Graph Theoretic Segmentation is an image segmentation method based on graph theory, which usually uses the similarity between pixels in an image to construct a graph, and then uses graph theory algorithms to segment the image into multiple regions. This approach is based on the assumption that similar pixels in an image should be assigned to the same region.
In graph-theoretic segmentation, each pixel in an image is regarded as a node of the graph, and the edges between nodes represent the similarity between them. According to different similarity measurement methods, different types of graphs can be constructed, such as fully connected graphs, k-neighbor graphs, etc. Then use graph theory algorithms, such as minimum cut algorithm, spectral clustering, etc. to segment the image into multiple regions.
The advantage of graph theory segmentation is that it can handle complex scenes, such as multiple objects overlapping each other, without knowing in advance the number of objects that need to be segmented. However, its disadvantage is that it is not sensitive to noise and edges in the image, and it is prone to over-segmentation or under-segmentation.
Common applications of graph theory segmentation include image segmentation, object tracking, face recognition, etc.
In graph theory segmentation, the initial seed point refers to a group of pixel points used to guide image segmentation. These points are usually considered as representative points belonging to different regions, such as object edges, obvious color change regions, etc. in the image. The selection of the initial seed point has a great influence on the segmentation results, and different initial seed points may lead to different segmentation results.
Commonly used initial seed point selection methods include manual selection and automatic selection.
Manual selection: Manual selection of initial seed points requires user interaction to select pixels representing different regions in the image via a mouse or other input devices. The advantage of manual selection is that it can select a suitable seed point based on user experience and knowledge, but it requires user interaction, which is time-consuming and impractical for large-scale images.
Automatic selection: automatic selection of initial seed points usually uses some heuristic algorithms to automatically select pixels representing different regions, such as region growing algorithms based on features such as color and texture, and seed point selection algorithms based on edge detection. The advantage of automatic selection is that it can automatically process large-scale images without user interaction, but it needs to select the appropriate algorithm and parameters according to the characteristics of the image.
It should be noted that the selection of the initial seed point has a great impact on the segmentation results, and the appropriate initial seed point selection method and parameters should be selected according to the specific situation.
Graph theory segmentation generally includes the following steps:
1. Construct a graph: The pixels in the image are used as nodes of the graph, and the edges between nodes represent the similarity between them. Commonly used similarity measurement methods include Euclidean distance, color similarity, texture similarity, etc. According to different similarity measurement methods, different types of graphs can be constructed, such as fully connected graphs, k-neighbor graphs, etc.
2. Graph partitioning: Divide an image into multiple regions, each region containing similar pixels. Commonly used graph partitioning algorithms include minimum cut algorithm and spectral clustering algorithm.
3. Minimum cut algorithm: The minimum cut algorithm is based on the minimum cut theorem, which divides the graph into two regions such that the sum of the weights of the edges between them is the smallest. The minimum cut algorithm can be solved by the maximum flow algorithm.
4. Spectral clustering algorithm: The spectral clustering algorithm transforms the image segmentation problem into a clustering problem of eigenvectors, and obtains a set of eigenvectors by decomposing the Laplacian matrix of the image, and then clusters these eigenvectors kind. Spectral clustering algorithms can handle images of different shapes and sizes, but the processing efficiency for large-scale images is low.
5. Post-processing: Post-processing the segmentation results, such as removing small areas, merging adjacent areas, etc., to obtain better segmentation results.
It should be noted that the result of graph theory segmentation may be affected by the initial seed point, so in practical applications, it is necessary to try different initial seed points multiple times to obtain better segmentation results.
In MATLAB, graph-theoretic segmentation can be implemented using functions in Image Processing Toolbox. The following is a basic graph theory segmentation:
% read in image
I = imread('example.jpg');
% Build graph
G = rgb2gray(I);
W = graydiffweight(G, 'GrayDifferenceCutoff', 25);
% Graph division
[~, labels] = graphcut(W, 2, 'MaxIter', 100, 'Verbose', true);
% Display segmentation results
BW = labels == 2;
imshowpair(I, BW, 'montage');
First read in an image, then convert it to a grayscale image. The graph is then constructed using the graydiffweight function, which converts the grayscale differences between pixels into edge weights. Then use the graphcut function for graph division, which uses the minimum cut algorithm to divide the image into two regions and returns a label matrix labels. Finally, set the pixel with a value of 2 in the label matrix labels to white, and set the remaining pixels to black, and use the imshowpair function to display the segmentation results.
To implement graph theory segmentation in C++, you can use the functions in the OpenCV library. The following is a basic graph theory split:
#include <opencv2/opencv.hpp>
#include <iostream>
using namespace cv;
using namespace std;
int main()
{ // read image Mat image = imread("example.jpg");
// 构建图
Mat grayImage;
cvtColor(image, grayImage, COLOR_BGR2GRAY);
Mat weight = Mat::zeros(image.rows*image.cols, image.rows*image.cols, CV_32FC1);
int n = 10; // k邻近图中的k值
for(int i = 0; i < image.rows; i++)
{
for(int j = 0; j < image.cols; j++)
{
int centerIndex = i*image.cols + j;
for(int m = -n; m <= n; m++)
{
for(int k = -n; k <= n; k++)
{
int rowIndex = i + m;
int colIndex = j + k;
if(rowIndex >= 0 && rowIndex < image.rows && colIndex >= 0 && colIndex < image.cols)
{
int neighborIndex = rowIndex*image.cols + colIndex;
float weightValue = abs(grayImage.at<uchar>(i, j) - grayImage.at<uchar>(rowIndex, colIndex));
weight.at<float>(centerIndex, neighborIndex) = weightValue;
weight.at<float>(neighborIndex, centerIndex) = weightValue;
}
}
}
}
}
// 图划分
Mat labels;
int numLabels = 2;
double t = threshold(weight, weight, 0, 255, THRESH_BINARY | THRESH_OTSU);
minCut(weight, labels, numLabels, t);
labels.convertTo(labels, CV_8U, 255 / (numLabels - 1));
// Display the segmentation result
Mat result;
bitwise_not(labels, result);
imshow("Result", result);
waitKey(0);
return 0;
}
In this example, an image is first read in and then converted to grayscale. Then use the k-neighbor graph method to construct a graph, and convert the gray level difference between pixels into edge weights. Then use the minCut function for graph partitioning, which uses the minimum cut algorithm to split the image into two regions and returns a label matrix labels. Finally, set the pixel with a value of 1 in the label matrix labels to white, and set the remaining pixels to black, and use the imshow function to display the segmentation results.
To implement graph segmentation in Python, you can use the functions in the scikit-image library. Here is a basic graph theory segmentation:
import numpy as np
import matplotlib.pyplot as plt
from skimage import data, segmentation, color
# read image
image = data.coffee()
# Graph division
labels = segmentation.slic(image, n_segments=2, compactness=10)
# Display segmentation results
plt.subplot(1, 2, 1)
plt.imshow(image)
plt.axis('off')
plt.title('Original image')
plt.subplot(1, 2, 2)
plt.imshow(color.label2rgb(labels, image))
plt.axis('off')
plt.title('Segmented image')
plt.show()
```
In this example, an image is first read in, and then the graph is divided using the slic function, which uses the superpixel segmentation method to divide the image into a fixed number of regions. Returns a label matrix labels. Finally, set the pixel with a value of 1 in the label matrix labels to white, and set the remaining pixels to black, and use the imshow function to display the segmentation results.