Three-dimensional (3D) measurement of complex surfaces is of great importance in industrial inspection and production. To solve the problem of high accuracy measurement on complex surfaces, a phase unwrapping method based on multi-frequency binary is proposed, which can directly calculate fringe order by using wrapped phase. First, the four-step phase shift fringe patterns whose period changes exponentially are projected onto the measured object (The base is 2, the index is n, n=1, 2, 3...). Then, the four-step phase shift algorithm is used to obtain the wrapped phase of each period. Binary fringe is generated by binarization of the wrapped phase of each period according to the threshold value of 0. The fringe order K is calculated by binary coding and decoding algorithm, and then the wrapped phase in the highest period is unwrapped by K which can obtain the continuous phase of the object. The simulation and experiment verify the validity of the proposed method, and it has high robustness for complex surface and isolated object. The proposed method is simple in calculation, flexible in control and easy to operate. It provides a simple and effective method for improving the accuracy and robustness of the fringe projection profilometry system.
Large scale global optimization problems are closely related to real-life; however, the existing test function sets for large scale optimization problems can not truly reflect the complexity of the actual optimization problem. This paper presents a method for constructing test function sets, it can generate complex test function with different correlation, different deception and different difficulty of solving by adjusting the key parameters such as encoding length, number of groups, equipartition, continuity and the upper and lower limits of the dimensions within the group, it can be controlled by correlation, deception and continuity among dimensions. Using the existing metric correlation index verified the validity of the new construction test functions, and it can effectively simulate the incompletely separable optimization problem with different complexity.
Large scale global optimization problems are closely related to real-life; however, the existing test function sets for large scale optimization problems can not truly reflect the complexity of the actual optimization problem. This paper presents a method for constructing test function sets, it can generate complex test function with different correlation, different deception and different difficulty of solving by adjusting the key parameters such as encoding length, number of groups, equipartition, continuity and the upper and lower limits of the dimensions within the group, it can be controlled by correlation, deception and continuity among dimensions. Using the existing metric correlation index verified the validity of the new construction test functions, and it can effectively simulate the incompletely separable optimization problem with different complexity.
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