From Phase to Phenomenon: Self-Supervised Learning of Subsurface Scattering with Minimal Phase-shift Inputs
Authors: Arjun Majumdar, Raphael Braun, Andreas Engelhardt, Hendrik PA. Lensch
Organizations: Eberhard Karls Universität Tübingen, Germany
Abstract
We propose a self-supervised pretraining framework for learning sub-surface scattering (SSS) light transport representations from minimal input. Our method leverages a stereo projector-camera setup that captures only eight high-frequency phase-shift profilometry (PSP) images per view to pretrain an encoder in a multi-view, multi-object setting. We introduce a tailored augmentation strategy for PSP-based SSS data, and show that it significantly outperforms standard ImageNet-style augmentations for SSL pretraining. The pretrained encoder learns generalizable SSS representations that transfer effectively to downstream tasks, including spatially varying relighting and representation evaluation using a kNN classifier. Combined with a decoder, the model reconstructs dense scattering footprint responses, trained using a dedicated cost function that improves accuracy, particularly for anisotropic footprints. Despite using only eight input images per view, our approach generalizes to unseen objects with complex geometry and material properties, achieving high-fidelity reconstructions while requiring orders of magnitude fewer images than prior methods.
We present a method to acquire and estimate the sub-surface scattering properties of light transport at a highly detailed level by learning the pixel footprint response at each point on the object surface. The reconstruction leverages 3D scanning techniques as input to a U-Net CNN. A stereo projector-camera setup using phase-shifted profilometry (PSP) patterns efficiently captures the data for a variety of scattering objects. Reconstructing dense pixel footprints allows for relighting with arbitrary high-resolution projector patterns. The final output is a relit color image. Qualitative and quantitative comparison against illuminated real-world captured images demonstrate that the predicted footprints are almost identical to the actual responses. The same model is trained for multiple views across multiple objects such that the learned representations can be used to generalize to unseen sub-surface scattering materials as well.
Single-shot fringe projection profilometry (FPP) has been actively studied for real-time measurement, dynamic object reconstruction, and motion-sensitive environments. Composite fringe patterns are advantageous in single-shot FPP because multiple frequency components can be encoded in a single pattern, enabling phase ambiguity resolution. Existing approaches mainly rely on Fourier transform-based methods or supervised deep learning methods. However, Fourier transform-based methods often suffer from limited accuracy and degraded performance in complex regions, while supervised methods require dense phase or depth labels, which are costly to obtain. In this work, we propose a self-supervised phase refinement framework for single-shot composite fringe patterns without requiring phase or depth labels. The proposed method exploits the scale and direction relationships between low- and high-frequency phase gradients, improving the reliability of phase separation. We also introduce a soft edge consistency loss to preserve object boundaries and fine geometric structures. Experimental results show that the proposed method achieves MAE_z and RMSE_z of 0.367 mm and 1.804 mm, respectively, outperforming the best-performing transform-based baseline, which obtains 0.402 mm and 2.785 mm. The proposed method also improves the valid-pixel ratio from 84.75 % to 95.07 %. These results demonstrate the effectiveness of self-supervised dual-frequency phase refinement for reliable single-shot 3D reconstruction without ground-truth label supervision.
Optical scattering has conventionally been regarded as an impediment in imaging research due to the degradation of image quality during reconstruction. Nevertheless, this study explores two cases in which optical scattering may serve a beneficial role in image reconstruction tasks. We compared the No Scattering MNIST dataset with three Scattering MNIST datasets, each generated under distinct scattering conditions. To assess the information content of the resulting speckle patterns, we employed a Variational Autoencoder (VAE) approach which achieves accuracy comparable to state-of-the-art deep learning approaches, but has an interpretable latent space. We find that scattering can enhance data robustness against spatial pixel loss by effectively distributing information. We also demonstrate that scattering can enable distinctions of focal depth information. We anticipate that these findings will contribute to more efficient imaging techniques, particularly in the presence of obstacles and three-dimensional signals.