IMD-Net: A Deep Learning-Based Icosahedral Mesh Denoising Network

Abstract

In this work, we propose a novel denoising technique, the icosahedral mesh denoising network (IMD-Net) for closed genus-0 meshes. IMD-Net is a deep neural network that produces a denoised mesh in a single end-to-end pass, preserving and emphasizing natural object features in the process. A preprocessing step, exploiting the homeomorphism between genus-0 mesh and sphere, remeshes an irregular mesh using the regular mesh structure of a frequency subdivided icosahedron. Enabled by gauge equivariant convolutional layers arranged in a residual U-net, IMD-Net denoises the remeshing invariant to global mesh transformations as well as local feature constellations and orientations, doing so with a computational complexity of traditional conv2D kernel. The network is equipped with carefully crafted loss function that leverages differences between positional, normal and curvature fields of target and noisy mesh in a numerically stable fashion. In a first, two large shape datasets commonly used in related fields, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ABC</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ShapeNetCore</i> , are introduced to evaluate mesh denoising. IMD-Net’s competitiveness with existing state-of-the-art techniques is established using both metric evaluations and visual inspection of denoised models. Our code is publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/jjabo/IMD-Net</uri> .