Patch-Based Optimization for Noise-Robust Reconstruction of Specular Surfaces

Surface reconstruction is a challenging task in computer vision, particularly when it involves specular or mirrored objects. The problem becomes even more complex due to real-world application limitations, such as having a single camera view and pattern plane. In this work, the problem of specular surface reconstruction from a single viewpoint is formulated as an optimization process that satisfies both geometrical and optical constraints. To this end, a patch-wise approach is developed to complete the entire depth map. For each patch, the optimization process aims to minimize the angle between geometric normals and normals derived from reflections. This process is propagated across the entire depth map to reconstruct the whole surface. Experimental results demonstrate that the proposed method is robust to noise in reflection point correspondences. Since there is no publicly-available dataset for this task, this paper develops a pipeline for generating synthetic data.