Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification

By Andy Tsai, Anthony J. Yezzi Jr., Alan S. Willsky. IEEE Transactions on Image Processing, 2001

976 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/035c3e0009b5623505af55bc68129e1343b31f9b

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Citations in the corpus

A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape (2007, methodology): “The probabilistic formulation of the segmentation problem presented in the following extends the statistical approaches pioneered in Leclerc (1989), Zhu and Yuille (1996), Paragios and Deriche (2002) and Tsai et al. (2001).”
Improving Iris Recognition Performance Using Segmentation, Quality Enhancement, Match Score Fusion, and Indexing (2008, methodology): “In the second stage, we apply the modified Mumford Shah functional [40] in a narrow band over the estimated boundaries to compute the exact inner and outer boundaries of the iris.”
An efficient local Chan-Vese model for image segmentation (2010, background): “It is well-known that some traditional level set methods used either the image gradient [6–8] or the global information [10,11] to drive the evolving curve(s) towards the true boundaries.”
Active contours driven by local image fitting energy (2010, methodology): “[16] proposed two similar models, which are called piecewise smooth (PS) model.”
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model (2002, methodology): “Most of the models need three level set functions, as in Zhao et al. (1996) and Samson et al.”
Digital inpainting based on the Mumford–Shah–Euler image model (2002, methodology): “[47] it serves as one of the major examples and applications for the numerical active contour algorithm.”
Active contours driven by local Gaussian distribution fitting energy (2009, methodology): “[12] have proposed the PS models to overcome the problems with the PC model in handling image inhomogeneities.”
Segmentation and tracking of migrating cells in videomicroscopy with parametric active contours: a tool for cell-based drug testing (2002, background): “, [18] and [19]), partly because it is able to overcome both of these shortcomings.”
An algorithm for minimizing the Mumford-Shah functional (2009, methodology): “A quite popular class of algorithms is based on the level set method [20, 19] or splines [10].”
State-of-the-Art Methods for Brain Tissue Segmentation: A Review (2017, background): “ima irrespective of initial contour choice [12], [43], [53], [54].”
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints (2010, methodology): “Other variational models are for example the Euler elastica model [38], the active contour model [114] which is based on the Mumford-Shah segmentation problem, but also higher order variational approaches.”
Variational PDE models in image processing (2002, background): “21, 53], and also in the related works [52, 55, 41, 44, 58].”
Minimization of Region-Scalable Fitting Energy for Image Segmentation (2008, background): “Existing active contour models can be categorized into two major classes: edge-based models [3], [10]–[12], [18], [19], [28], [30], and region-based models [4], [23], [25]–[27], [29].”
A Level Set Method for Image Segmentation in the Presence of Intensity Inhomogeneities With Application to MRI (2011, methodology): “In [20], [22], level set methods were proposed as PS models for image segmentation.”
A nonparametric statistical method for image segmentation using information theory and curve evolution (2005, positive): “…which provide the basis for a variety of more recent methods, include boundary-based segmentation such as Canny edge detection [5], region-based segmentation such as region growing [2], [25], and global optimization approaches such as those based on the Mumford-Shah functional [28], [9], [39].”