Graph cuts in computer vision: Difference between revisions

Revision as of 05:04, 20 July 2018

Revision as of 05:07, 20 July 2018

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Although the general <math>k</math>[[Graph coloring|-colour problem]] remains unsolved for <math>k > 2,</math> the approach of Greig, Porteous and Seheult<ref name="D.M. Greig, B.T 1989"/> has turned out<ref>Y. Boykov, O. Veksler and R. Zabih (1998), "[http://www.cs.cornell.edu/~rdz/Papers/BVZ-cvpr98.pdf Markov Random Fields with Efficient Approximations]", ''International Conference on Computer Vision and Pattern Recognition (CVPR)''.</ref><ref name="boykov2001fast">Y. Boykov, O. Veksler and R. Zabih (2001), "[http://www.cs.cornell.edu/~rdz/Papers/BVZ-pami01-final.pdf Fast approximate energy minimisation via graph cuts]", ''IEEE Transactions on Pattern Analysis and Machine Intelligence'', '''29''', 1222–1239.</ref> to have wide applicability in general computer vision problems. Greig, Porteous and Seheult approaches are often applied iteratively to a sequence of binary problems, usually yielding near optimal solutions.

In 2011, C. Couprie et al. <ref>Camille Couprie, Leo Grady, Laurent Najman and Hugues Talbot, “Power"[http://leogrady.net/wp-content/uploads/2017/01/couprie2011power.pdf Power Watersheds: A Unifying Graph-Based Optimization Framework”Framework]”, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 33, No. 7, pp. 1384-1399, July 2011 http://leogrady.net/wp-content/uploads/2017/01/couprie2011power.pdf</ref> proposed a general image segmentation framework, called the "Power Watershed", that minimized a real-valued indicator function from [0,1] over a graph, constrained by user seeds (or unary terms) set to 0 or 1, in which the minimization of the indicator function over the graph is optimized with respect to an exponent <math>p</math>. When <math>p=1</math>, the Power Watershed is optimized by graph cuts, when <math>p=0</math> the Power Watershed is optimized by shortest paths, <math>p=2</math> is optimized by the [[Random walker algorithm]] and <math>p=\infty</math> is optimized by the [[Watershed (image processing)]] algorithm. In this way, the Power Watershed may be viewed as a generalization of graph cuts that provides a straightforward connection with other energy optimization segmentation/clustering algorithms.

==Binary segmentation of images==

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==Criticism ==

Graph cuts methods have become popular alternatives to the level set-based approaches for optimizing the ___location of a contour (see<ref>Leo Grady and Christopher Alvino (2009), "[http://wwwleogrady.cns.bu.edunet/wp-content/uploads/2017/~lgrady01/grady2009combinatorial.pdf The Piecewise Smooth Mumford-Shah Functional on an Arbitrary Graph]", IEEE Trans. on Image Processing, pp. 2547–2561</ref> for an extensive comparison). However, graph cut approaches have been criticized in the literature for several issues:

* Metrication artifacts: When an image is represented by a 4-connected lattice, graph cuts methods can exhibit unwanted "blockiness" artifacts. Various methods have been proposed for addressing this issue, such as using additional edges<ref>Yuri Boykov and Vladimir Kolmogorov (2003), "Computing Geodesics and Minimal Surfaces via Graph Cuts", Proc. of ICCV</ref> or by formulating the max-flow problem in continuous space.<ref>Ben Appleton and Hugues Talbot (2006), "Globally Minimal Surfaces by Continuous Maximal Flows", IEEE Trans. on Pattern Analysis and Machine Intelligence, pp. 106–118</ref>

* Shrinking bias: Since graph cuts finds a minimum cut, the algorithm can be biased toward producing a small contour.<ref>Ali Kemal Sinop and Leo Grady, "A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm", Proc. of ICCV, 2007</ref> For example, the algorithm is not well-suited for segmentation of thin objects like blood vessels (see<ref>Vladimir Kolmogorov and Yuri Boykov (2005), "What Metrics Can Be Approximated by Geo-Cuts, or Global Optimization of Length/Area and Flux", Proc. of ICCV pp. 564–571</ref> for a proposed fix).