Revisiting One-Stage Deep Uncalibrated Photometric Stereo via Fourier Embedding

This paper introduces a one-stage deep uncalibrated photometric stereo (UPS) network, namely Fourier Uncalibrated Photometric Stereo Network (FUPS-Net), for non-Lambertian objects under unknown light directions. It departs from traditional two-stage methods that first explicitly learn lighting information and then estimate surface normals. Two-stage methods were deployed because the interplay of lighting with shading cues presents challenges for directly estimating surface normals without explicit lighting information. However, these two-stage networks are disjointed and separately trained so that the error in explicit light calibration will propagate to the second stage and cannot be eliminated. In contrast, the proposed FUPS-Net utilizes an embedded Fourier transform network to implicitly learn lighting features by decomposing inputs, rather than employing a disjointed light estimation network. Our approach is motivated from observations in the Fourier domain of photometric stereo images: lighting information is mainly encoded in amplitudes, while geometry information is mainly associated with phases. Leveraging this property, our method “decomposes” geometry and lighting in the Fourier domain as guidance, via the proposed Fourier Embedding Extraction (FEE) block and Fourier Embedding Aggregation (FEA) block, which generate lighting and geometry features for the FUPS-Net to implicitly resolve the geometry-lighting ambiguity. Furthermore, we propose a Frequency-Spatial Weighted (FSW) block that assigns weights to combine features extracted from the frequency domain and those from the spatial domain for enhancing surface reconstructions. FUPS-Net overcomes the limitations of two-stage UPS methods, offering better training stability, a concise end-to-end structure, and avoiding accumulated errors in disjointed networks. Experimental results on synthetic and real datasets demonstrate the superior performance of our approach, and its simpler training setup, potentially paving the way for a new strategy in deep learning-based UPS methods.