Nonlinear error full-field compensation method for phase measuring profilometry.

Phase measuring profilometry (PMP) has the highest measuring accuracy among structured light projection-based three-dimensional (3D) sensing methods. Due to their low-cost and high-resolution features, commercial projectors are extensively used in PMP, but they are all designed with a gamma effect purpose that considers the characteristics of human vision. Affected by the gamma effect, a set of phase-shifting sinusoidal deformed patterns captured in PMP may contain high-order harmonics which lead to nonlinear phase errors. Then, a novel nonlinear error full-field compensation method is proposed. First, the unwrapped phases modulated by the reference plane are measured several times, and their average phase is taken as the measured phase modulated by the reference plane to eliminate random errors as much as possible. Second, an expected phase plane is fitted from this average phase with the least-squares method. Third, the nonlinear phase error can be detected by subtracting the fitted expected phase from this average phase. Finally, the full-field look-up table (LUT) can be established between the nonlinear phase error and the measured phase. When an object is measured, the unwrapped phase modulated by the object is taken as the measured phase of the LUT, so the corresponding nonlinear phase error can be directly searched in the LUT. In this way, the full-field nonlinear phase error can be efficiently compensated. Experimental results show the feasibility and validity of the proposed method. The mean absolute error (MAE) can be improved from 0.48 mm to 0.06 mm, and the root mean square error (RMSE) can be improved from 0.55 mm to 0.07 mm.

Spatial-temporal phase unwrapping algorithm for fringe projection profilometry.

In this paper, a generalized spatial-temporal phase unwrapping algorithm (STPUA) is proposed for extracting the absolute phase of the isolated objects with intricate surfaces. This proposed algorithm can eliminate thoroughly the order jumps of various temporal phase unwrapping algorithms (TPUAs), while inheriting the high measuring accuracy of quality-guided phase unwrapping algorithms (QGPUAs). Differing from the traditional phase unwrapping algorithms, wrapped phase is first divided into several regional wrapped phases, which can be extracted successively according to its areas and unwrapped individually by QGPUAs. Meanwhile, a series of reliable points from the fringe order map obtained from the code deformed patterns are selected to map the corresponding regional unwrapped phases into an absolute phase. The radii of selecting reliable points can provide the high measuring robustness compared with the classical point-to-point TPUAs for the complex surfaces and the motion blur, while keeping the same number of patterns. Therefore, the proposed STPUA combining SPUAs and TPUAs also can be employed in real-time three-dimensional (3D) reconstruction. Theoretical analysis and experimental results are performed to verify the effectiveness and capability of the proposed algorithm.

Ultrafast spatial phase unwrapping algorithm with accurately correcting transient phase error.

In fringe projection profilometry, the wrapped phase is easily polluted by many factors such as noise, shadow, and so on. In this Letter, we propose an ultrafast bi-staggered spatial phase unwrapping (BSPU) method. By constructing another staggered phase, the fringe order jump (FOJ) and local transient phase error (LTPE) can be accurately and quickly located at the same time owing to a simple difference operation. For the first time, to the best of our knowledge, a pioneering threshold separation model is established to precisely distinguish FOJ and LTPE. Based on the continuity assumption, LTPE is effectively corrected by introducing the concept of "non-integer fringe order." The range of measurable discontinuity height is improved owing to the distinction between real phase jump and random error in the spatial phase unwrapping. In addition, it is thousands of times faster than the traditional path-dependent algorithm and even has higher measurement accuracy. Experimental results show the effectiveness and robustness of the proposed method in various complex measurement environments.

High-precision 3D shape measurement of rigid moving objects based on the Hilbert transform.

Phase-shifting profilometry (PSP) is a three-dimensional (3D) measurement method of point-to-point calculation. The consistency of object position is the prerequisite to ensure the successful application of PSP in moving objects. The position information of an object can be well characterized by the modulation patterns, and hence a high-quality modulation pattern is the guarantee of pixel-matching accuracy. In this paper, a generic modulation pattern enhancement method for rigid moving objects based on the Hilbert transform is proposed. First, the Hilbert transform is employed to suppress the zero-frequency components of the fringe pattern, and a hybrid digital filter window is applied to filter out the positive fundamental frequency components for a higher signal-to-noise ratio. Then the grid-based motion statistics for fast, ultra-robust feature correspondence algorithm is used to match the high-quality modulation patterns between two adjacent frames, and the object positions in the three deformed patterns are made consistent by image clipping. Finally, the three-step PSP is used to reconstruct the 3D shape of the measured object. Experimental results demonstrate that the proposed method can substantially improve the quality of the modulation pattern, achieve high-precision pixel matching, and ultimately reduce the motion-introduced phase error.

