title: Fast cartoon + texture image filters.
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.
authors.affiliation: Department Mathématiques Appliquées, Université Paris V, Paris, France. toni.buades@uib.es
authors.forename: Antoni
authors.initials: A
authors.lastname: Buades
authors.forename: Triet M
authors.initials: TM
authors.lastname: Le
authors.forename: Jean-Michel
authors.initials: JM
authors.lastname: Morel
authors.forename: Luminita A
authors.initials: LA
authors.lastname: Vese
mesh_terms: D000465:Algorithms; D002359:Cartoons as Topic; D057225:Data Mining / Q000379:methods; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique