Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation
To avoid the irregularities during the level set evolution, a fractional distance regularized variational model is proposed for image segmentation. We first define a fractional distance regularization term which punishes the deviation of the level set function (LSF) and the signed distance function....
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doaj-78506d7e20814fe68234fc0413f84c4f2021-03-30T01:42:47ZengIEEEIEEE Access2169-35362020-01-018846048461710.1109/ACCESS.2020.29917279084105Fractional Distance Regularized Level Set Evolution With Its Application to Image SegmentationMeng Li0Yi Zhan1https://orcid.org/0000-0001-5208-7396Yongxin Ge2https://orcid.org/0000-0003-3266-1009College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, ChinaCollege of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, ChinaSchool of Big Data and Software Engineering, Chongqing University, Chongqing, ChinaTo avoid the irregularities during the level set evolution, a fractional distance regularized variational model is proposed for image segmentation. We first define a fractional distance regularization term which punishes the deviation of the level set function (LSF) and the signed distance function. Since the fractional derivative of the constant value function outside the starting point is nonzero, the fractional gradient modular of the LSF does not approach infinity where the integer order gradient modular is close to 0. This prevents the sharp reverse diffusion of LSF in flat areas and ensures the smooth evolution of LSF. Then, we use the Grünwald-Letnikov (G-L) fractional derivative to derive the discrete forms of the conjugate of fractional derivatives and fractional divergence. To facilitate the calculation of fractional derivatives and their conjugates, we designed their covering templates. Finally, a numerical solution to the minimization of the energy functional is obtained from these discrete forms and covering templates. Numerical experiments of medical images with different modalities show that the model in this paper can well segment weak images and intensity inhomogeneity images.https://ieeexplore.ieee.org/document/9084105/Image segmentationfractional distance regularizationlevel set evolutionfractional derivativefractional divergence |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Meng Li Yi Zhan Yongxin Ge |
spellingShingle |
Meng Li Yi Zhan Yongxin Ge Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation IEEE Access Image segmentation fractional distance regularization level set evolution fractional derivative fractional divergence |
author_facet |
Meng Li Yi Zhan Yongxin Ge |
author_sort |
Meng Li |
title |
Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation |
title_short |
Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation |
title_full |
Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation |
title_fullStr |
Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation |
title_full_unstemmed |
Fractional Distance Regularized Level Set Evolution With Its Application to Image Segmentation |
title_sort |
fractional distance regularized level set evolution with its application to image segmentation |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2020-01-01 |
description |
To avoid the irregularities during the level set evolution, a fractional distance regularized variational model is proposed for image segmentation. We first define a fractional distance regularization term which punishes the deviation of the level set function (LSF) and the signed distance function. Since the fractional derivative of the constant value function outside the starting point is nonzero, the fractional gradient modular of the LSF does not approach infinity where the integer order gradient modular is close to 0. This prevents the sharp reverse diffusion of LSF in flat areas and ensures the smooth evolution of LSF. Then, we use the Grünwald-Letnikov (G-L) fractional derivative to derive the discrete forms of the conjugate of fractional derivatives and fractional divergence. To facilitate the calculation of fractional derivatives and their conjugates, we designed their covering templates. Finally, a numerical solution to the minimization of the energy functional is obtained from these discrete forms and covering templates. Numerical experiments of medical images with different modalities show that the model in this paper can well segment weak images and intensity inhomogeneity images. |
topic |
Image segmentation fractional distance regularization level set evolution fractional derivative fractional divergence |
url |
https://ieeexplore.ieee.org/document/9084105/ |
work_keys_str_mv |
AT mengli fractionaldistanceregularizedlevelsetevolutionwithitsapplicationtoimagesegmentation AT yizhan fractionaldistanceregularizedlevelsetevolutionwithitsapplicationtoimagesegmentation AT yongxinge fractionaldistanceregularizedlevelsetevolutionwithitsapplicationtoimagesegmentation |
_version_ |
1724186555084439552 |