Surface normal integration is a fundamental problem in computer vision, dealing with the objective of reconstructing a surface from its corresponding normal map. Existing approaches require an iterative global optimization to jointly estimate the depth of each pixel, which scales poorly to larger normal maps. In this paper, we address this problem by recasting normal integration as the estimation of relative scales of continuous components. By constraining pixels belonging to the same component to jointly vary their scale, we drastically reduce the number of optimization variables. Our framework includes a heuristic to accurately estimate continuous components from the start, a strategy to rebalance optimization terms, and a technique to iteratively merge components to further reduce the size of the problem. Our method achieves state-of-the-art results on the standard normal integration benchmark in as little as a few seconds and achieves one-order-of-magnitude speedup over pixel-level approaches on large-resolution normal maps.

翻译：表面法向积分是计算机视觉中的一个基础问题，其目标是从对应的法向图重建表面。现有方法需要通过迭代全局优化来联合估计每个像素的深度，在处理较大法向图时扩展性较差。本文通过将法向积分重新定义为连续分量相对尺度的估计来解决这一问题。通过约束属于同一分量的像素共同调整其尺度，我们大幅减少了优化变量的数量。我们的框架包含一种从初始阶段准确估计连续分量的启发式方法、一种重新平衡优化项的策略，以及一种迭代合并分量以进一步缩小问题规模的技术。我们的方法在标准法向积分基准测试中仅需数秒即可达到最先进的结果，并在高分辨率法向图上相比像素级方法实现了一个数量级的加速。