Reconstrucción 3D de objetos especulares cóncavos mediante imágenes de un solo píxel y representaciones implícitas

3D reconstruction of concave specular objects poses significant challenges in computer vision, industrial inspection, optical calibration, and augmented reality. Their complex geometry, strong specular reflections, and multiple interreflections make accurate light-path correspondence extraction difficult, rendering it an open problem in 3D vision. To address this, we propose a two-stage framework that combines Fourier-based single-pixel imaging and implicit surface representation. First, reflected light is captured and decomposed into single and multiple reflection components to obtain reliable point-to-ray correspondences. Then, these correspondences serve as physical priors to constrain SDF-based reconstruction, enabling precise geometry recovery. Experiments on synthetic and real data demonstrate superior robustness and adaptability over traditional methods under complex reflective conditions.