A survey of graph theoretical approaches to image segmentation

TLDR: A systematic survey of graph theoretical methods for image segmentation, where the problem is modeled in terms of partitioning a graph into several sub-graphs such that each of them represents a meaningful object of interest in the image.

About: This article is published in Pattern Recognition.The article was published on 2013-03-01 and is currently open access. It has received 345 citations till now. The article focuses on the topics: Scale-space segmentation & Segmentation-based object categorization.

Figures

Figure 1: An example of graph cuts and the corresponding vertex labeling. (a) shows a graph whose vertices are image pixels, and maintains the 4-neighborhood system. Graph cuts separate the graph into three subgraphs. A labeling shown in (b) assigns some label Lp∈{0,1,2} to each pixel w.r.t. the graph cuts. Thick lines show labeling discontinuities between neighboring pixels.

Figure 3: (a) The original image. (b) The segmentation result of Ncut algorithm [46]. (c-h) The eigenvectors corresponding to the second smallest to the seventh smallest eigenvalues of the system. The eigenvectors are reshaped to be the size of the image. The code is provided by Shi et al. [46] (http://www.cis.upenn.edu/~jshi/software/).

Figure 4: Graph cut model and labeling for a 3×3 image. (a) An s/t graph cut model (left), where the boundary term in Eq. (8) defines the n-links and the regional term defines the t-links. A cut partitions the graph into two sets (right). (b) A multi-label graph cut model (left) and a multiway cut (right).

Figure 12: Histograms of the best PR, NPR, GCE, VOI and BDE scores on 500 images by the FH method [40], Ncut method [46], Rcut method [52] and mean-shift method [108], respectively.

Figure 14: Segmentation results of GC [57], IGC [69], LS [81] and RW [32] with the same input seeds. The first column shows the original images with seeds. The second to the fifth columns show the segmentation results obtained by GC, IGC, LS and RW, respectively.

Figure 13: Segmentation results under different sets of parameters for FH, Ncut and Rcut algorithms. The number of segments is the same for the three methods on the same image, and changes ascendingly from left to right.

Frequently asked questions

Q1. What are the contributions in "A survey of graph theoretical approaches to image segmentation" ?

In this paper, the authors conduct a systematic survey of graph theoretical methods for image segmentation, where the problem is modeled in terms of partitioning a graph into several sub-graphs such that each of them represents a meaningful object of interest in the image. The authors present motivations and detailed technical descriptions for each category of methods. 

Q2. What future works have the authors mentioned in the paper "A survey of graph theoretical approaches to image segmentation" ?

The use of graph as a representation of the image provides us an effective way to study the problem of image segmentation. The close relationship between them is not by accident and can be easily understood in two folds. Particularly, in recent years the emergence of many new algorithms proves that this category of techniques is still a promising research direction in the image segmentation community. Further study can refer to versatile graph based algorithms for a wide range of practical applications.