3D shape measurement with temporal phase unwrapping and 1-D continuous wavelet transform

Abstract

The correct phase unwrapping in the presence of noise is a di cult problem and it has been of great interest since the last decades as observed in the literature. This is due to the spatial dependency that exists in traditional 2-D phase-unwrapping algorithms and, as a consequence, spreads errors in the reconstructed phase map. To solve this, algorithms known as temporal phase unwrapping (TPU) have been proposed; here the intensity of a fringe image sequence changes as a function of time, and therefore the elements of the phase-map are independent of each other. Thus, the 3-D measurement vision system by projection of fringe images presented here consists in capturing a sequence of images with sinusoidal fringes deformed by the height of the object. Then, the phase is processed by using a TPU technique based the one-dimensional Continuous Wavelet Transform (CWT). It should be noted that the use of CWT in one dimension is to analyze the intensity variations of the temporal sampled phase images, and the importance of this is in the detection of the frequency from which the phase is obtained as a linear function by means of an unwrapping in one dimension. We present simulated experiments and some real applications in digital archaeology and zoological morphometrics that validate the proposal.