Hierarchical Color-Assisted Absolute Phase Retrieval with Guide-Phase Refinement for Dual-Projector Fringe Projection Profilometry

Accurate three-dimensional reconstruction of discontinuous and discrete objects remains challenging in fringe projection profilometry because abrupt depth changes, self-occlusion, and shadowed regions can introduce fringe-order ambiguities and phase artifacts. We propose a dual-projector color-coded fringe projection method that combines hierarchical staircase phase coding, guide-phase refinement, and complementary phase measurements for absolute phase reconstruction. For each projector, four grayscale phase-shifting patterns are used for wrapped-phase recovery, while four color-encoded patterns simultaneously provide fine and coarse fringe-order information. The red-channel code determines the local fringe-order state, whereas the blue-channel code resolves periodicity ambiguities over the measurement range. The decoded fringe-order map is combined with the wrapped phase to obtain an initial absolute phase. A median-filtered version of this phase is then used as a guide in a G = 1 phase-refinement formulation to suppress localized artifacts while preserving the measured phase variation. Finally, modulation-based validity masks combine complementary phase maps from the two projection directions, improving surface coverage in self-occluded regions. Experimental results with discontinuous and discrete three-dimensional objects demonstrate successful fringe-order decoding, artifact suppression, and complementary surface reconstruction. The proposed method provides absolute phase recovery using eight projected patterns per projector and enables efficient reconstruction of complex surfaces containing abrupt depth discontinuities and limited-visibility regions.