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Graph based methods have been used for medical image segmentation problems. Each pixel (voxel in 3D) in the image is represented by a node in the graph while edges connect neighboring nodes. In addition, two nodes namely source and sink are added. A cost is defined for each node (except source and sink) based on which a minimum cost closed set is computed. This set corresponds to a boundary (surface in 3D) which separates nodes belonging to the source from those belonging to the sink. Usually this boundary gives the segmentation required. Details are in this paper.

I have seen quite a few works using this approach but some call their method graph search (Garvin et al.) while others call theirs graph cut (Kaba et al). Upon reading, these works appear very similar.

There is another work which implies a difference between graph search and graph cut but even after reading this work, I am unable to understand the difference.

Can someone please clarify the difference, if any?

Ruchir
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2 Answers2

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Graph search is any way of traversing a graph.

Graph cut is a graph partitioning algorithm that assigns labels to define a minimal cut. To do that, it has to traverse the graph, search the graph.

Eric Leschinski
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aledalgrande
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  • That sounds logical, @aledalgrande. However, this implies that any segmentation has to involve graph cut since labeling can't be done by just traversing the graph. This is not always true since there are methods (cited in my question) which claim to perform the segmentation with graph search. They don't even mention about graph cut. – Ruchir Sep 02 '15 at 03:59
  • Maybe I didn't explain well, but I didn't mean that graph cut and graph search are equivalent, just that graph cut uses graph search as a part of the algorithm. There are other segmentation methods, which still go through the graph, but are not graph cut. – aledalgrande Sep 02 '15 at 04:04
  • Thanks for the answer :) Yeah you are right. As you said, "There are segmentation methods which go through the graph but are not graph cut". My question is how exactly do they differ from graph cut. – Ruchir Sep 02 '15 at 06:29
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I think the Garvin et al (graph search) article you linked is using uncommon terminology. As far as I can tell from skimming the article, "graph search" is supposed to mean "we're searching for a set of vertices in a graph the minimizes some cost function". (But using this loose understanding, almost any graph algorithm could be called a "graph search"). The algorithm they're using for this search is the same as the graph-cut algorithm:

The minimum-cost closed set was then found by computing a minimum s-t cut in a closely related graph

So I think you are right, they actually mean graph cut here. But if you read the term "graph search" elsewhere, it might mean something completely different (e.g. searching for the shortest path in a graph)

Niki
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  • you sound correct to me in your definition of graph search. I wanted to add something. A reviewer commented on a paper about the difference between graph cut and graph search (He may or may not be right, though). He said that graph search refers to algorithms similar to Dykstra's algorithm while methods employing graph cut use maxflow algorithm proposed by Boykov & Kolmogorov [IEEE Trans. Pattern Anal. Mach. Intell. 26(9): 1124-1137 (2004)]. To avoid any confusion I prefer to use the term 'graph-based method'. – Ruchir Dec 10 '15 at 07:53