Coherent Enhancement of Depth Images and Normal Maps Using Second-Order Geometric Models on Weighted Finite Graphs

High-quality depth and normal maps play a crucial role in various image processing and computer vision applications. However, the noisy data from sensors requires meticulous pre-processing. Denoising depth and normals separately, can lead to inconsistent geometric information, neg. atively impacting the performance of applications relying on this data. While some recent studies have suggested joint denoising approaches that aim to achieve coherent geometric representations, these methods are based on simple geometric assumptions, such as piecewise planar regions, and thus suffer from lower accuracy for non-planar geometry. In this paper, we present a versatile non-planar model specifically designed to handle both planar and non-planar geometry. To achieve this, we formulate the underlying problem as a partitioning of our non-planar model parameters on weighted finite graphs. Solving this problem involves utilizing a modified version of the Cut Pursuit algorithm, which efficiently divides input data into regions of similar geometric models. Finally, we leverage these resulting partitions and their associated model parameters to compute a denoised and infilled depth image, along with its coherent normal map.