Bilateral Normal Integration

Xu Cao, Hiroaki Santo, Boxin Shi, Fumio Okura, Yasuyuki Matsushita

Abstract: This paper studies the discontinuity preservation problem in recovering a surface from its surface normal map. To model discontinuities, we introduce the assumption that the surface to be recovered is semi-smooth, i.e., the surface is one-sided differentiable (hence one-sided continuous) everywhere in the horizontal and vertical directions. Under the semi-smooth surface assumption, we propose a bilaterally weighted functional for discontinuity preserving normal integration. The key idea is to relatively weight the one-sided differentiability at each point’s two sides based on the definition of one-sided depth discontinuity. As a result, our method effectively preserves discontinuities and alleviates the under- or over-segmentation artifacts in the recovered surfaces compared to existing methods. Further, we unify the normal integration problem in the orthographic and perspective cases in a new way and show effective discontinuity preservation results in both cases (Source code is available at https://github.com/hoshino042/bilateral_normal_integration .).