https://github.com/steq28/jpeg-algorithm-dct2

JPEG Compression Algorithm using DCT2 and Fast Fourier Transform
https://github.com/steq28/jpeg-algorithm-dct2

Last synced: 12 days ago
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JPEG Compression Algorithm using DCT2 and Fast Fourier Transform

• Host: GitHub
• URL: https://github.com/steq28/jpeg-algorithm-dct2
• Owner: steq28
• License: mit
• Created: 2024-05-26T13:58:29.000Z (9 months ago)
• Default Branch: main
• Last Pushed: 2024-07-30T09:06:26.000Z (6 months ago)
• Last Synced: 2024-07-30T12:14:17.140Z (6 months ago)
• Language: Jupyter Notebook
• Homepage:
• Size: 1.09 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Implementation of DCT2 and Study of JPEG-like Compression Effects

## Overview

The goal of this project is to implement the 2D Discrete Cosine Transform (DCT2) in an open-source environment and study the effects of a JPEG-like compression algorithm (without using a quantization matrix) on grayscale images. The project consists of two main parts: implementing DCT2 and comparing execution times with an optimized version, and developing software for image compression with a user interface.

## Project Structure

- **Part 1: DCT2 Implementation and Execution Time Comparison**

- **Part 2: Image Compression Software**

## Requirements

- Python 3.x

- Jupyter Notebook

- Libraries: NumPy, Matplotlib, scikit-image (or other image processing libraries)

## Part 1: DCT2 Implementation and Execution Time Comparison

### Objective

Implement DCT2 as discussed in lectures and compare execution times with the fast (optimized) version available in the chosen library (e.g., using FFT-based implementations).

### Implementation Details

1. **Homemade DCT2 Implementation:**

   - Develop a function for DCT2 according to the theoretical definition.

   - Measure execution times on square arrays of increasing sizes (N×N).

2. **Comparison with Optimized DCT2:**

   - Use an optimized DCT2 function from the library (e.g., `scipy.fftpack.dct` with type `2`).

   - Compare execution times with the homemade DCT2.

3. **Graphical Representation:**

   - Create a semilogarithmic graph showing execution times as a function of N for both implementations.

   - The x-axis represents the array sizes (N), while the y-axis represents the logarithm of the execution times.

### Expected Results

- Execution times proportional to \( N3 \) for the homemade DCT2.

- Execution times proportional to \( N2 \log(N) \) for the optimized version, with potential irregularities due to the algorithm used.

## Part 2: Image Compression Software

### Objective

Develop software with a user interface that allows applying DCT2 to grayscale images, with the ability to select specific parameters for compression.

### Software Features

- **Image Selection:**

  - Interface for selecting a `.bmp` grayscale image from the filesystem.

- **User Settings:**

  - Select an integer \( F \) for defining the block size (macro-blocks) for DCT2.

  - Select an integer \( d \) (between 0 and \( 2F-2 \)) as the frequency cutoff threshold.

- **Image Processing:**

  - Divide the image into square blocks of size \( F \times F \).

  - Apply DCT2 to each block.

  - Compress the image by retaining only the principal frequencies defined by the threshold \( d \).

### Output

- Display the compressed image and compare it with the original.

## Running the Project

1. **Clone the repository:**

   ```bash

   git clone https://github.com/steq28/JPEG-Algorithm-DCT2.git

   ```

2. **Run the Notebooks:**

   - Follow the instructions in the notebooks to execute the various steps of the project.

## License

This project is licensed under the MIT License. For more details, see the [LICENSE](LICENSE) file.