On a generalized 5 × 5 stencil scheme for nonlinear diffusion filtering
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Optimized kernels for approximating first order spatial derivatives in the regularized Perona–Malik diffusion filter reveal an excellent degree of rotational invariance but produce small checkerboard artifacts in the processed image. In this work, our focus is to reduce these checkerboard artifacts, without a compromise in rotational invariance. To achieve the same, we propose a new 5 × 5 stencil scheme based on generalized finite difference idea. The free parameter in the proposed scheme can be set to recover various well-known schemes. Based on the numerical experiments, we suggest a value of the parameter to have less checkerboard artifacts. We also prove the consistency and the stability of the proposed scheme. A pre-smoothing with 3 × 3 Gaussian mask at every iteration step further improves the quality of the processed image. Simulation results show that the hybrid scheme obtained with such a pre-smoothing is more efficient in computational cost.
KeywordsNonlinear diffusion Rotational invariance Numerical dissipativity Finite difference method Checkerboard artifacts
Mathematics Subject Classification65N06 35K55 94A08
Second author thanks the Council of Scientific and Industrial Research, India (Grant number: 09/084(0584)/2011-EMR-I) for financial support. We are thankful to the High Performance Computing Center, IIT Madras, India for providing their computing facility to carry out these experiments. We are also thankful to Dr. Arun Kumar and Ms. Raisa Dsouza for final proof reading of this draft.
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