This paper proposes an absolute phase retrieval method for complex object measurement based on quantized phase-coding and connected region labeling. A specific code sequence is embedded into quantized phase of three coded fringes. Connected regions of different codes are labeled and assigned with 3-digit-codes combining the current period and its neighbors. Wrapped phase, more than 36 periods, can be restored with reference to the code sequence. Experimental results verify the capability of the proposed method to measure multiple isolated objects.

Fringe projection profilometry has been widely used for 3-D measurement, but the gamma nonlinearity severely affects the accuracy. Ideally, the histogram of the undistorted phase is uniform, but that of the distorted phase becomes nonuniform. In practice, adequate sampling pixels are required to calculate the phase histogram from modulated fringe patterns. Therefore, this article proposes an effective shifted-phase histogram equalization (SHE) method for nonlinear correction. Based on the finding that the distorted histogram contains three symmetric valleys in theory, if we shift the wrapped phase by $\pm 2\pi $ /3, the shifted phases will share the same histogram as the original phase. Without additional patterns, we can easily obtain two shifted phases. Combining the original and two shifted phases, the number of sampling pixels will increase by three times, and we can obtain more accurate histogram than the original phase. To make the histogram of the distorted phase be uniform as that of the undistorted phase, we directly apply histogram equalization on the distorted phase to estimate the undistorted phase. Moreover, this article proposes a spline interpolation optimization (SIO) method to eliminate the discretization error caused by histogram equalization. Simulations and experiments have been carried out, and their results indicate that the proposed SHE method performs better than the conventional phase histogram equalization (PHE) method, and the proposed SIO method can further reduce the discretization error.

For conventional camera calibration methods, well-focused images are necessary to detect features accurately. However, this requirement causes practical inconveniences to image acquisition for long- and short-distance photogrammetry. In this study, three active phase-shift circular grating (PCG) arrays are used as calibration patterns. The PCGs’ centers are regarded as feature points that can be accurately extracted by ellipse fitting of $2\pi$-phase points even though patterns are substantially blurred. In the experiments, Gaussian filters are utilized to blur pattern images, and different standard deviations are set for different fuzzy degrees. Pattern images with different defocusing degrees are also captured. The period and number of PCGs and noise are considered. Experimental results indicate that our method is accurate, reliable, and insensitive to image defocusing.

Stereo cameras have been widely used for three-dimensional (3D) photogrammetry, and stereo calibration is a crucial process to estimate the intrinsic and extrinsic parameters. This paper proposes a stereo calibration method with absolute phase target by using horizontal and vertical phase-shifting fringes. The one-to-one mapping from the world points to the image points that can be recovered by referring to the absolute phase and then used to calibrate the stereo cameras. Compared with traditional methods that only use feature points within the overlapping field-of-view (FOV), the proposed method can use all feature points within the overlapping and non-overlapping FOVs. Besides, since phase is more robust against camera defocusing than intensity, the target images can be captured regardless of the depth-of-field (DOF). With the advantages of whole-field capability and defocusing tolerability, the target placement becomes very flexible. Both simulations and experiment results demonstrate the robustness and accuracy of the proposed method.