Unsupervised-clustering-driven noise-residue filter for phase images

Abstract

We analyze the characteristics of noise-induced phase inconsistencies, or residues, in a wrapped phase map. Because residues are the potential source of phase-error propagation, it is essential to filter them before two-dimensional phase unwrapping. We propose an unsupervised-clustering-driven noise-residue filter, and apply it as a preprocessing procedure of phase unwrapping. The filter is based on the fact that most residues are present in the form of adjacency caused by noisy wrapped phases. These noisy phases differ from the other correct ones numerically within the local k(1) x k(2) window containing the adjacent residues, and it is possible to group the correct and noisy wrapped phases into different clusters. The window size is determined adaptively according to the local noise level. The proposed procedure avoids constructing branch cuts, and converts path-following unwrapping to path independence, which improves the operating speed of phase unwrapping significantly. The tests performed on simulated and real projected fringe patterns confirm the validity of our approach in residue reduction, fringe preservation, and rapidity.

Adaptive phase denoising based on first order local polynomial analysis

“…If the absolute gradient difference of two adjacent pixels is less than (Itoh condition [3]), we can easily do the unwrapping by adding or minusing a multiples of 2 row by row or column by column. However, the Itoh condition is not always satisfied because of three reasons [4]: (1) under sampling, (2) uncontinuous surfaces and (3) noise.…”

“…There are lots of unwrapping method which can be classified into two classes [4]: (a) algorithm driven and (b) residue-removal. In the algorithm driven unwrapping method, models are given which avoid the effects of residues in the unwrapping procedure.…”

“…We conclude the denoising methods into three: (a) spatial filter; (b) frequency filter, and (c) regularization method. The spatial filter do the denoising by multiplying different masks [13], averaging based on nonlocal self-similarity [14], carrying on the non-linear local filter [4,15] or using the local polynomial approximation [16,17] to get rid of the noise. The frequency filter removes the noise by using a low pass or high pass filter in the frequency domain [18,9,19].…”

Modified detection scheme for locating phase jumps and reducing detection errors

“…Residual noise is distributed in parts of regions in the wrapped phase map, caused by a contamination of either the sample or the optical system. The noise at the height discontinuities arises due to the inherent diffraction and depth-of-field limitations of the optical system [1,2,6,12]. The above three different types of noise easily cause the spatial phase unwrapping algorithms to fail.…”

“…Prior to phase unwrapping, the filtering algorithms commonly remove or reduce the noise in order to improve the unwrapping result. Filtering algorithms can be broadly classified as either linear [20] or nonlinear [1,2,12,21]. Unfortunately, since the linear-filtering algorithms filter the noise and the phase jumps, they remove the noise and also seriously smear the phase jumps.…”