Color Fringe Pattern Research Articles

End-to-end color fringe depth estimation based on a three-branch U-net network

In fringe projection profilometry (FPP), end-to-end depth estimation from fringe patterns for FPP attracts more and more attention from fringe patterns. However, color images provide additional information from the RGB channel for FPP, which has been paid little attention in depth estimation. To this end, in this paper we present for the first time, to the best of our knowledge, an end-to-end network for depth estimation using color composite fringes with better performance. In order to take advantage of the color fringe pattern, a multi-branch structure is designed in this paper, which learns the multi-channel details of the object under test by using three encoders for each RGB channel and introduces an attention module to better capture the complex features and modalities information in the input data. Experiments from simulated and real datasets show that the proposed method with color fringe pattern is effective for depth estimation, and it outperforms other deep learning methods such as UNet, R2Unet, PCTNet, and DNCNN.

New high sensitivity approach for a quantitative visualization of the continuous whole-field stress evolution in digital photoelasticity

Digital photoelasticity is a widely used technique for experimental stress analysis on mechanical models subjected to loading conditions, due to its ability to reveal the stress information through color fringe patterns and consequently demodulate it computationally to achieve a quantitative evaluation. In this process, some limitations persist, such as, expertise dependence, experimental repeatability, sensitivity to load increments, and weak performance under experimental conditions, especially in time-dependent scenarios. In response to these weaknesses, the method “Quantitative Visualization of the Continuous Whole-Field Stress Evolution” introduced the ability to perform a complete demodulation of the fringe patterns generated in time-dependent applications, achieving high performance compared to conventional photoelasticity methods. This paper proposes a new highly sensitive approach for a quantitative visualization of the continuous whole-field stress evolution in digital photoelasticity by incorporating an inverse signal process and a multi-stage strategy. The algorithm aims to ensure the performance under high fringe order conditions while exhibiting high sensitivity in cases where the maximum stress obtained is less than one fringe order. The results presented validate its effectiveness in demodulating full-field stress distributions, especially in scenarios where the loading condition induces fringe orders less than one, thus contributing to the broader applicability of digital photoelasticity.

A robust phase unwrapping method for phase shifting coding high-frequency color fringe projection profilometry

Phase unwrapping is one of the key problems in fringe projection profilometry (FPP). How to achieve unambiguous fringe step order to perform phase unwrapping with few patterns still face a major challenge. We propose a robust phase unwrapping method by using a pair of encoded color fringe patterns, one is a conventional three-step phase-shifting color fringe pattern with equal phase shifts, another is added an additional phase shift valve t(k) to the former, in which t(k) is related to the order of fringe periods. A single-valued solution function for t(k) is constructed and used to determine the unique fringe order. Besides, multiplexing this pair of fringes can help denoise the extracted wrapped phase to improve the accuracy. The simulation and experimental results proved that the proposed method can achieve unambiguous phase unwrapping for high-frequency fringe patterns. The proposed method is also applicable for isolated objects.

Surface structured light sensor with simultaneous color mapping

To obtain geometric information and color texture simultaneously, a surface structured light sensor consisting of a monochrome camera, a color camera, and a projector is proposed. The sensor uses a color camera to acquire surface color information while using it as a geometric measurement unit and matching with the monochrome camera to obtain geometric information. Due to the Bayer array and demosaicing algorithm of the color camera, pixel RGB components are always coupled with interference from other channels. However, existing color de-crosstalk in reconstruction is merely applied to the decoupling of color composite patterns, ignoring the intensity errors present in color fringe patterns under monochrome illumination. In our sensor, de-crosstalk of monochromatic patterns is considered to guarantee the reconstruction accuracy. The high-accuracy measurement of the sensor is validated by reconstructing standard steps, yielding a mean absolute error of 0.008 mm for distance measurements. In addition, the reconstruction experiment of a terracotta warrior verifies that the proposed sensor has potential application in the digital preservation of cultural relics.

