Fast cartoon + texture image filters

Authors:
Antoni Buades;Triet M. Le;Jean-Michel Morel;Luminita A. Vese
Affiliations:
Department Mathématiques Appliquées, Université Paris V, Paris, France;Mathematics Department, Yale University, New Haven, CT;Centre de Mathématiques et de Leurs Applications, École Normale Supérieure de Cachan, France;Mathematics Department, University of California at Los Angeles, Los Angeles, CA
Venue:
IEEE Transactions on Image Processing
Year:
2010

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Abstract

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.