Improved differential 3D shape retrieval

•The improved algorithm is suitable for orthogonal fringes in any direction.•The proposed method is almost unaffected by the changing angle.•The proposed method can get the partial differentiation by spectral processing.•Fourier differentiation theorem can decrease the computing complexity.

Phase unwrapping is a complex step in three-dimensional (3D) surface measurement. To simplify the computation process, Martino et al. proposed a differential algorithm. However, it will result in large error when the orthogonal fringes are not in horizontal or vertical direction. To solve this problem, the relationship between projector׳s and camera׳s coordinate systems is introduced. With the data obtained from coordinate transformation, the improved differential algorithm can be used for orthogonal fringes in any direction. Besides that, taking advantage of Fourier differentiation theorem makes operation and calculation simpler. By contrast, the results of experiments show that the proposed method is applicable to the patterns with orthogonal fringes in every direction. In addition, Fourier differentiation theorem effectively increases the speed of differential process.