Polynomial color compensation model with neural network solver for color-coded fringe patterns in phase-measuring deflectometry

The total image display/projection and image acquisition time in a projector-based phase-measuring deflectometry (PMD) measurement is reduced when color-coded fringe patterns are used since only a single image of the fringe pattern is sufficient to extract phase information using the phase-stepping method. This benefit is, however, offset by the difficulty in resolving various sources of color intensity errors of the fringe patterns in the camera view, such as uneven illumination, color imbalance, color crosstalk, and deviation of color intensity response of the camera and the projector from the calibrated color targets. Thus, a polynomial color compensation model is proposed in this study to compensate for color intensity errors. The model coefficients were estimated using the relationship between the captured and targeted color intensities, which are sequences of monochromatic 8-bit red, green, and blue (RGB) images for projection. The model was applied to modify the color intensities of the generated fringe patterns before projection. The modified color fringe patterns were then used for PMD measurement on spherical concave and convex mirrors. Based on the experimental results, the root-mean-squared (RMS) color intensity errors in R, G, and B channels were reduced by 33.3%, 58.3%, and 36.4%, respectively, after conducting the polynomial color compensation. The RMS phase errors in the fringe patterns were reduced by 71.9%. The RMS height errors and the radius percentage errors of the reconstructed concave and convex heightmaps were 1.87 μm (0.12%) and 1.55 μm (0.17%), respectively. The performance of the proposed polynomial color compensation model in reducing color intensity errors of the captured fringe patterns for accurate PMD measurement was demonstrated successfully.

Isochromatic-Art: A Computational Dataset for Digital Photoelasticity Studies

The importance of evaluating the stress field of loaded structures lies in the need for identifying the forces which make them fail, redesigning their geometry to increase the mechanical resistance, or characterizing unstressed regions to remove material. In such work line, digital photoelasticity highlights with the possibility of revealing the stress information through isochromatic color fringes, and quantifying it through inverse problem strategies. However, the absence of public data with a high variety of spatial fringe distribution has limited developing new proposals which generalize the stress evaluation in a wider variety of industrial applications. This dataset shares a variated collection of stress maps and their respective representation in color fringe patterns. In this case, the data were generated following a computational strategy that emulates the circular polariscope in dark field, but assuming stress surfaces and patches derived from analytical stress models, 3D reconstructions, saliency maps, and superpositions of Gaussian surfaces. In total, two sets of ‘101430’ raw images were separately generated for stress maps and isochromatic color fringes, respectively. This dataset can be valuable for researchers interested in characterizing the mechanical response in loaded models, engineers in computer science interested in modeling inverse problems, and scientists who work in physical phenomena such as 3D reconstruction in visible light, bubble analysis, oil surfaces, and film thickness.

Single frame color fringe projection profilometry based on empirical mode decomposition imbalance correction algorithm for fast three-dimensional reconstruction

Phase-shifting profilometry (PSP) is considered to be the most accurate technique for phase retrieval with fringe projection profilometry (FPP) systems. However, PSP requires that multiple phase-shifted fringe patterns be acquired, usually sequentially, which limits PSP to static or quasistatic imaging. We introduce color FPP (CFPP), which provides three-dimensional (3D) imaging using a single acquisition, for the application of real-time profiling. A single frame acquisition provides all three phase-shifted fringe patterns needed for the PSP phase retrieval algorithm. However, some problems must be overcome in CFPP, namely, color coupling and imbalance. Following up on the study, we propose a fixed coefficient decoupling method based on point-to-point correction and then introduce the empirical mode decomposition algorithm to decompose a color fringe pattern into three high-frequency components and three low-frequency components for imbalance correction, which improves measurement accuracy and realizes a single frame measurement for complex and discontinuous objects. After correction by the proposed method, the shape of the tested object can be recovered by one a single frame color fringe pattern, which meets the need for dynamic measurement, and the accuracy is not limited by the movement speed of object. The simulations and experimental results show that the proposed method can significantly reduce the influence of color coupling and imbalance in CFPP, and thus realize dynamic and high-precision 3D reconstruction.

Rapid 3D measurement of colour objects based on three-channel sinusoidal fringe projection

A rapid 3D measurement method based on three-channel projection is proposed in this paper. Project a composite color fringe map and an all-white map to the object to be measured. Firstly, crosstalk correction is performed on the composite color fringe pattern collected by the camera then the reflectivity of fringe image is corrected by all-white image. Then, the background normalization principle is used to solve the spectrum aliasing problem when the Fourier transform obtains a truncated phase. Finally, the three-frequency heterodyne method is used for phase unwrapping to obtain the continuous phase and 3D shape. Compared with the traditional color fringe projection method, this method not only eliminates the spectrum aliasing problem but also solves the uneven fringe reflectivity problem when measuring color objects using an all-white map. This method only requires two images to achieve measurement of 3D color dynamic objects.

