Discontinuity-preserving Normal Integration with Auxiliary Edges (2404.03138v1)
Abstract: Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To reconstruct an accurate depth map from the input normal map, hidden surface gradients occurring from the jumps must be handled. To model these jumps correctly, we design a novel discretization scheme for the domain of normal integration. Our key idea is to introduce auxiliary edges, which bridge between piecewise-smooth patches in the domain so that the magnitude of hidden jumps can be explicitly expressed. Using the auxiliary edges, we design a novel algorithm to optimize the discontinuity and the depth map from the input normal map. Our method optimizes discontinuities by using a combination of iterative re-weighted least squares and iterative filtering of the jump magnitudes on auxiliary edges to provide strong sparsity regularization. Compared to previous discontinuity-preserving normal integration methods, which model the magnitudes of jumps only implicitly, our method reconstructs subtle discontinuities accurately thanks to our explicit representation of jumps allowing for strong sparsity regularization.
- Renderpeople-scanned 3d people models provider. http://renderpeople.com.
- A survey of photometric stereo techniques. Foundations and Trends in Computer Graphics and Vision, 9(3-4):149–254, 2015.
- An algebraic approach to surface reconstruction from gradient fields. In Proc. ICCV, Beijing, China, 2005. IEEE.
- What Is the Range of Surface Reconstructions from a Gradient Field? In Proc. ECCV, Berlin, Heidelberg, 2006. Springer Berlin Heidelberg.
- Bilateral normal integration. In Proc. ECCV. Springer, 2022.
- Iteratively reweighted algorithms for compressive sensing. In Proc. ICASSP. IEEE, 2008.
- Combinatorial Surface Integration. In Proc. ICPR, Hong Kong, China, 2006. IEEE.
- Mesh denoising via l 0 minimization. ACM Transactions on Graphics (TOG), 32(4):1–8, 2013.
- Methods of conjugate gradients for solving linear systems. Journal of research of the National Bureau of Standards, 49(6):409–436, 1952.
- The variational approach to shape from shading. Computer Vision, Graphics, and Image Processing, 33(2):174–208, 1986.
- Reconstructing discontinuous surfaces from a given gradient field using partial integrability. Computer Vision and Image Understanding, 92(1):78–111, 2003.
- Sgdr: Stochastic gradient descent with warm restarts. In Proc. ICLR, 2016.
- Normal Integration: A Survey. Journal of Mathematical Imaging and Vision, 60(4):576–593, 2018a.
- Variational Methods for Normal Integration. Journal of Mathematical Imaging and Vision, 60(4):609–632, 2018b.
- A robust multi-scale integration method to obtain the depth from gradient maps. Computer Vision and Image Understanding, 116(8):882–895, 2012.
- A benchmark dataset and evaluation for non-lambertian and uncalibrated photometric stereo. In Proc. CVPR, pages 3707–3716, 2016.
- Visible Surface Reconstruction from Normals with Discontinuity Consideration. In Proc. CVPR, New York, NY, USA, 2006. IEEE.
- Surface-from-Gradients: An Approach Based on Discrete Geometry Processing. In Proc. CVPR, 2014.
- Econ: Explicit clothed humans optimized via normal integration. In Proc. CVPR, 2023.
- Image smoothing via l 0 gradient minimization. In Proc. SIGGRAPH Asia, 2011.