Directional Balance: A General Design Principle for Binary Fringe Projection

High-speed structured-light imaging often relies on binary-defocusing fringe projection, in which binary patterns are optically low-pass filtered into approximately sinusoidal fringes. Under shallow defocus, error diffusion is the preferred way to preserve sinusoidal fidelity, but its kernel is usually selected by hand or by black-box search, so the direction-dependent phase bias is not explicitly controlled. Rather than correcting this bias at the fringe patterns, we analyze the diffusion kernel itself and introduce a normalized balance coefficient that measures the asymmetry between forward and backward error propagation. The dominant directional phase bias vanishes when this coefficient is zero. This condition yields the Guideline-Based Optimization (GBO) kernels for horizontal and vertical fringes with no additional run-time overhead and no change to the downstream reconstruction process. Unlike sequence-level inter-fringe compensation, our approach does not reorganize the phase-shifting sequence. On real measurements, GBO reduces AE by 17.84% and RMSE by 22.45% relative to the second-best baseline.