Abstract
To meet the requirements of high accuracy and high efficiency in three-dimensional (3D) measurement, a phase difference-3D coordinate mapping model is proposed based on extreme learning machine (ELM) network. First, the reconstruction model of the ideal measurement system is set following the geometric structure of the system. Subsequently, by generalizing camera and world coordinates, a generalized measurement model is built. Lastly, ELM network is employed to solve the mapping coefficients. During measurement, only one phase difference map is required to complete the 3D reconstruction of the object, which simplifies the data processing process and saves time. The result indicates that the mean square errors (MSEs) of the X, Y and Z of the testing sample are 3.5955×10 -4 mm, 9.5113×10 -4 mm and 4.4×10 -3 mm, respectively. Moreover, the reconstruction experiments of objects with different geometric structures are performed to demonstrate the general application of the proposed method.
Highlights
3D imaging technology can be split into contact and noncontact measurement
extreme learning machine (ELM) network is used to predict the output of training samples and testing samples respectively
The result shows that the predicted absolute error of the X and Y coordinates is concentrated within 0.05mm, while the absolute error of the Z coordinates is concentrated within 0.3mm
Summary
It is assumed that the physical size of each camera pixel along the ui-axis and vi-axis are denoted as dx and dy, the camera coordinate of D’ is expressed as Eq (4). During the ELM network training, the connection weight and threshold values between input and hidden layers are randomly generated. The connection weight β between the hidden layer and the output layer that minimizes the loss function can be calculated by Eq (13), Q+ denotes the Moore-Penrose generalized inverse matrix of Q. System calibration: the input vector of ELM network is the pixel coordinate (u, v) and phase difference φ of the imaging point, and the output vector is the 3D world coordinate (X, Y, Z) of the corresponding object point. According to the imaging model presented, the pixel coordinate (u, v) and phase difference φ of each point are inputted by ELM network, while the output is the 3D world coordinate (X, Y, Z). With the use of training error and testing error for the double check of the performance of the ELM network, the measurement accuracy of the model can be effectively ensured in the practical application
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