# Image-based graphs

Last time I showed you the basics of using the new graph theory functionality in MATLAB R2015b. Today I want to talk about some functions I put on the File Exchange for making graphs from images. Those of you working with graph-based image analysis algorithms might find them useful. I would be very interested in receiving feedback on these functions.

The function `imageGraph` creates a graph representing the neighbor relationships for every pixel in an image with a specified size. `imageGraph3` does the same thing for a 3-D image array.

The function `binaryImageGraph` creates a graph representing the neighbor relationships for every foreground pixel in a binary image. `binaryImageGraph3` creates a graph from a 3-D binary image array.

The function `plotImageGraph` plots a graph created by `imageGraph` or `binaryImageGraph` with the graph nodes arranged on a pixel grid.

Finally, the function `adjacentRegionGraph` creates a graph from a label matrix defining image regions. The graph represents the region adjacency relationships.

### Contents

#### Example: Image graph with 8-connected pixels

Create a graph for a 480-by-640 image with 8-connected pixels.

g = imageGraph([480 640],8)

g = graph with properties: Edges: [1225442x2 table] Nodes: [307200x3 table]

Graph nodes contain the x-coordinate, y-coordinate, and linear index of the corresponding image pixels.

g.Nodes(1:5,:)

ans = x y PixelIndex _ _ __________ 1 1 1 1 2 2 1 3 3 1 4 4 1 5 5

Plot the image graph using `plotImageGraph`.

plotImageGraph(g) axis([100 110 220 230])

#### Example: Image graph with 4-connected pixels

Create a graph for a 480-by-640 image with 4-connected pixels.

g = imageGraph([480 640],4)

g = graph with properties: Edges: [613280x2 table] Nodes: [307200x3 table]

plotImageGraph(g) axis([100 110 220 230])

#### Example: Image graph with special connectivity

Use a 3-by-3 connectivity matrix to create an image graph with 6-connected pixels. Each pixel is connected to its north, northeast, east, south, southwest, and west neighbors.

conn = [0 1 1; 1 1 1; 1 1 0]; g = imageGraph([480 640],conn); plotImageGraph(g) axis([100 110 220 230])

#### Example: Binary image graph

Create a graph whose nodes are the foreground pixels of the binary image text.png (a sample image that is included with the Image Processing Toolbox).

bw = imread('text.png'); imshow(bw) title('Original image')

g = binaryImageGraph(bw); figure plotImageGraph(g) axis([60 85 30 45])

#### Region Graphs

A label matrix defines a set of regions based on each unique element value in the matrix. For example, suppose you had the following label matrix:

L = [10 10 3 4.5 4.5; 10 10 3 4.5 4.5; 20 20 3 15 15; 20 20 3 15 15]

L = 10.0000 10.0000 3.0000 4.5000 4.5000 10.0000 10.0000 3.0000 4.5000 4.5000 20.0000 20.0000 3.0000 15.0000 15.0000 20.0000 20.0000 3.0000 15.0000 15.0000

This label matrix defines 5 regions:

- A 2-by-2 region in the upper left labeled with the value 10.
- A 2-by-2 region in the lower left labeled with the value 20.
- A one-pixel-wide vertical region in the middle labeled with the value 3.
- A 2-by-2 region in the upper right labeled with the value 4.5.
- A 2-by-2 region at the lower right labeled with the value 15.

The function `adjacentRegionsGraph` returns a graph with the same number of nodes as labeled regions. Edges in the graph indicate pairs of adjacent regions.

#### Example: Region graph

Compute an adjacent regions graph. Plot the graph, highlighting the nodes connected to the label 15.

g = adjacentRegionsGraph(L)

g = graph with properties: Edges: [6x2 table] Nodes: [5x1 table]

The graph nodes contain the region labels.

g.Nodes

ans = Label _____ 3 4.5 10 15 20

The graph edges contain the labels for each adjacent region pair.

g.Edges

ans = EndNodes Labels ________ __________ 1 2 3 4.5 1 3 3 10 1 4 3 15 1 5 3 20 2 4 4.5 15 3 5 10 20

Plot the graph, capturing the GraphPlot object as an output argument.

```
gp = plot(g,'NodeLabel',g.Nodes.Label)
```

gp = GraphPlot with properties: NodeColor: [0 0.4470 0.7410] MarkerSize: 4 Marker: 'o' EdgeColor: [0 0.4470 0.7410] LineWidth: 0.5000 LineStyle: '-' NodeLabel: {'3' '4.5' '10' '15' '20'} EdgeLabel: {} XData: [0.0011 0.4051 -1.3642 1.3629 -0.4048] YData: [0.0015 1.5564 -0.8540 0.8538 -1.5577] Use GET to show all properties

Find the neighbors of the region labeled 15.

node_num = find(g.Nodes.Label == 15); neighbors_15 = neighbors(g,node_num); highlight(gp,node_num,neighbors_15)

Next time I plan to show you a graph-based maze solver ... that cheats.

I'd love for you try Image Graphs. Please let me know what you think.

Copyright 2015 The MathWorks, Inc.

Published with MATLAB® R2015b

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