Phase unwrapping via shadow-embedded ordinal regression for fringe projection measurement of discontinuous objects

In fringe projection profilometry, deep learning (DL) techniques have been applied for phase-unwrapping to enhance the robustness of measurement under low signal-to-noise ratio (SNR) conditions. However, conventional DL-based phase-unwrapping methods exhibit inherent limitations in processing phase maps of discontinuous or isolated surfaces. To address this issue, this paper proposes a shadow-embedded ordinal regression method. It formulates phase-unwrapping procedure as an ordinal regression task instead of a conventional classification or direct regression task, thereby reducing large erroneous phase jumps and simultaneously avoiding edge blurring. To bridge the phase gaps between discontinuous or isolated surfaces, object shadows in fringe patterns are exploited as informative cues, owing to their inherent dependence on object heights. A shadow-distance transform map as a constraint is integrated into the network, thus enabling it to infer true phase jumps across isolated regions. Experimental results demonstrate that, when measuring the phases of discontinuous or isolated surfaces, this method achieves substantially higher robustness compared to the existing methods.