Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 19, Issue 8, Pages 1978-1986Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2010.2046605
Keywords
Cartoon; filter; image decomposition; texture; total variation
Funding
- National Science Foundation [DMS-0714945, DMS-0312222]
- Centre National d'Etudes Spatiales
- Office of Naval Research [N00014-97-1-0839]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1053675] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0809270] Funding Source: National Science Foundation
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Can images be decomposed into the sum of a geometric part and a textural part? In a theoretical breakthrough, [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. Providence, RI: American Mathematical Society, 2001] proposed variational models that force the geometric part into the space of functions with bounded variation, and the textural part into a space of oscillatory distributions. Meyer's models are simple minimization problems extending the famous total variation model. However, their numerical solution has proved challenging. It is the object of a literature rich in variants and numerical attempts. This paper starts with the linear model, which reduces to a low-pass/high-pass filter pair. A simple conversion of the linear filter pair into a nonlinear filter pair involving the total variation is introduced. This new-proposed nonlinear filter pair retains both the essential features of Meyer's models and the simplicity and rapidity of the linear model. It depends upon only one transparent parameter: the texture scale, measured in pixel mesh. Comparative experiments show a better and faster separation of cartoon from texture. One application is illustrated: edge detection.
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