Frontiers of Mathematics in China >
Approximations for modulus of gradients and their applications to neighborhood filters
Received date: 08 Jan 2013
Accepted date: 27 Feb 2013
Published date: 01 Aug 2013
Copyright
We define an integral approximation for the modulus of the gradient |∇u(x)| for functions f:Ω⊂→ 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 |∇u(x)|. We also show some numerical experiments and evaluate the effectiveness of our filters.
Yan CHEN , Zhuangji WANG , Kewei ZHANG . Approximations for modulus of gradients and their applications to neighborhood filters[J]. Frontiers of Mathematics in China, 2013 , 8(4) : 761 -782 . DOI: 10.1007/s11464-013-0297-7
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