Volume 7, Issue 3
A Nonlocal Total Variation Model for Image Decomposition: Illumination and Reflectance

Wei Wang & Michael K. Ng

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 334-355.

Published online: 2014-07

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  • Abstract

In this paper, we study to use nonlocal bounded variation (NLBV) techniques to decompose an image intensity into the illumination and reflectance components. By considering spatial smoothness of the illumination component and nonlocal total variation (NLTV) of the reflectance component in the decomposition framework, an energy functional is constructed. We establish the theoretical results of the space of NLBV functions such as lower semicontinuity, approximation and compactness. These essential properties of NLBV functions are important tools to show the existence of solution of the proposed energy functional. Experimental results on both grey-level and color images are shown to illustrate the usefulness of the nonlocal total variation image decomposition model, and demonstrate the performance of the proposed method is better than the other testing methods.

  • Keywords

Image decomposition, illumination, reflectance, nonlocal total variation, iterative method.

  • AMS Subject Headings

68U10, 65K05, 65N21

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-334, author = {}, title = {A Nonlocal Total Variation Model for Image Decomposition: Illumination and Reflectance}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {3}, pages = {334--355}, abstract = {

In this paper, we study to use nonlocal bounded variation (NLBV) techniques to decompose an image intensity into the illumination and reflectance components. By considering spatial smoothness of the illumination component and nonlocal total variation (NLTV) of the reflectance component in the decomposition framework, an energy functional is constructed. We establish the theoretical results of the space of NLBV functions such as lower semicontinuity, approximation and compactness. These essential properties of NLBV functions are important tools to show the existence of solution of the proposed energy functional. Experimental results on both grey-level and color images are shown to illustrate the usefulness of the nonlocal total variation image decomposition model, and demonstrate the performance of the proposed method is better than the other testing methods.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1326nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5878.html} }
TY - JOUR T1 - A Nonlocal Total Variation Model for Image Decomposition: Illumination and Reflectance JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 334 EP - 355 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1326nm UR - https://global-sci.org/intro/article_detail/nmtma/5878.html KW - Image decomposition, illumination, reflectance, nonlocal total variation, iterative method. AB -

In this paper, we study to use nonlocal bounded variation (NLBV) techniques to decompose an image intensity into the illumination and reflectance components. By considering spatial smoothness of the illumination component and nonlocal total variation (NLTV) of the reflectance component in the decomposition framework, an energy functional is constructed. We establish the theoretical results of the space of NLBV functions such as lower semicontinuity, approximation and compactness. These essential properties of NLBV functions are important tools to show the existence of solution of the proposed energy functional. Experimental results on both grey-level and color images are shown to illustrate the usefulness of the nonlocal total variation image decomposition model, and demonstrate the performance of the proposed method is better than the other testing methods.

Wei Wang & Michael K. Ng. (2020). A Nonlocal Total Variation Model for Image Decomposition: Illumination and Reflectance. Numerical Mathematics: Theory, Methods and Applications. 7 (3). 334-355. doi:10.4208/nmtma.2014.1326nm
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