M ay 2 00 7 L 1 TV computes the flat norm for boundaries
نویسندگان
چکیده
We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. Furthermore, using L1TV, we also obtain the flat norm decomposition. Conversely, using the flat norm as the precise generalization of L1TV functional, we obtain a method for denoising non-boundary or higher co-dimension sets. The flat norm decomposition of differences can made to depend on scale using the flat norm with scale which we define in direct analogy to the L1TV functional. We illustrate the results and implications with examples and figures.
منابع مشابه
L 1 TV Computes the Flat Norm for Boundaries
We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for codimension one boundaries. Furthermore, using L1TV, we also obtain the flat norm decomposition. Conversely, using the flat norm as the precise generalization of L1TV functional, we obtain a method for denoising nonboundary or higher codimension sets. The flat norm decomposition of differenc...
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متن کاملcomputes the flat norm for boundaries
We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for co-dimension one boundaries. While this observation alone is very useful, other important implications for image analysis and shape statistics include a method for denoising sets which are not boundaries or which have higher co-dimension and the fact that using the flat norm to compute dista...
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