Evolution-Operator-Based Single-Step Method for Image Processing
This work proposes an evolution-operator-based single-time-step method for image and signal processing. The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Biomedical Imaging |
| Online Access: | http://dx.doi.org/10.1155/IJBI/2006/83847 |
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| _version_ | 1832567048118468608 |
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| author | Yuhui Sun Peiru Wu G. W. Wei Ge Wang |
| author_facet | Yuhui Sun Peiru Wu G. W. Wei Ge Wang |
| author_sort | Yuhui Sun |
| collection | DOAJ |
| description | This work proposes an evolution-operator-based single-time-step
method for image and signal processing. The key component of the
proposed method is a local spectral evolution kernel (LSEK) that
analytically integrates a class of evolution partial differential
equations (PDEs). From the point of view PDEs, the LSEK provides
the analytical solution in a single time step, and is of spectral
accuracy, free of instability constraint. From the point of
image/signal processing, the LSEK gives rise to a family of
lowpass filters. These filters contain controllable time delay and
amplitude scaling. The new evolution operator-based method is
constructed by pointwise adaptation of anisotropy to the
coefficients of the LSEK. The Perona-Malik-type of anisotropic
diffusion schemes is incorporated in the LSEK for image denoising.
A forward-backward diffusion process is adopted to the LSEK for
image deblurring or sharpening. A coupled PDE system is modified
for image edge detection. The resulting image edge is utilized for
image enhancement. Extensive computer experiments are carried out
to demonstrate the performance of the proposed method. The major
advantages of the proposed method are its single-step solution and
readiness for multidimensional data analysis. |
| format | Article |
| id | doaj-art-a3e061f1596b4b9ea160071a3af58f3f |
| institution | Kabale University |
| issn | 1687-4188 1687-4196 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Biomedical Imaging |
| spelling | doaj-art-a3e061f1596b4b9ea160071a3af58f3f2025-02-03T01:02:31ZengWileyInternational Journal of Biomedical Imaging1687-41881687-41962006-01-01200610.1155/IJBI/2006/8384783847Evolution-Operator-Based Single-Step Method for Image ProcessingYuhui Sun0Peiru Wu1G. W. Wei2Ge Wang3Department of Mathematics, College of Natural Science, Michigan State University, MI 48824, USADepartment of Mathematics, College of Natural Science, Michigan State University, MI 48824, USADepartment of Mathematics, College of Natural Science, Michigan State University, MI 48824, USADepartment of Radiology and Department of Biomedical Engineering, University of Iowa, Iowa City, IA 52242, USAThis work proposes an evolution-operator-based single-time-step method for image and signal processing. The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. From the point of image/signal processing, the LSEK gives rise to a family of lowpass filters. These filters contain controllable time delay and amplitude scaling. The new evolution operator-based method is constructed by pointwise adaptation of anisotropy to the coefficients of the LSEK. The Perona-Malik-type of anisotropic diffusion schemes is incorporated in the LSEK for image denoising. A forward-backward diffusion process is adopted to the LSEK for image deblurring or sharpening. A coupled PDE system is modified for image edge detection. The resulting image edge is utilized for image enhancement. Extensive computer experiments are carried out to demonstrate the performance of the proposed method. The major advantages of the proposed method are its single-step solution and readiness for multidimensional data analysis.http://dx.doi.org/10.1155/IJBI/2006/83847 |
| spellingShingle | Yuhui Sun Peiru Wu G. W. Wei Ge Wang Evolution-Operator-Based Single-Step Method for Image Processing International Journal of Biomedical Imaging |
| title | Evolution-Operator-Based Single-Step Method for Image Processing |
| title_full | Evolution-Operator-Based Single-Step Method for Image Processing |
| title_fullStr | Evolution-Operator-Based Single-Step Method for Image Processing |
| title_full_unstemmed | Evolution-Operator-Based Single-Step Method for Image Processing |
| title_short | Evolution-Operator-Based Single-Step Method for Image Processing |
| title_sort | evolution operator based single step method for image processing |
| url | http://dx.doi.org/10.1155/IJBI/2006/83847 |
| work_keys_str_mv | AT yuhuisun evolutionoperatorbasedsinglestepmethodforimageprocessing AT peiruwu evolutionoperatorbasedsinglestepmethodforimageprocessing AT gwwei evolutionoperatorbasedsinglestepmethodforimageprocessing AT gewang evolutionoperatorbasedsinglestepmethodforimageprocessing |