A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations
We introduce a variational model for multi-phase image segmentation that uses a multiscale sparse representation frame (wavelets or other) in a modified diffuse interface context. The segmentation model we present differs from other state-of-the-art models in several ways. The diffusive nature of th...
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doaj-287e78db52f04eadae3dca49533cef9c2020-11-25T00:38:14ZengMDPI AGJournal of Imaging2313-433X2017-07-01332610.3390/jimaging3030026jimaging3030026A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse RepresentationsJulia Dobrosotskaya0Weihong Guo1Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USADepartment of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USAWe introduce a variational model for multi-phase image segmentation that uses a multiscale sparse representation frame (wavelets or other) in a modified diffuse interface context. The segmentation model we present differs from other state-of-the-art models in several ways. The diffusive nature of the method originates from the sparse representations and thus propagates information in a different manner comparing to any existing PDE models, allowing one to combine the advantages of non-local information processing with sharp edges in the output. The regularizing part of the model is based on the wavelet Ginzburg–Landau (WGL) functional, and the fidelity part consists of two terms: one ensures the mean square proximity of the output to the original image; the other takes care of preserving the main edge set. Multiple numerical experiments show that the model is robust to noise yet can preserve the edge information. This method outperforms the algorithms from other classes in cases of images with significant presence of noise or highly uneven illuminationhttps://www.mdpi.com/2313-433X/3/3/26multiphase segmentationvariational methoddiffuse interfacewavelets |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Julia Dobrosotskaya Weihong Guo |
spellingShingle |
Julia Dobrosotskaya Weihong Guo A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations Journal of Imaging multiphase segmentation variational method diffuse interface wavelets |
author_facet |
Julia Dobrosotskaya Weihong Guo |
author_sort |
Julia Dobrosotskaya |
title |
A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations |
title_short |
A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations |
title_full |
A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations |
title_fullStr |
A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations |
title_full_unstemmed |
A PDE-Free Variational Method for Multi-Phase Image Segmentation Based on Multiscale Sparse Representations |
title_sort |
pde-free variational method for multi-phase image segmentation based on multiscale sparse representations |
publisher |
MDPI AG |
series |
Journal of Imaging |
issn |
2313-433X |
publishDate |
2017-07-01 |
description |
We introduce a variational model for multi-phase image segmentation that uses a multiscale sparse representation frame (wavelets or other) in a modified diffuse interface context. The segmentation model we present differs from other state-of-the-art models in several ways. The diffusive nature of the method originates from the sparse representations and thus propagates information in a different manner comparing to any existing PDE models, allowing one to combine the advantages of non-local information processing with sharp edges in the output. The regularizing part of the model is based on the wavelet Ginzburg–Landau (WGL) functional, and the fidelity part consists of two terms: one ensures the mean square proximity of the output to the original image; the other takes care of preserving the main edge set. Multiple numerical experiments show that the model is robust to noise yet can preserve the edge information. This method outperforms the algorithms from other classes in cases of images with significant presence of noise or highly uneven illumination |
topic |
multiphase segmentation variational method diffuse interface wavelets |
url |
https://www.mdpi.com/2313-433X/3/3/26 |
work_keys_str_mv |
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1725298299410317312 |