An Adaptive Screen-Space Meshing Approach for Normal Integration

TL;DR

This paper presents an adaptive mesh-based method for normal integration in photometric stereo, significantly reducing vertex count and computational time compared to pixel-based approaches by leveraging surface curvature for local detail adaptation.

Contribution

It introduces a novel adaptive surface triangulation technique that improves efficiency and resolution control in normal integration by utilizing differential geometry principles.

Findings

Achieves 10 to 100 times fewer vertices than pixel grids.

Runs in minutes for high-resolution data, outperforming hours needed by pixel-based methods.

Provides well-conditioned linear systems for robust surface reconstruction.

Abstract

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.