Cookie Settings

We use cookies to optimize our website. These include cookies that are necessary for the operation of the site, as well as those that are only used for anonymous statistic. You can decide for yourself which categories you want to allow. Further information can be found in our data privacy protection .


These cookies are necessary to run the core functionalities of this website and cannot be disabled.

Name Webedition CMS
Purpose This cookie is required by the CMS (Content Management System) Webedition for the system to function correctly. Typically, this cookie is deleted when the browser is closed.
Name econda
Purpose Session cookie emos_jcsid for the web analysis software econda. This runs in the “anonymized measurement” mode. There is no personal reference. As soon as the user leaves the site, tracking is ended and all data in the browser are automatically deleted.

These cookies help us understand how visitors interact with our website by collecting and analyzing information anonymously. Depending on the tool, one or more cookies are set by the provider.

Name econda
Purpose Statistics
External media

Content from external media platforms is blocked by default. If cookies from external media are accepted, access to this content no longer requires manual consent.

Name YouTube
Purpose Show YouTube content
Name Twitter
Purpose activate Twitter Feeds

Interactive Segmentation with Graph-Cuts

Resistor-Network is equivalent to a weighted Graph.

The image is interpreted as a graph G=(V,E), V are the image voxels and E is a set of edges connecting neighboring voxels. The identification of certain vertices as labels is used to partition the graph and hence the image into different regions corresponding to an optimal graph-cut. These regions correspond to the final segmentation of the image. For the partition of the The Random-Walk algorithm [1,2] is a graph-cut approach to interactive image segmentation. With the help of user defined labels several structures in medical images can be segmented at the same time. The segmentation is equivalent to the solution of a system of linear equations. The remaining (non-label) vertices are grouped according to the Random-Walker theory. A vertex belongs to a certain label if the probability of a random walk is highest to arrive at one of those vertices belonging to this label. This problem can be solved analytically. The resulting system of linear equations is equivalent to the inversion problem of a symmetric, sparse matrix.

In graph theory these edges can have weights attached to them. For this algorithm the weight wij connecting the Voxel i and j with i, j in V is calculated with a Gaussian weighting function, i. e.:

wij = exp (-ß(gj - gi)2)

where gi, gj are the gray values of the voxels i and j. The parameterbregularizes the influence of the image data on the weighting factor.

Picture with three different Labels (left). Segmentation result (right).


[1] Grady L, Gareth Funka-Lea. Multi-Label Image Segmentation for Medical Applications Based on Graph-Theoretic Electrical Potentials. In: Proceedings of the 8th ECCV04, Workshop on Computer Vision Approaches to Medical Image Analysis and Mathematical Methods in Biomedical Image Analysis, p. 230-245, May 15th, 2004, Prague, Czech Republic, Springer-Verlag.

[2] Grady L, Schwartz EL. Isoperimetric graph partitioning for image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 2006;28(3):469–475.

to top
powered by webEdition CMS