2D Neural Fields with Learned Discontinuities
This addresses the limitation of existing neural fields in handling discontinuities for digital image processing tasks like denoising and super-resolution, representing an incremental advance.
The paper tackled the problem of representing 2D images with sharp discontinuities using neural fields, achieving improvements of over 5dB in denoising and 10dB in super-resolution compared to InstantNGP, and Chamfer distances 3.5x closer to ground truth for discontinuity capture.
Effective representation of 2D images is fundamental in digital image processing, where traditional methods like raster and vector graphics struggle with sharpness and textural complexity respectively. Current neural fields offer high-fidelity and resolution independence but require predefined meshes with known discontinuities, restricting their utility. We observe that by treating all mesh edges as potential discontinuities, we can represent the magnitude of discontinuities with continuous variables and optimize. Based on this observation, we introduce a novel discontinuous neural field model that jointly approximate the target image and recovers discontinuities. Through systematic evaluations, our neural field demonstrates superior performance in denoising and super-resolution tasks compared to InstantNGP, achieving improvements of over 5dB and 10dB, respectively. Our model also outperforms Mumford-Shah-based methods in accurately capturing discontinuities, with Chamfer distances 3.5x closer to the ground truth. Additionally, our approach shows remarkable capability in handling complex artistic drawings and natural images.