and aggregate pixels into triangles. The approximation quality is controlled by a single user parameter facilitating a seamless generation of low- to high-resolution meshes. Compared to pixel grids, our triangle meshes adapt locally to surface details and allow for a sparser representation. Our new mesh-based formulation of the normal integration problem is strictly derived from discrete differential geometry and leads to well-conditioned linear systems. Results on real and synthetic data show that 10 to 100 times less vertices are required than pixels. Experiments suggest that this sparsity translates into a sublinear runtime in the number of pixels. For 64 MP normal maps, our meshing-first approach generates and integrates meshes in minutes while pixel-based approaches require hours just for the integration.