Skip to content

Latest commit

 

History

History
76 lines (50 loc) · 3.26 KB

README.md

File metadata and controls

76 lines (50 loc) · 3.26 KB
Raw

Image Segmentation Using Random Walker Algorithm

This repository contains the implementation of the Random Walker Algorithm for image segmentation. This technique is part of a computational approach to segmenting images based on probability calculations and pixel value analysis.

Overview

The Random Walker Algorithm is a powerful method for image segmentation that treats pixel nodes in an image as a part of a graph. Segmentation is achieved by marking nodes and calculating the probability of a neighbor taking the same pixel value, inversely proportional to the difference between the pixel values.

Random Walk Algorithm Formulas

The Random Walk Algorithm for image segmentation is based on the following steps and formulas:

Random Walk Algorithm Formulas

The Random Walk Algorithm for image segmentation is based on the following steps and formulas:

  1. Node Marking: The nodes in the image are marked based on the following criteria:

    • Let $p(i, j)$ be the pixel value at position (i, j) in the image.
    • Mark the nodes as follows:
      • If $p(i, j) > 110$, then mark as 255 (white).
      • If $p(i, j) < 75$, then mark as 0 (black).

  2. Matrix Operations: All the unmarked nodes will be marked in subsequent steps. The key formula in the Random Walk Algorithm for image segmentation is: $$L_u \cdot X = (-B)^T \cdot M$$ Where:

    • $L_u$ is a submatrix of the L matrix containing information about all the unmarked to unmarked nodes.
    • $X$ is the matrix representing probabilities.
    • $B^T$ is a submatrix of the L matrix that contains inforation about all the unmarked nodes to marked nodes.
    • $M$ matrix is defined for zero and 255 class $M_0$ and $M_{255}$.

  3. Calculating Probabilities: First, calculate $X$ using the formula: $$X = L^{-1} \cdot (B^T) \cdot M$$ where $L^{-1}$ is the inverse of matrix $L$, $B^T$ is the transpose of matrix $B$, and $M$ is the predefined matrix.

    The probability for pixel $k$ taking the value 0 is given by the corresponding element in matrix $X$ for $M_0$, which can be represented as: $$P(k \text{ takes value } 0) = X_k \text{ for } M_0$$ where $X_k$ is the k-th element in the matrix $X$.

Results and Performance

The algorithm's performance is evaluated based on the accuracy of segmentation. The accuracy is calculated as:

$$ \text{Accuracy} = \frac{|\text{White Pixels in SkitLearn} - \text{White Pixels in New Image}|}{\text{Total White Pixels} + \text{Total Black Pixels}} $$

Overall accuracy achieved: 93.682%

Usage

  1. Run the provided Jupyter Notebook: ImageSegmentation.ipynb.
  2. To process a different image, change the image path in the notebook accordingly.
  3. The notebook includes code and visualizations demonstrating the segmentation process.

Dependencies

  • Python
  • Numpy
  • Matplotlib
  • (Any other libraries used in the project)

Future Work

  • Improving the algorithm to handle more complex image structures.
  • Optimizing performance for large-scale images.
  • Exploring the use of the algorithm in various application areas such as medical imaging or satellite imagery.

License

This project is open-source and available under the MIT License.