IEEE Trans Image Process - Revisiting the relationship between adaptive smoothing and anisotropic diffusion with modified filters.

Tópicos

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{ model(3480) simul(1196) paramet(876) }
{ framework(1458) process(801) describ(734) }
{ problem(2511) optim(1539) algorithm(950) }
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Resumo

Anisotropic diffusion has been known to be closely related to adaptive smoothing and discretized in a similar manner. This paper revisits a fundamental relationship between two approaches. It is shown that adaptive smoothing and anisotropic diffusion have different theoretical backgrounds by exploring their characteristics with the perspective of normalization, evolution step size, and energy flow. Based on this principle, adaptive smoothing is derived from a second order partial differential equation (PDE), not a conventional anisotropic diffusion, via the coupling of Fick's law with a generalized continuity equation where a "source" or "sink" exists, which has not been extensively exploited. We show that the source or sink is closely related to the asymmetry of energy flow as well as the normalization term of adaptive smoothing. It enables us to analyze behaviors of adaptive smoothing, such as the maximum principle and stability with a perspective of a PDE. Ultimately, this relationship provides new insights into application-specific filtering algorithm design. By modeling the source or sink in the PDE, we introduce two specific diffusion filters, the robust anisotropic diffusion and the robust coherence enhancing diffusion, as novel instantiations which are more robust against the outliers than the conventional filters.

Resumo Limpo

anisotrop diffus known close relat adapt smooth discret similar manner paper revisit fundament relationship two approach shown adapt smooth anisotrop diffus differ theoret background explor characterist perspect normal evolut step size energi flow base principl adapt smooth deriv second order partial differenti equat pde convent anisotrop diffus via coupl fick law general continu equat sourc sink exist extens exploit show sourc sink close relat asymmetri energi flow well normal term adapt smooth enabl us analyz behavior adapt smooth maximum principl stabil perspect pde ultim relationship provid new insight applicationspecif filter algorithm design model sourc sink pde introduc two specif diffus filter robust anisotrop diffus robust coher enhanc diffus novel instanti robust outlier convent filter

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