Title :
Fast Cartoon + Texture Image Filters
Author :
Buades, Antoni ; Le, Triet M. ; Morel, Jean-Michel ; Vese, Luminita A.
Author_Institution :
Dept. Math. Appl., Univ. Paris V, Paris, France
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.
Keywords :
edge detection; geometry; high-pass filters; image colour analysis; image resolution; image texture; low-pass filters; nonlinear filters; Meyer´s models; edge detection; fast cartoon; linear filter pair; low-pass-high-pass filter pair; minimization problems; nonlinear filter pair; oscillatory distributions; pixel mesh; texture image filters; Cartoon; filter; image decomposition; texture; total variation; Algorithms; Cartoons as Topic; Data Mining; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted; Subtraction Technique;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2010.2046605