Calibration-free single-pixel 3D imaging

The pursuit of high-fidelity single-pixel 3D imaging has been limited by complex system calibration and extensive measurements. Here, we present a calibration-free photometric stereo framework that integrates Fourier single-pixel imaging with deep learning for efficient 3D reconstruction. A single-pixel system is developed to acquire photometric measurements from different viewpoints based on the Helmholtz reciprocity principle. By combining physics-informed reconstruction with data-driven degradation compensation, the proposed framework enables robust normal estimation from degraded Fourier single-pixel measurements without explicit system calibration. Experiments demonstrate reliable reconstruction from experimentally acquired undersampled measurements, where two photometric measurements are sufficient for objects without significant self-occlusion. The reconstructed standard sphere achieves a mean absolute height error of 0.35 pixels, corresponding to 1.95% of the fitted sphere radius. Quantitative evaluations on the public DiLiGenT dataset further validate accurate normal reconstruction on complex objects. This work provides an effective approach for calibration-free and measurement-efficient single-pixel 3D imaging.