Boundary correction for total variation regularized L^1 function with applications to image decomposition and segmentation

Terrence Chen, Thomas S. Huang

Abstract: The total variation model with L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> norm fidelity term (TV-L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> ) has been proposed to serve as an effective cartoon-texture image decomposition tool because of its unique scale-dependent decomposition ability. Nevertheless, one of its largely overlooked limitations is its inability to perfectly retain the original contours of the selected patterns when the fidelity term is not sufficiently weighted. In this paper, we propose a boundary correction method to refine the contours of extracted patterns under such circumstances. A scale-driven image segmentation algorithm extended from the boundary correction method is presented as an application. Experimental results demonstrate that our works overcome the drawbacks of existing TV-L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> model and provide an alternative segmentation method