Single-shot high-precision 3D reconstruction with color fringe projection profilometry based BP neural network

In order to reduce the influence of nonlinear factors such as gamma nonlinearity and color crosstalk on the phase retrieval accuracy with color fringe projection profilometry (CFPP) in rapid measurement, a single-shot high-precision backpropagation (BP) neural network based CFPP is proposed. Firstly, neural networks are trained from samples through a training process. The neural network inputs are the RGB components of composite color fringe patterns. The numerator and denominator of the arctangent function are used as network outputs. The monochromatic fringe patterns are adopted. The numerator and denominator of the arctangent function are calculated by the 15-step phase-shift method, which serves as the network training target. Applying this neural network to the prediction of the standard phase can reduce the influence of nonlinear factors on the phase accuracy. Then, the absolute phase was unwrapped by using geometric constraints. Finally, the 3D reconstruction with high precision can be realized by using only a single-shot color fringe. The theoretical model of the proposed method and the process of neural network training are introduced. The results of 3D reconstruction are compared with other algorithms in the same condition. The experimental results demonstrate that the RMS of the proposed algorithm can reach 0.0107 mm, compared with 0.0121 mm of the traditional 3-step phase-shift method. The proposed method is applied to the online quality inspection of relay components, and the results verify the high accuracy and high efficiency of measurement.

Intensity-Averaged Double Three-Step Phase-Shifting Algorithm with Color-Encoded Fringe Projection

Fringe projection profilometry (FPP) has been broadly employed for three-dimensional shape measurements. However, the measurement accuracy suffers from gamma nonlinearity. This paper proposes an intensity-averaged double three-step phase-shifting (IDTP) algorithm making use of color-encoded fringe projection, which does not require complex calibration processes or extra fringe patterns. Specifically, two phase maps with π/2 phase shift are encoded into the red and blue channels of color fringe patterns. The average fringe patterns of the red and blue channels are approximately in sinusoidal waveform with little harmonics, thus can be directly used for accurate phase recovery. Additionally, an adaptive weight is also estimated for average operation to suppress the effect of color crosstalk. Both simulations and experiments demonstrate that the proposed IDTP algorithm can effectively eliminate nonlinear phase errors.

PhotoelastNet: a deep convolutional neural network for evaluating the stress field by using a single color photoelasticity image.

Quantifying the stress field induced into a piece when it is loaded is important for engineering areas since it allows the possibility to characterize mechanical behaviors and fails caused by stress. For this task, digital photoelasticity has been highlighted by its visual capability of representing the stress information through images with isochromatic fringe patterns. Unfortunately, demodulating such fringes remains a complicated process that, in some cases, depends on several acquisitions, e.g., pixel-by-pixel comparisons, dynamic conditions of load applications, inconsistence corrections, dependence of users, fringe unwrapping processes, etc. Under these drawbacks and taking advantage of the power results reported on deep learning, such as the fringe unwrapping process, this paper develops a deep convolutional neural network for recovering the stress field wrapped into color fringe patterns acquired through digital photoelasticity studies. Our model relies on an untrained convolutional neural network to accurately demodulate the stress maps by inputting only one single photoelasticity image. We demonstrate that the proposed method faithfully recovers the stress field of complex fringe distributions on simulated images with an averaged performance of 92.41% according to the SSIM metric. With this, experimental cases of a disk and ring under compression were evaluated, achieving an averaged performance of 85% in the SSIM metric. These results, on the one hand, are in concordance with new tendencies in the optic community to deal with complicated problems through machine-learning strategies; on the other hand, it creates a new perspective in digital photoelasticity toward demodulating the stress field for a wider quantity of fringe distributions by requiring one single acquisition.

Three-dimensional measurement method of color fringe projection based on an improved three-step phase-shifting method.

A three-dimensional (3D) measurement method of color fringe projection based on an improved three-step phase-shifting method is proposed. The color fringe pattern is encoded by two cosine fringe patterns with the same frequency but different shifting phase and a uniform gray flat image into three color channels R, G, and B. Although the measurement speed of the traditional three-step phase-shifting method can meet the requirements of measuring 3D objects, it makes the noise and inaccuracy of the captured images increase, and each image will cause measurement error. Therefore, we improve the three-step phase-shifting method and introduce the Hilbert transform into the three-step phase-shift method. The DC component of the fringe pattern is obtained by using the Hilbert transform principle, and the third fringe pattern in the three-step phase-shift method is replaced by the captured light intensity distribution of the DC component. The phase difference of the other two fringe patterns is fixed as π/2 by the Hilbert transform. The improved three-step phase-shifting method is used to obtain the phase information of the deformed color fringe image, and then the phase-unwrapping algorithm is used to obtain the phase distribution information of the whole field. The results show that the improved method can not only accurately calculate the phase information but also greatly improve the measurement speed and quality.

