Image Compression and Restoration

This repository contains two projects related to image compression techniques:

1. JPEG Compression Engine: A custom implementation inspired by the JPEG compression algorithm.
2. Edge-Based Image Compression: An implementation of a research paper that employs edge detection and homogeneous diffusion for image compression.

Click here for the detailed project report summarizing the methods, experiments, and results.

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Repository Contents

• JPEG_compression_engine.ipynb: Implements a JPEG-like compression algorithm.
• Research_Paper_Implementation.ipynb: Implements edge-based image compression from a research paper (link to paper).
• CS663_Project_Report.pdf: Comprehensive report detailing methodologies, experiments, and results of both projects.

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Features

1. JPEG Compression Engine

• Techniques Used:
  • Discrete Cosine Transform (DCT): Converts image data from spatial to frequency domain.

$$ C(u, v) = \frac{1}{\sqrt{2N}} \sum_{x=0}^{N-1} \sum_{y=0}^{N-1} I(x, y) \cos \left( \frac{\pi(2x+1)u}{2N} \right) \cos \left( \frac{\pi(2y+1)v}{2N} \right) $$

where:

• $I(x, y)$ represents the intensity value of the pixel at position $(x, y)$ in the image block.

• $C(u, v)$ is the DCT coefficient at position $(u, v)$ in the frequency domain.

• $N$ is the size of the block ($N=8$ in JPEG compression).

• The $u$ and $v$ indices correspond to frequencies in the horizontal and vertical directions, respectively.

  • Quantization: Reduces precision for compression.

$$ Q(u, v) = \text{round}\left(\frac{C(u, v)}{Q_{\text{table}}(u, v)}\right) $$

where:

• $C(u, v)$ represents the DCT coefficient at position $(u, v)$,

• $Q_{\text{table}}(u, v)$ is the corresponding value in the quantization matrix,

• $Q(u, v)$ is the quantized coefficient.

  • Huffman Encoding: Entropy coding for efficient data representation.

• Objectives:

  • Implement core JPEG compression steps for grayscale images.
  • Evaluate compression with metrics such as Bits Per Pixel (BPP) and Root Mean Squared Error (RMSE).
  • Simulate varying quality factors and plot RMSE vs. BPP curves.

• Sample Results:

Quality Factor	File Size (bytes)	Compression Rate	Compression Ratio
Original	186368	-	-
10	3116.50	59.80	0.017
40	3932.88	47.39	0.021
80	4967.62	37.52	0.027

Table 1: File Size, Compression Rate, and Compression Ratio at different Quality Factors

2. Edge-Based Image Compression

• Stages:
  • Edge Detection and Mask Generation: Identifies edges for efficient compression.
  • Subsampling: Reduces redundant data storage near edges.
  • Supersampling: Improves reconstruction near edges.
  • Reconstruction: Uses homogeneous diffusion to fill missing data.
• Sample Results:
  
  

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Installation and Usage

Prerequisites

• Python 3.8 or above
• Required libraries:
  • numpy
  • opencv-python
  • scipy
  • matplotlib
  • jupyterlab

Install dependencies using:

pip install numpy opencv-python scipy matplotlib jupyterlab

Execution

Clone the repository:

git clone https://github.com/SRAVAN-IITB/Image-Compression-Algorithms.git
cd Image-Compression-Algorithms

Run the notebooks:

1. Open JPEG_compression_engine.ipynb or Research_Paper_Implementation.ipynb in Jupyter Lab/Notebook.
2. Execute cells sequentially to see results and visualizations.

Results and Analysis

JPEG Compression

• Significant compression achieved with minimal loss in visual quality.
• Observed inverse exponential decay of RMSE with increasing BPP.

Edge-Based Compression

• Moderate compression rates with limitations in Peak Signal-to-Noise Ratio (PSNR) for detailed images.
• For detailed analysis, refer to CS663_Project_Report.pdf.

Contributions

Feel free to contribute by opening issues or submitting pull requests. Feedback is highly appreciated!

Acknowledgments

• Prof. Ajit Rajwade, Indian Institute of Technology Bombay.
• Research paper authors for their innovative methods in image compression.
• Libraries: NumPy, OpenCV, SciPy, and Matplotlib.

License

This project is licensed under the MIT License. See the LICENSE file for details.

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