Temporal phase unwrapping based on unequal phase-shifting code.

In fringe projection profilometry (FPP) based on temporal phase unwrapping (TPU), reducing the number of projecting patterns has become one of the most important works in recent years. To remove the 2π ambiguity independently, this paper proposes a TPU method based on unequal phase-shifting code. Wrapped phase is still calculated from N-step conventional phase-shifting patterns with equal phase-shifting amount to guarantee the measuring accuracy. Particularly, a series of different phase-shifting amounts relative to the first phase-shifting pattern are set as codewords, and encoded to different periods to generate one coded pattern. When decoding, Fringe order with a large number can be determined from the conventional and coded wrapped phases. In addition, we develop a self-correction method to eliminate the deviation between the edge of fringe order and the 2π discontinuity. Thus, the proposed method can achieve TPU but need to only project one additional coded pattern (e. g. 3+1), which can significantly benefit dynamic 3D shape reconstruction. The theoretical and experimental analysis verify that the proposed method performs high robustness on the reflectivity of the isolated object while ensuring the measuring speed.

A Polylobar Nucleus Identifying and Extracting Method for Leukocyte Counting.

Accurate counting of leukocytes is an important method for diagnosing human blood diseases. Because most nuclei of neutrophils and eosinophils are polylobar, it is easily confused with the unilobar nuclei in nucleus segmentation. Therefore, it is very essential to accurately identify and determine the polylobar leukocytes. In this paper, a polylobar nucleus identification and extracting method is proposed. Firstly, by using the Otsu threshold and area threshold method, the nuclei of leukocytes are accurately segmented. According to the morphological characteristics of polylobar leukocytes, the edges of the mitotic polylobar leukocytes are detected, and the numbers of polylobar leukocytes are determined according to the minimal distance rule. Therefore, the accurate counting of leukocytes can be realized. From the experimental results, we can see that using the Otsu method and the area threshold to segment the polylobar nuclear leukocytes, the segmentation ratio of the leukocyte nucleus reached 98.3%. After using the morphological features, the polylobar nuclear leukocytes can be accurately counted. The experimental results have verified the feasibility and practicability of the proposed method.

Real-time profilometry by bicolor grating video projection.

A novel real-time 2+1 three-dimensional(3D) measuring method based on bicolor grating video projection is proposed. Firstly, only two frames of bicolor gratings, in which the red channels are two sinusoidal fringes with a shifting phase of π/2 and the blue channels are the same background light equivalent to the DC component of the two sinusoidal fringes are encoded and arranged alternatively to synthesize into a repetitive bicolor grating video, While this video is projected onto the measured object, the real-time bicolor deformed pattern video can be recorded by using a color CMOS camera, and the bicolor deformed pattern sequence at different moments can be extracted by computer processing, so that the 2+1 algorithm can be used to accomplish real-time 3D measurement of moving object. Before measuring, we used the same method to design two sinusoidal fringes with a difference of π in their red channels, respectively, to calibrate the sensitivity ratio between the red and blue channels of the CMOS camera, which can effectively eliminate the chromaticity imbalance between R and B channels and reduce the color crosstalk. Experimental results and analysis confirm the feasibility and effectiveness of the proposed method. Because the proposed method needs a repetitive bicolor grating video synthesized with only two-frame bicolor gratings to be projected, the 3D measurement acquisition speed and real-time accuracy will be improved compared with the traditional 2+1 3D measuring method.

A super-grayscale and real-time computer-generated Moiré profilometry using video grating projection.

By using the time-division multiplexing characteristics of the projector and the integral exposure characteristics of the charge coupled device (CCD) camera, a super-grayscale and real-time computer-generated Moiré profilometry based on video grating projection is proposed. The traditional digital static grating is of 256-grayscale at most. If an expected super-grayscale grating with a maximum grayscale of 766 is designed and divided into three 256-grayscale fringe patterns with balanced grayscale as far as possible, they can be synthesized into a repeated playing video grating instead of the traditional static grating. When the video grating is projected onto the measured object, as long as the exposure time is set to three times the refresh cycle of the video grating, the super-grayscale deformed patterns in the 766-grayscale can be captured with a 10-bit CCD camera, so that the deformed patterns are realistic. The digital error in computer-generated Moiré profilometry is effectively reduced. In addition, this method can expand the linear range of the deformed pattern by 20% in computer Moiré profilometry. Therefore, the proposed method has the perspectives of high accuracy and real-time measurement. Theoretical analysis and experimental results demonstrate the validity and capability of the proposed method.