Is there any difference between graph cut and graph search?

Question

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?

Answer 1

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)

Answer 2

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.