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Region Adjacency Graph (RAG)

version 1.3 (180 KB) by

Computes the graph of adjacent regions in a labeled image



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Computes region adjacency graph of a labeled 2D or 3D image.

Two regions are considered as neighbor if they are separated by a small number of pixel in the horizontal or vertical direction, as well as depth direction for 3D images.

The result is a N*2 array, containing 2 indices for each couple of neighbor regions.

ADJ has the format [LBL1 LBL2], LBL1 and LBL2 being vertical arrays the same size.

LBL1 is given in ascending order, LBL2 is given in ascending order for each LBL1. Ex :
[1 2]
[1 3]
[1 4]
[2 3]
[2 5]
[3 4]

Alternative syntax:
Return two arrays: the first one is a [N*2] array containing centroids of the N labeled region, and ADJ is the adjacency previously described.

For 3D images, the node array is [N*3].

The algorithm proceed in scanning each line (horizontal, vertical, and in z-direction for 3D images), and by detection transitions in the labels. A background gap of width 1 pixel/voxel is assumed to exist between regions. It is possible to specify different gaps:

* gap = 0 if regions are contiguous (no background),
* gap = 1, when considering the result of a watershed, for example
* gap > 1 if regions are separated by thick background (some neignborhoods can be missed)

Comments and Ratings (10)


Works well.


Good tool

Ilya Belevich

Great tool, thank you for sharing!

G. Sken

G. Sken (view profile)

helpfull to compute adjacency relationship between 3D regions segmented via watershed methods.

David Legland

David Legland (view profile)

Hi Kerem,
I have submitted an updated version, in which you can control the "gap" between two regions. If you chosse a gap value equal to 2, it should fit your needs (hopefully !).

Kerem Sahin

Any help for the extension to 8-connected neighborhood of this implementation is appreciated.


Chen (view profile)


Ryan (view profile)

Very useful.

Joao Henriques

Perrine Paul

Very efficient. Some example of use would be of interest, for accessing data.



correct processing of gap>1, and simplification of the code


changes the algorithms to remove the 'diff' function, reducing the amount of memory required, and add psb to use different gaps between regions.


removed dependencies to image processing toolbox, updated doc

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MATLAB 7.9 (R2009b)

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