Morphological operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns

Abstract

A modified bi-dimensional empirical mode decomposition (BEMD) method is proposed for sparsely decomposing a fringe pattern into two components, namely, a single intrinsic mode function (IMF) and a residue. The main idea of this method is a modified sifting process which employs morphological operations to detect ridges and troughs of the fringes, and uses weighted moving average algorithm to estimate envelopes of the IMF, replacing respective local extrema detection and envelope interpolation of conventional BEMDs. The background intensity of the fringe pattern is automatically removed by extracting the single IMF, thereby relieving the mode mixing problem of the BEMDs. A fast algorithm based on 2D convolution is also presented for reducing the calculation time to several seconds only. This approach is applied to process simulated and real fringe patterns, and the results obtained are compared with Fourier transform, discrete wavelet transform, and other EMD methods. The MATLAB code is downloadable at http://gr.xjtu.edu.cn/web/zhouxiang.

Hilbert-Huang processing and analysis of complex fringe patterns

“…Some comparison of different interpolation techniques is given in [49]. Reported applications of BEMD in the fringe pattern processing and analysis deal with noise reduction in digital speckle interferometry [50], fringe pattern normalization [51], phase measurement in temporal speckle interferometry [52], evaluation of amplitude encoded fringe patterns [53] and, most recently, background and noise removal from fringe patterns [54][55][56]. The practical impact of BEMD is limited by the calculation time lengthened by very costly 2D surface spline interpolation on the irregular extrema grid.…”

Denoising and extracting background from fringe patterns using midpoint-based bidimensional empirical mode decomposition

“…They include Fourier transform [1-3], windowed Fourier [5] or Gabor transform [6], wavelet transform [7,8], smoothed space-frequency distribution [9], and S-transform [10]. As mentioned in [11], however, these integral transform techniques suffer from an uncertainty problem and non-adaptive character.…”

“…As the components are data driven (in contrary to the signal representation using arbitrary basis functions), they are referred to as the Intrinsic Mode Functions (IMFs). Comprehensive surveys of the development of EMD applications for fringe pattern processing can be found in [11,[13][14][15]. References [13,14] describe, in detail, powerful methods for the fringe pattern enhancement including background determination and removal (realized within the general processing frame of the fringe pattern normalization prior to its phase demodulation).…”

Morphological operation-based bi-dimensional empirical mode decomposition for adaptive texture extraction of images

“…That is, images should be represented by as few coefficients as possible to facilitate the proper selection of coefficients for image reconstruction. Based on the idea in [10], this paper presents a morphological operationbased BEMD (MO-BEMD) for sparsely decomposing an image into two components, namely, a single intrinsic mode function (IMF) and a residue, which correspond to the textures with zero local mean and the background intensity of the image, respectively. The sift process of the new method employs morphological operations to detect the ridges and troughs of images, and uses weighted moving averaging algorithm to estimate envelopes.…”