Journal
SIAM JOURNAL ON IMAGING SCIENCES
Volume 10, Issue 3, Pages 1258-1290Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1075247
Keywords
total variation; variational image processing; coarea formula; finite-difference schemes
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We propose a new definition for the gradient field of a discrete image defined on a twice finer grid. The differentiation process from an image to its gradient field is viewed as the inverse operation of linear integration, and the proposed mapping is nonlinear. Then, we define the total variation of an image as the Li norm of its gradient field amplitude. This new definition of the total variation yields sharp edges and has better isotropy than the classical definition.
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