Simplification of high order polynomial calibration model for fringe projection profilometry

Abstract

In fringe projection profilometry systems, high order polynomial calibration models can be employed to improve the accuracy. However, it is not stable to fit a high order polynomial model with least-squares algorithms. In this paper, a novel method is presented to analyze the significance of each polynomial term and simplify the high order polynomial calibration model. Term significance is evaluated by comparing the loading vector elements of the first few principal components which are obtained with the principal component analysis, and trivial terms are identified and neglected from the high order polynomial calibration model. As a result, the high order model is simplified with significant improvement of computation stability and little loss of reconstruction accuracy. An interesting finding is that some terms of 0 and 1st order, as well as some high order terms related to the image direction that is vertical to the phase change direction, are trivial terms for this specific problem. Experimental results are shown to validate of the proposed method.

Fast Three-Dimensional Profilometry with Large Depth of Field

“…In an FPP system, a 3D reconstruction model is required to convert the distribution of projector coordinates into 3D coordinates. Among the existing 3D reconstruction models, the polynomial reconstruction model is more flexible to take nonlinear factors (such as lens distortion in the camera and projector) into account [21]. Although the polynomial reconstruction model with higher order is more accurate, it is prone to be ill conditioned if the order is higher than three [21].…”

“…Among the existing 3D reconstruction models, the polynomial reconstruction model is more flexible to take nonlinear factors (such as lens distortion in the camera and projector) into account [21]. Although the polynomial reconstruction model with higher order is more accurate, it is prone to be ill conditioned if the order is higher than three [21]. Therefore, a third-order polynomial model is employed in this work, which can be formulated as the following:…”

Beyond phase error compensation: pixel mapping-based error correction for high-accuracy 3D surface measurement

“…Two co-prime fringe periods p 1 = 19 pixels and p 2 = 30 pixels were used. To show the effectiveness of the pixel mapping, reconstructed images (figures 5(c) and (f)) were established by submitting the pixel mapping into equation (1). Compared with the initial images (figures 5(a) and (d)), the reconstructed images are more evenly and finely filled with sinusoidal fringes.…”

“…Phase-shifting profilometry (PSP) has been widely employed in industry, such as reverse engineering, defect detection, object recognition, 3D printing, etc, as one of the most effective and convenient non-contact methods for 3D shape measurement [1][2][3][4]. Typically, a PSP system consists of a projector and a camera.…”

Fast and accurate 3D topography measurement based on a novel synthesis pattern method

“…With the development of science, technology, and precision manufacturing, especially in the fields of automobile, ship, and aircraft manufacturing, there are increasingly more geometric quantities and free-form surface inspection tasks involving large quantities and complex shapes, which require higher accuracy and speed of three-dimensional (3D) contour measurement [1]. Owing to its advantages of fast computing speed, high resolution, and full-field data acquisition, contour measurement technology based on structured light projection has attracted considerable attention and has been widely investigated and applied in practice [2,3]. However, the structured-light projection-based contour measurement * Author to whom any correspondence should be addressed.…”