Point-to-point coupling and imbalance correction in color fringe projection profilometry based on multi-confusion matrix

Fringe projection profilometry (FPP) has been widely used in three-dimensional (3D) profile measurements for its efficiency and high accuracy. As an offshoot of FPP, color fringe projection profilometry (CFPP) has the advantage of being dynamic, non-contact, and full-field, which makes it one of the most valuable 3D profile measurement techniques. However, phase errors may arise in CFPP when the phase is retrieved by phase-shifting algorithms. This is due to the gamma nonlinear response, color coupling, and color imbalance of electro-optical devices. In this paper, a multi-confusion matrices (MCM) correction technique is proposed to reduce the phase error by compensating the captured color fringe pattern intensity. This can be accomplished in three steps. Firstly, project 30 ~ 220 (with the step of ten gray levels) uniform intensity patterns on a calibration plate, and then extract the intensity information to construct multi-confusion matrices (MCM) and LUTs (look up tables). Secondly, search optimal confusion matrix (OCM) from MCM to correct the fringe pattern. Finally, retrive the unwrapping phase using the corrected fringe pattern. The simulation and experimental results indicate that the proposed approach can reduce phase errors and use one color fringe pattern to reconstruct 3D topography.

Single-Shot Phase Measuring Profilometry Based on Quaternary Grating Projection

In this paper, we propose a new single-shot three-dimensional (3D) measuring method based on quaternary grating projection. In traditional binary grating phase measuring profilometry (PMP), a multi-step or color fringe pattern are usually used to extract the sinusoidal fringes. In our proposed method, by using the DLP4500’s 2-bit gray coding mode, the grayscale is quaternary. The three non-zero grayscales cyclically arranged in equal width, and the fourth grey value is 0 which is not encoded in the fringe pattern but represents the shadow information in the deformed pattern, where a quaternary grating is encoded. When the DLP4500 projects the quaternary grating onto the measured object, the charge coupled device (CCD) captures the corresponding deformed pattern synchronously. Three frames of binary deformed patterns with 1/3 duty cycle and a relative displacement of 1/3 period can be decomposed by the segmentation algorithm proposed in this paper. Three sinusoidal deformed patterns with a 2π/3 shift-phase can be obtained by extracting the fundamental frequency of the three binary deformed patterns correspondingly, and the 3D shape of the object can be reconstructed by PMP. Experimental results show the effectiveness and feasibility of the proposed method. Because the DLP4500 only needs 2-bit coded grating for projection, the refresh rate of the projected grating is as high as 1428 Hz, which will have a broad application prospect in real time and fast online measurement.

Point-to-point compensation method for color coupling and imbalance in color-fringe pattern profilometry

Color-fringe pattern profilometry is widely developed for high-speed 3D shape measurement due to more information can be extracted through a single color pattern. However, previous researches show that the color coupling and imbalance of the system cause significant errors, which severely influence the accuracy of the color-fringe pattern profilometry. We proposed a point-to-point method to compensate the errors caused by color coupling and imbalance. Different from previous methods, the proposed method bases on the correspondence between camera pixels and projector pixels, which achieves point-to-point compensation of the full field. Experimental results verify that the proposed easy-to-operated method reduces the measurement errors significantly.

An inverse error compensation method for color-fringe pattern profilometry

Color-fringe pattern profilometry is a widely used method for high-speed measuring 3D surface because the RGB (red, green and blue) channels provide more information. However, the nonlinear response of the digital projector usually causes periodical phase errors. In this paper, we analyze the nonlinear error in color-fringe pattern profilometry, and propose a multi-frequency fringe inverse error compensation method to reduce the phase error caused by the nonlinear response of the projector. The proposed method only needs to add one highest frequency RGB pattern, thus improving the measurement accuracy of color-fringe pattern profilometry. Different from other compensation methods, the proposed method does not need gamma calibration, the construction of a look-up-table of gamma values or many additional patterns, which are really time consuming. The experimental results demonstrated that the proposed method can effectively reduce the nonlinear effect of the projector and improve the measurement accuracy of color-fringe pattern profilometry.

