| Citation: | Manli WANG, Zijian TIAN, Yuangang ZHANG. Minimal Surface Filter Driven by Curvature Difference[J]. Journal of Electronics & Information Technology, 2020, 42(3): 764-771. doi: 10.11999/JEIT190216
|
To improve performance of denoising and edge preservation of the total variational image denoising model, a curvature difference driven minimal surface filter is proposed. Firstly, the presented filter model is constructed by adding an adaptive edge detection function of curvature difference to the mean curvature filter model. After that, from the perspective of differential geometry theory, the physical meaning of the energy functional model and the method of reducing the average curvature energy are elaborated. Finally, in the discrete image domain, the surface in the neighborhood of each pixel of the image is iteratively evolved to the minimal surface to minimize the average curvature energy of the energy functional, so that the total energy of the energy functional is also minimized. Experiments show that the filter can not only remove Gauss noise and salt and pepper noise, but also remove the mixed noise composed of these two kinds of noise. Its performance of noise reduction and edge preservation is better than the other five total variational algorithms of the same kind.
|
RUDIN L I, OSHER S, and FATEMI E. Nonlinear total variation based noise removal algorithms[J]. Physica D: Nonlinear Phenomena, 1992, 60(1/4): 259–268. doi: 10.1016/0167-2789(92)90242-F
|
|
DING Meng, HUANG Tingzhu, WANG Si, et al. Total variation with overlapping group sparsity for deblurring images under Cauchy noise[J]. Applied Mathematics and Computation, 2019, 341: 128–147. doi: 10.1016/j.amc.2018.08.014
|
|
SHEN Zhengwei and CHENG Lishuang. Convex composite wavelet frame and total variation-based image deblurring using nonconvex penalty functions[J]. Journal of Electronic Imaging, 2017, 26(5): 053005. doi: 10.1117/1.JEI.26.5.053005
|
|
郭从洲, 秦志远, 时文俊. 基于能量泛函和视觉特性的全变分图像降噪模型[J]. 中国图象图形学报, 2014, 19(9): 1282–1287. doi: 10.11834/jig.20140904
GUO Congzhou, QIN Zhiyuan, and SHI Wenjun. TV image denoising model based on energy functionals and HVS[J]. Journal of Image and Graphics, 2014, 19(9): 1282–1287. doi: 10.11834/jig.20140904
|
|
LIU Zexian, LIU Hongwei, and WANG Xiping. Accelerated augmented Lagrangian method for total variation minimization[J]. Computational and Applied Mathematics, 2019, 38(2): 50–64. doi: 10.1007/s40314-019-0787-7
|
|
GAO Tianling, WANG Xiaofei, LIU Qiang, et al. A fixed-point algorithm for second-order total variation models in image denoising[J]. Computational and Applied Mathematics, 2019, 38(1): 8–22. doi: 10.1007/s40314-019-0763-2
|
|
ZOU Jian, SHEN Marui, ZHANG Ya, et al. Total variation denoising with non-convex regularizers[J]. IEEE Access, 2019, 7: 4422–4431. doi: 10.1109/ACCESS.2018.2888944
|
|
BEN SAID A, HADJIDJ R, and FOUFOU S. Total variation for image denoising based on a novel smart edge detector: An application to medical images[J]. Journal of Mathematical Imaging and Vision, 2019, 61(1): 106–121. doi: 10.1007/s10851-018-0829-6
|
|
LI Mingqiang, HAN Congying, WANG Ruxin, et al. Shrinking gradient descent algorithms for total variation regularized image denoising[J]. Computational Optimization and Applications, 2017, 68(3): 643–660. doi: 10.1007/s10589-017-9931-8
|
|
王宇, 汤心溢, 罗易雪, 等. 自适应Split Bregman迭代的红外图像降噪算法[J]. 红外与毫米波学报, 2014, 33(5): 546–551. doi: 10.3724/SP.J.1010.2014.00546
WANG Yu, TANG Xinyi, LUO Yixue, et al. IR image denoising algorithm based on adaptive split bregman method[J]. Journal of Infrared and Millimeter Waves, 2014, 33(5): 546–551. doi: 10.3724/SP.J.1010.2014.00546
|
|
FIRSOV D and LUI S H. Domain decomposition methods in image denoising using Gaussian curvature[J]. Journal of Computational and Applied Mathematics, 2006, 193(2): 460–473. doi: 10.1016/j.cam.2005.05.032
|
|
JIDESH P and GEORGE S. Gauss curvature-driven image inpainting for image reconstruction[J]. Journal of the Chinese Institute of Engineers, 2014, 37(1): 122–133. doi: 10.1080/02533839.2012.751332
|
|
ZHU Wei and CHAN T. Image denoising using mean curvature of image surface[J]. SIAM Journal on Imaging Sciences, 2012, 5(1): 1–32. doi: 10.1137/110822268
|
|
GONG Yuanhao. Spectrally regularized surfaces[D]. [Ph.D dissertation], ETH-Zürich, 2015: 127–165. doi: 10.3929/ethz-a-010438292.
|
|
GONG Yuanhao and SBALZARINI I F. Curvature filters efficiently reduce certain variational energies[J]. IEEE Transactions on Image Processing, 2017, 26(4): 1786–1798. doi: 10.1109/tip.2017.2658954
|
|
BAI Yunjiao, ZHANG Quan, HONG Shangguan, et al. Patch similarity modulus and difference curvature based fourth-order partial differential equation for image denoising[J]. Mathematical Problems in Engineering, 2015, 2015: 636295. doi: 10.1155/2015/636295
|
|
YIN Xuehui and ZHOU Shangbo. Image structure-preserving denoising based on difference curvature driven fractional nonlinear diffusion[J]. Mathematical Problems in Engineering, 2015, 2015: 930984. doi: 10.1155/2015/930984
|
|
DONOHO D L and JOHNSTONE J M. Ideal spatial adaptation by wavelet shrinkage[J]. Biometrika, 1994, 81(3): 425–455. doi: 10.1093/biomet/81.3.425
|
Figures(8) / Tables(1)
DownLoad:
