Gradient vector fields based on variational image decomposition for skeletonization of electronic speckle pattern interferometry fringe patterns with variable density and their applications.

The skeletonization methods based on gradient vector fields (GVFs) have been a powerful tool for electronic speckle pattern interferometry (ESPI) fringe patterns. However, the skeletonization of ESPI fringe patterns with variable density has been an open problem in this area. In this paper, we propose a novel method for calculating GVFs based on the variational image decomposition of ESPI fringe patterns with variable density. In the proposed method, the GVFs of low-density regions are described in Beppo-Levi space, the high-density regions in Hilbert space and the noise regions in curvelet space. The GVFs of a whole image are the sum of the decomposed GVFs of low-density regions and high-density regions. The skeletons of ESPI fringe patterns with variable density can be obtained based on the topological analysis of the GVFs of a whole image. We apply the proposed method to a computer-simulated and two experimentally obtained ESPI fringe patterns with variable density and compare them with the related skeleton methods based on GVFs. The experimental results have demonstrated that the proposed method outperforms the other methods, even when the quality of the ESPI fringe patterns is considerably low.