Approximations for modulus of gradients and their applications to neighborhood filters

作者：Chen Yan; Wang Zhuangji; Zhang Kewei^*

来源：Frontiers of Mathematics in China, 2013, 8(4): 761-782.

DOI：10.1007/s11464-013-0297-7

• BMO
• modulus of gradient
• harmonic analysis and PDE
• neighborhood filter
• image processing

We define an integral approximation for the modulus of the gradient |a double dagger u(x)| for functions f: Omega aS, a%26quot;e (n) -%26gt; a%26quot;e by modifying a classical result due to Calderon and Zygmund. Our integral approximations are more stable than the pointwise defined derivatives when applied to numerical differentiation for discrete data. We apply our results to design and analyse neighborhood filters. These filters correspond to well-behaved nonlinear heat equations with the conductivity decreasing with respect to the modulus of gradient |a double dagger u(x)|. We also show some numerical experiments and evaluate the effectiveness of our filters.

• 出版日期2013-8
• 单位中国农业大学