Comparison of stress distribution in a three unit cement retained implant supported prosthesis with different implant abutment connections: A photoelastic analysis

Aim: With the emphasis on success of implant supported prosthesis, and health of the surrounding tissues that are related to accuracy, and fit between the implant components, stability at implant abutment interface is of prime importance. The aim of this study is to evaluate and compare the stress distribution in three unit cement retained implant supported fixed partial denture with different implant abutment connections through photo elasticity. Materials and methods: Two photo elastic resin models were fabricated of standard dimensions (44mmx22mmx10mm). Group I sample: Three unit cement retained implant supported fixed partial denture with Internal implant abutment connection (Internal hexagonal connection) (Paltop Advanced, Keystone Dental Company, US)Group II sample: Three unit cement retained implant supported fixed partial denture with conical Morse taper connection (1.5 degree Morse taper) (Paltop Conical Active, Keystone Dental Company, US). Three unit cement retained implant supported fixed partial denture simulated missing mandibular first molar. Axial and oblique loads of 100N were placed on each implant and pontic area for 10 sec. Ten tests were done for each group. The stress values around the implants were derived from the colored fringe patterns obtained through polariscope, which were photographed after load applications from which values were derived. Results: Under axial loading, there was statistically significant difference between internal hexagonal connection and Morse taper connection in three unit implant supported prosthesis. Stresses were more in Group II sample with Morse taper connection. Under oblique loading, there was no statistically significant difference between Group I and Group II samples. Conclusion: Within the limitations of this in vitro study, it can be concluded that Internal hexagonal connection showed less stresses as compared to Morse taper connection in a three unit cement retained implant supported prosthesis. Stresses were concentrated more in apical area under axial loading; while under oblique loading stresses were seen on the side of application of force on the body of the implant and on the apical region. However, stresses were uniformly distributed in both groups I and group II samples. In both groups stresses under oblique loading were more than axial loading, but that was not statistically significant.

Active phase error suppression for color phase-shifting fringe projection based on hue pre-correction

Color phase-shifting fringe projection is one of the single-shot three-dimensional shape measurement techniques based on fringe projection profilometry. In practice, the nonlinearity and color crosstalk of the projector-camera system yield undesired phase errors when using phase-shifting algorithm. In this paper, an active phase error suppression method based on hue pre-correction is proposed. Theoretical analysis of phase error is performed taking account of the gamma nonlinearity of the camera. Based on the analysis, the distortion of hue component of the acquired color fringe pattern is employed to represent the overall phase error induced by the combined effect of nonlinearity and color crosstalk. In this method, the hue is pre-corrected to be linear by measuring the function of the combined effect and modifying the computer-generated hue according to the source-distorted relationship. Then, the new modified color fringe pattern can be generated and saved for the further measurement of objects. Experimental results demonstrate the feasibility of the proposed method and it can effectively suppress the induced overall phase error caused by the nonlinearity and color crosstalk of the projector-camera system.

Dynamic 3D shape measurement by iterative phase shifting algorithms and colored fringe patterns.

In this work, we propose a novel technique to retrieve 3D shape of dynamic objects by the simultaneous projection of a fringe pattern and a homogeneous white light pattern, both coded in an RGB image. The first one is used to retrieve the phase map by an iterative least-squares method. The second one is used to match object pixels in consecutive images, acquired at various object positions. The proposed method successfully accomplishes the requirement of projecting simultaneously two different patterns. One extracts the object's information while the other retrieves the phase map. Experimental results demonstrate the feasibility of the proposed scheme.

Adaptive pixel-to-pixel projection intensity adjustment for measuring a shiny surface using orthogonal color fringe pattern projection

Three-dimensional (3D) shape measurement based on fringe pattern projection techniques has been commonly used in various fields. One of the remaining challenges in fringe pattern projection is that camera sensor saturation may occur if there is a large range of reflectivity variation across the surface that causes measurement errors. To overcome this problem, a novel fringe pattern projection method is proposed to avoid image saturation and maintain high-intensity modulation for measuring shiny surfaces by adaptively adjusting the pixel-to-pixel projection intensity according to the surface reflectivity. First, three sets of orthogonal color fringe patterns and a sequence of uniform gray-level patterns with different gray levels are projected onto a measured surface by a projector. The patterns are deformed with respect to the object surface and captured by a camera from a different viewpoint. Subsequently, the optimal projection intensity at each pixel is determined by fusing different gray levels and transforming the camera pixel coordinate system into the projector pixel coordinate system. Finally, the adapted fringe patterns are created and used for 3D shape measurement. Experimental results on a flat checkerboard and shiny objects demonstrate that the proposed method can measure shiny surfaces with high accuracy.