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Selective Segmentation -- Segment a given 3D image -- (2015)

Software for Selecting an Object in a large image using an active surface based variational model
Jianping Zhang, Ke Chen and Derek Gould (2015)
"A Fast Algorithm for Automatic Segmentation and Extraction of A Single Object By Active Surfaces"
International Journal of Computer Mathematics, Volume 92 (6), pp.1251-1274, 2015.

See the paper in PDF. [Once a close 3D surface is segmented, computing the organ' volume etc is immediate.]

See the left image for an example of selection by 4 /6/4 vertices (on 3 slices) and the segmented result.
Part of Inout Data
Selective Segmentation A -- Segment a given 2D image (CV2 with prior knowledge: AOS solver) --- (2010)

Software for Selecting an Object in a large image using an improved Chan-Vese model
Communications in Computational Physics (CiCP) ``Image Selective Segmentation under Geometrical Constraints Using an Active Contour Approach'' Noor Badshah and Ke Chen (2010)
``Image Selective Segmentation under Geometrical Constraints Using an Active Contour Approach",
Communications in Computational Physics (CiCP), Vol. 7, pp. 759-778, 2010. See PDF file.
See the left image for an example of selection by 4 vertices and the segmented result below.
(Note: as with CV2, this model is not convex so the result might be sensitive to initial contours and also the input parameter α.
Selective Segmentation B -- Segment a given 2D image (CV2 with prior knowledge: fast banding / MGM re-init) --- (2014)

Software for Selecting an Object in a large image using a band based variational model
Jianping Zhang, Ke Chen, Bo Yu and Derek Gould (2014)
``A Local Information Based Variational Model for Selective Image Segmentation",
J. Inverse Problems and Imaging, Volume 8(1), pp. 293-320, 2014. See PDF file.
See the left image for an example of selection by 4 vertices and the segmented result below.
(Note: as with CV2, this model is not convex so the result might be sensitive to initial contours and also the input parameter α. We shall release our convex model / code shortly)
Image Segmentation -- Fast Multigrid Code for the Chan-Vese Model (CV2) -- (2008)
Software for Image Segmentation by CV2 model and NMG
Noor Badshah and Ke Chen (2008),
``Multigrid Method for the Chan-Vese Model in Variational Segmentation",
Communications in Computational Physics, Vol.4 (2), pp.294-316.
See PDF (zip) file.
See the left images for an example of segmented result in 4 NMG cycles.
Fractional α-order restoration -- New Image Denoising Model (2015)
Software for demostrating a total fractional α-order derivatives based variational model for image denoising

Jianping Zhang and Ke Chen (2015),
``A Total Fractional-Order Variation Model for Image Restoration with Non-homogeneous Boundary Conditions and its Numerical Solution",
SIAM Journal on Imaging Sciences, Vol 8 (4), 2015, pp. 2487-2518
See PDF file.
 ------ Applicable to Deblurring and Registration ------

See the left image for an example of restoring a very smooth image (better than TV / mean curvature -- yet convex)
(Note: the code works without knowing the true z of course, but PSNR would need this z.)
TV restoration -- Finding the optimal parameters γ and λ in Image Deblurring and Denoising (2014)
Software for Computing the optimal γ and λ for TV deblurring
Ke Chen, Elena L Piccolomini and Fabiana Zama (2014),
``An automatic regularization parameter selection algorithm in the total variation model for image deblurring",
J. Numer. Algorithms,, Vol 67 (1), pp.73-92, 2014. See PDF file.
See the left image for an example with Gaussian noise and its optimal restoration result by the method. (Note: the code works without knowing the true I of course, but PSNR can be shown for a test image I.)
TV restoration -- Finding the optimal parameter γ in Image Denoising -- (2012)
Software for Computing the optimal γ for TV denoising
Jianping Zhang, Ke Chen and Bo Yu (2012),
``An Iterative Lagrange Multiplier Method for Constrained Total Variation-Based Image Denoising"
SIAM J. Numer. Analysis, Vol 50(3) pp. 983-1003, 2012. See PDF file.
See the left image for an example with Gaussian noise and its optimal restoration result by the method. (Note: with optimal γ=524.66, PSNR=29.98 but with a fixed γ=2000, psnr=28.52); of course for TV, a Bregman idea can be combined for even better results.
TV restoration -- Fast Multilevel Code for Poisson Noise Removal -- (2007)
Software for Poisson Noise Removal by Opt MG
Raymond Chan and Ke Chen (2007),
``Multilevel Algorithm for a Poisson Noise Removal Model with Total-Variation Regularization"
International Journal of Computer Mathematics, 84(8):1183-1198, 2007. See PDF (zip) file.
See the left image for an example with Poisson noise and its restored result by the method.
High Order Restoration -- Fast Multigrid Code for Gaussian Noise Removal by a Mean Curvature Model -- (2010)
Software for Gaussian Noise Removal by High Order Model and NMG
Carlos Brito and Ke Chen (2010),
``Multigrid Algorithm for High Order Denoising",
SIAM Journal on Imaging Sciences, Vol 3(3), pp.363-389. See PDF file.
See the left (Gaussian) for a noisy image and its restored result by the method.
Image Co-registration -- Robust affine code phi(x)=Ax+b -- (2009)
Software for Image Co-registration by multiresolution affine model
Noppadol Chumchob and Ke Chen (2009),
``A Robust Affine Image Registration Method"
International Journal of Numerical Analysis and Modeling, Vol 6 (3), pp.311-334, 2009. See PDF file.
See the left images (top R T) for an example and its registration result (bottom T_k) by the method.
Image Co-registration -- Multigrid Code for a Diffusion Model u=(u1(x,y), u2(x,y)) -- (2011)
Software for Image Co-registration by H1 model and NMG
Noppadol Chumchob and Ke Chen (2011),
``A Robust Multigrid Approach for Variational Image Registration Models",
Journal of Computational and Applied Mathematics, 236:653-674. See PDF file.
See the left images (top R T) for an example and its registration result T_k by the method.
TV restoration -- Fast Multilevel Code for Blur and Noise Removal (2010)
Software for Blur and Gaussian Noise Removal by TV Model and Opt MG
Raymond H Chan and Ke Chen (2010),
``A Multilevel Algorithm for Simultaneously Denoising and Deblurring Images'',
SIAM Journal on Scientific Computing Vol.32, Issue 2, pp. 1043-1063. See PDF file.
See the left images for an example and its deblurred result by NMG.
TV restoration -- Fast Multilevel Code for Gaussian Noise Removal -- (2006)
Software for Gausisan Noise Removal by Optimisaton MG
Tony F. Chan and Ke Chen (2006),
``An Optimization-based Multilevel Algorithm for Total Variation image denoising",
SIAM J. Multiscale Modeling and Simulation Vol 5(2), pp.615-645. See PDF.gz file.
See the left images for 2 examples of denoised results in 4 ML cycles.

(Below setting iout=1 from the above codes) 




iprob=1