Three-Dimensional Measurement of Complex Textured Objects Based on Bidirectional Fringe Projection
Objective Fringe projection profilometry(FPP)has been widely adopted in numerous fields recently,owing to its advantages such as rapid measurement speed,high precision,non-contact,and cost-effectiveness.However,for objects with complex textures,the camera defocus,which is unavoidable,implies that each pixel on the imaging plane of the camera essentially represents the convolution of the point spread function(PSF)and the reflected light intensity from each point within the region.In regions where reflectivity changes abruptly,diverse reflectivities are displayed by points within the range of the PSF.This leads to cross-contamination,resulting in subsequent phase errors that ultimately impact the final reconstruction accuracy.Within the PSF range,due to the different reflectivity of each point in the area of reflectivity mutation,the reflected light at each point contaminates each other after camera defocus,resulting m phase errors that ultimately impact the final reconstruction accuracy.Conventional solutions are principally divided into two categories:One approach is to estimate the PSF distribution by dividing the phase into correct and erroneous regions and compensating for the erroneous regions using the adjacent correct regions.However,this approach relies heavily on the accuracy of the PSF estimation.The other approach incorporates the single-pixel imaging method(SIM)for error compensation,but this method is inefficient in terms of measurements and fails to accommodate a high degree of camera defocus.To address these issues,we propose a three-dimensional(3D)measurement method for complex textured objects based on bidirectional fringe projection,and a structured light 3D measurement system has been established.The results of the comparison experiments demonstrate that the proposed method can reconstruct complex textured objects with a higher level of precision under the same measurement efficiency.Methods In our work,we proposed a 3D measurement of complex textured objects based on bidirectional fringe projection to reduce the reconstruction errors caused by abrupt reflectivity changes of complex textures.A phase error model of the reflectivity mutation region under camera defocus was first built by theoretical analysis and simulation experiments.The model pointed out the correlation among the phase error,phase gradient,and gray gradient.Accordingly,a high-precision measurement methodology for complex textured objects based on bidirectional fringe projection was proposed.The method obtained bidirectional phase information by projecting the horizontal and vertical fringes and mapped the horizontal phase to the vertical direction using the proposed mapping method,which was linearly operated with the original vertical phase to obtain the average phase.Subsequently,the angle between the tangent line of the extracted texture edges of the object and the rectified phase gradient was computed,and the corresponding error compensation algorithm was used to process the average phase.Finally,the corrected point cloud was obtained by reconstruction.Results and Discussions The proposed method in this paper is compared with the horizontal conventional FPP method,the vertical conventional FPP method,and the existing method(Rao)of compensating for the phase error by estimating the PSF distribution,respectively.To ensure consistent measurement efficiency,the comparison methods are repeatedly projected.To quantitatively articulate the measurement accuracy for planar objects,such as the calibration plate and the card holder,we compute the mean absolute error(MAE)and root mean square error(RMSE)by planar fit.The measurement results of the calibration plate(Fig.10 and Table 1)show that the proposed method has the highest reconstruction accuracy,with 45.4％and 32.0％reduction in MAE and 44.1％and 31.5％reduction in RMSE compared to the traditional repeated projection and Rao's method,respectively.The measurement results of the card holder(Figs.11-12 and Table 2)demonstrate that the proposed method reconstructs optimally and performs the best at the detailed texture,reducing the MAE by 33.2％and 23.1％and the RMSE by 38.5％and 28.8％compared to the traditional repeated projection method and Rao's method,respectively.To prove the generalizability of our method,a curved object with complex texture,such as a vase,is measured,and the point clouds(Fig.13)show that the reconstruction result by using this method is the smoothest,or in other words,it has the highest reconstruction accuracy.In order to describe the effectiveness of the proposed method more objectively,two measurements are made on a pure white standard step block,and a black texture is drawn on its surface during the second measurement.The MAE and RMSE of the point cloud obtained from the second measurement are calculated by taking the reconstructed point cloud before drawing the texture as the ground truth.The measurement results(Fig.15 and Table 3)indicate that the proposed method has the highest reconstruction accuracy,with 43.2％and 29.9％reduction in MAE and 50.1％and 37.3％reduction in RMSE compared to the traditional repeated projection method and Rao's method,respectively.Conclusions In response to the challenge of measurement errors resulting from discontinuous reflectivity in complex textures within the structured light system,we propose a 3D measurement method of complex textured objects based on bidirectional fringe projection.In this paper,a phase error model for the reflectivity mutation area under camera defocus is initially established,which indicates that the phase error is associated with both the phase gradient and gray gradient.Consequently,a method is proposed,which uses bidirectional fringe to compensate for the error in differing regions according to their angles.Given the necessity to employ bidirectional phase information,another method is proposed,which maps the horizontal phase to the vertical direction.In order to verify the effectiveness of the proposed method,an FPP system is built to measure multiple complex textured objects on both flat and curved surfaces,and the proposed method is compared with other existing methods.The results of the comparison experiments demonstrate that the proposed method can reconstruct complex textured objects with a higher level of precision under the same measurement efficiency.The MAE and RMSE of the proposed method are reduced by up to 45.4％and 50.1％,respectively.
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