This code was developed by Yuanhao Gong during his PhD at MOSAIC Group. Please cite Yuanhao's PhD thesis if you use this code in your work. Thank you!

@phdthesis{gong:phd, title={Spectrally regularized surfaces}, author={Gong, Yuanhao}, year={2015}, school={ETH Zurich, Nr. 22616},note={http://dx.doi.org/10.3929/ethz-a-010438292}}

Chapter Six in PhD thesis (downloaded 200+), Gaussian Curvature Filter (Talk Slides)

source code in C++ and Java can also be found at MOSAIC

These filters are three or four order of magnitude faster than traditional solvers.

These filter solvers can handle arbitrary imaging model, as long as the imaging model can be evaluated(black box).

The convergence is theoretically guaranteed and the numerical convergence rate is around 1.4 for natural images.

These filters can be implemented in about 40 lines in Matlab and about 100 lines in C++.

GC = Gaussian Curvature, MC = Mean Curvature, TV = Total Variation

The noise free test image can be downloaded here

1. Why dual mesh (DM) structure is needed?

There are two reasons. First, these four sets guarantee the convergence. Second, we can use the updated neighbors for current position. Therefore, it is more computational efficient.

==== 2) What is the difference between these three filters?

In general, GC filter is better in preserving details, compared with the other two. And TV filter is better in removing noise as well as details. MC filter is between these two.

These three filters are correspond to three types of variational models. User should decide which prior is to be assumed about the ground truth.

==== 3) What is the difference between split and nosplit scheme?

In general, splitting the image into four sets and looping on them is computational faster. However, in some cases like deconvolution, we need to merge the four sets after every iteration. So, it is better do nosplit scheme.

These two lead to exactly the same result. The split code is just more cache friendly.