Total Variation in Imaging

Automatic 3D model-based method for liver segmentation in MRI based on active contours and total variation minimization

“…Specifically, we follow the dual approach to the minimization of the variational energies proposed by Chambolle in [18] for the 2D case. This approach has been adopted in general segmentation and denoising applications [18][19][20]. However, it has not been applied previously to liver segmentation in MRI.…”

Approximating the total variation with finite differences or finite elements

“…This regularizer is not so widely used nowadays as its performances are below many state-of-the art reconstruction methods (in particular, based on deep learning or other non-local techniques), yet, being convex and relatively simple, it is still useful and popular for large scale inverse problems (typically, medical imaging applications) or in low noise regimes. We refer to [25,23] for a quick introduction to total variation for imaging and to [32] for more numerical details and algorithms. In fact, these notes are not only focused on imaging applications, as one might need to minimize the total variation for other goals, such as computing minimal surfaces, equilibrium configurations of mixtures with surface tension, etc.…”

Variational approximation of interface energies and applications

“…The main reason is that there is no unique ground-truth classification of an image with respect to which the output an algorithm can be compared. In the literature many models for restoration and/or segmentation of image have been developed, such as the Mumford-Shah [9,42] and the TV-L 2 and TV-L 1 functionals [22,48].…”