Real-time 3D surface-shape measurement using fringe projection and system-geometry constraints

Optical three-dimensional (3D) surface-shape measurement has diverse applications in engineering, computer vision and medical science. Fringe projection profilometry (FPP), uses a camera-projector system to permit high-accuracy full-field 3D surface-shape measurement by projecting fringe patterns onto an object surface, capturing images of the deformed patterns, and computing the 3D surface geometry. A wrapped phase map can be computed from the camera images by phase analysis techniques. Phase-unwrapping can solve the phase ambiguity of the wrapped phase map and permit determination of camera-projector correspondences. The object surface geometry can then be reconstructed by stereovision techniques after system calibration. 
\nFor real-time 3D measurement, geometry-constraint based methods may be a preferred technique over other phase-unwrapping methods, since geometry-constraint methods can handle surface discontinuities, which are problematic for spatial phase unwrapping, and they do not require additional patterns, which are needed in temporal phase unwrapping. However, the fringe patterns used in geometry-constraint based methods are usually designed with a low frequency in order to maximize the reliability of correspondence determination. Although using high-frequency fringe patterns have proven to be effective in increasing the measurement accuracy by suppressing the phase error, high-frequency fringe patterns may reduce the reliability and thus are not commonly used.
\nTo address the limitations of current geometry-constraint based methods, a new fringe projection method for surface-shape measurement was developed using modulation of background and amplitude intensities of the fringe patterns to permit identification of the fringe order, and thus unwrap the phase, for high-frequency fringe patterns. Another method was developed with background modulation only, using four high-frequency phase-shifted fringe patterns. The pattern frequency is determined using a new fringe-wavelength geometry-constraint model that allows only two point candidates in the measurement volume. The correct corresponding point is selected with high reliability using a binary pattern computed from the background intensity. Equations of geometry-constraint parameters permit parameter calculation prior to measurement, thus reducing computational cost during measurement. In a further development, a new real-time 3D measurement method was devised using new background-modulated modified Fourier transform profilometry (FTP) fringe patterns and geometry constraints. The new method reduced the number of fringe patterns required for 3D surface reconstruction to two. A short camera-projector baseline allows reliable corresponding-point selection, even with high-frequency fringe patterns, and a new calibration approach reduces error induced by the short baseline. Experiments demonstrated the ability of the methods to perform real-time 3D measurement for a surface with geometric discontinuity, and for spatially isolated objects.
\nAlthough multi-image FPP techniques can achieve higher accuracy than single-image methods, they suffer from motion artifacts when measuring dynamic object surfaces that are either moving or deforming. To reduce the motion-induced measurement error for multi-image FPP techniques, a new method was developed to first estimate the motion-induced phase shift errors by computing the differences between phase maps over a multiple measurement sequence. Then, a phase map with reduced motion-induced error is computed using the estimated phase shift errors. This motion-induced error compensation is computed pixel-wise for non-homogeneous surface motion. Experiments demonstrated the ability of the method to reduce motion-induced error in real-time, for real-time shape measurement of surfaces with high depth variation, and moving and deforming surfaces.

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