# Chapter 9. Image Segmentation

Image segmentation is the process of partitioning an image into meaningful regions. Regions can be foreground versus background or individual objects in the image. The regions are constructed using some feature such as color, edges, or neighbor similarity. In this chapter we will look at some different techniques for segmentation.

# 9.1 Graph Cuts

A *graph* is a set of nodes (sometimes called vertices) with edges between them. See Figure 9-1 for an example.^{[26]} The edges can be directed (as illustrated with arrows in Figure 9-1) or undirected, and may have weights associated with them.

A *graph cut* is the partitioning of a directed graph into two disjoint sets. Graph cuts can be used for solving many different computer vision problems like stereo depth reconstruction, image stitching, and image segmentation. By creating a graph from image pixels and their neighbors and introducing an energy or a “cost,” it is possible to use a graph cut process to segment an image in two or more regions. The basic idea is that similar pixels that are also close to each other should belong to the same partition.

The cost of a graph cut *C* (where *C* is a set of edges) is defined as the sum of the edge weights of the cuts

Equation 9-1.

where *w _{ij}* is the weight of the edge (

*i*,

*j*) from node

*i*to node

*j*in the graph and the sum is taken over all edges in the cut

*C*.

The idea behind graph ...

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