Neural network model for phase-height relationship of each image pixel in 3D shape measurement by machine vision

In a three-dimensional measurement system based on a digital light processing projector and a camera, a height estimating function is very important. Sinusoidal fringe patterns of the projector are projected onto the object, and the phase of the measuring point is calculated from the camera image. Then, the height of the measuring point is inferred by the phase. The phase-to-height relationship is unique at each image point. However it is nonlinearly different according to the image coordinates. It is also difficult to obtain the geometrical model because of lens distortion. Even though some studies have been performed on neural network models to find the height from the phase and the related coordinates, the results are not good because of the complex relationship. Therefore, this paper proposes a hybrid method that combines a geometric analysis and a neural network model. The proposed method first finds the phase-to-height relationship from a geometric analysis for each image pixel, and then uses a neural network model to find the related parameters for the relationship. The experimental results show that the proposed method is superior to previous neural network methods.