## Abstract

In optical phase shift profilometry (PSP), parallel fringe patterns are projected onto an object and the deformed fringes are captured using a digital camera. It is of particular interest in real time three- dimensional (3D) modeling applications because it enables 3D reconstruction using just a few image captures. When using this approach in a real life environment, however, the noise in the captured images can greatly affect the quality of the reconstructed 3D model. In this paper, a new image enhancement algorithm based on the oriented two-dimenional dual-tree complex wavelet transform (DT-CWT) is proposed for denoising the captured fringe images. The proposed algorithm makes use of the special analytic property of DT-CWT to obtain a sparse representation of the fringe image. Based on the sparse representation, a new iterative regularization procedure is applied for enhancing the noisy fringe image. The new approach introduces an additional preprocessing step to improve the initial guess of the iterative algorithm. Compared with the traditional image enhancement techniques, the proposed algorithm achieves a further improvement of $7.2\text{\hspace{0.17em}}\mathrm{dB}$ on average in the signal-to-noise ratio (SNR). When applying the proposed algorithm to optical PSP, the new approach enables the reconstruction of 3D models with improved accuracy from 6 to $20\text{\hspace{0.17em}}\mathrm{dB}$ in the SNR over the traditional approaches if the fringe images are noisy.

© 2011 Optical Society of America

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