Implementation of the Centroid Method for the Correction of Turbulence

Abstract

The centroid method for the correction of turbulence consists in computing the Karcher-Fréchet mean of the sequence of input images. The direction of deformation between a pair of images is determined by the optical flow. A distinguishing feature of the centroid method is that it can produce useful results from an arbitrarily small set of input images. Source CodeThe source code and a online demo are accessible at the IPOL web page of this article 1 .

Restoration of atmospheric turbulence-distorted images via RPCA and quasiconformal maps

“…The registration process is furthered complicated by the lack of a good reference frame for the observed image sequence. Meinhardt-Llopis and Micheli [12] proposed a reference extraction method which was coined the centroid method. In its scheme, the deformation fields between each pair of images are computed via optical flow and are assumed to have zero mean.…”

“…For the proposed method, the reference image is reconstructed from a good subsampled sequence, which minimizes the energy (9) considering similarity and sharpness and improves iteratively. As a result, the edges are sharp, the geometric structure 2. http://www.cse.cuhk.edu.hk/leojia/programs/deblurring/ deblurring.htm (a) Ground truth (b) A frame from the synthetic sequence (c) Sobolev gradient-Laplacian method [16] (d) Centroid method [12], deblurred with [26] (e) Two-stage reconstruction method [28] (f) Near-diffraction limited method [11], deblurred with [26] (g) Proposed method is preserved and the texture details are kept. The energy plot of (9) is shown in Figure 14.…”

“…This method is a common tool to tackle the turbulence-degraded video and gives satisfactory registration results in most cases. However, if the turbulence is strong in the sense that the frames are very blurry and severely distorted, the method may not (a) Ground truth (b) A frame from the synthetic sequence (c) Sobolev gradient-Laplacian method [16] (d) Centroid method [12], deblurred with [26] (e) Two-stage reconstruction method [28] (f) Near-diffraction limited method [11] (g) Proposed method (h) Zoom-in of (a) (i) Zoom-in of (b) (j) Zoom-in of (c) (k) Zoom-in of (d) (l) Zoom-in of (e) (m) Zoom-in of (f) (n) Zoom-in of (g) Figure 16 and Figure 18. As shown in Figure 16, the registration results are improved significantly in the sense that the textures are not distorted (zoomed part (f) and (h)) and the edges are sharp (zoomed part (j) and (l)) after applying stabilization.…”

“…Each frame of the simulated sequences is generated from a single image by randomly selecting width×height 250 positions, and considering an image patch centered at each chosen position. A uniform motion vector patch with the same size of the image patch is generated, whereas the vec-(a) Ground truth (b) A frame from the synthetic sequence (c) Sobolev gradient-Laplacian method [16] (d) Centroid method [12], deblurred with [26] (e) Two-stage reconstruction method [28] (f) Near-diffraction limited method [11], deblurred with [26] (g) Proposed method…”

“…The majority of the frames in the Desert and Road sequences are strongly distorted, whereas the remaining are mildly distorted. The restoration results of the sequences are shown (a) An aligned and clear frame from the original sequence (b) A distorted and blurry frame from the original sequence (c) Sobolev gradient-Laplacian method [16] (d) Centroid method [12], deblurred with [26] (e) Two-stage reconstruction method [28] (f) Near-diffraction limited method [11], deblurred with [26] (g) Proposed method (h) Zoom-in of (a) (i) Zoom-in of (b) (j) Zoom-in of (c) (k) Zoom-in of (d) (l) Zoom-in of (e) (m) Zoom-in of (f) (n) Zoom-in of (g) (o) Zoom-in of (a) (p) Zoom-in of (b) (q) Zoom-in of (c) (r) Zoom-in of (d) (s) Zoom-in of (e) (t) Zoom-in of (f) (u) Zoom-in of (g) Fig. 23: Comparison of results on the Chimney sequence in Figure 21 and Figure 22.…”