Luís Felipe Krause de Castro

📦 Image Compression: JPEG and Transforms

This project implements two image compression algorithms based on the JPEG standard:

1. The file JPEG_Algorithm_Quantization.py runs the JPEG algorithm using three different quantization matrices:

   • standard: matrix used in the baseline JPEG.
   • moderate: intermediate compression.
   • aggressive: strong compression, with greater size reduction.

   For each image, the script:

   • Splits the image into 8x8 blocks.
   • Applies the DCT (Discrete Cosine Transform) to each block.
   • Quantizes the coefficients using the selected quantization table.
   • Reconstructs the image using IDCT.
   • Computes quality and compression metrics:
     • PSNR (Peak Signal-to-Noise Ratio)
     • SSIM (Structural Similarity Index)
     • % of zeroed coefficients
     • Original and compressed size
     • Compression ratio
   • Displays comparative visualizations between the original and reconstructed images.

2. The file JPEG_Algorithm_Transform.py performs compression using alternative transforms beyond DCT, allowing tests with:

   • Fourier
   • Laplace
   • Wavelet

   For each transform, the script:

   • Processes the image in blocks.
   • Applies quantization.
   • Reconstructs the image.
   • Computes the same quality and compression metrics as JPEG.
   • Generates comparative plots between the original and reconstructed images.

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✨ Overview

The processing flow includes:

1. Application of transforms

   • Can be DCT, Fourier, Laplace, or Wavelet (Haar).
   • Executed on 8x8 blocks.

2. Coefficient quantization

   • For JPEG, three quantization matrices are used: standard, moderate, and aggressive.

3. Image reconstruction

   • The image is reconstructed from the transformed coefficients using IDCT, iFFT, or IDWT, depending on the transform used.

4. Huffman compression

   • The quantized coefficients are encoded using Huffman coding to estimate the compressed file size.

5. Quality and compression metrics

   • PSNR (Peak Signal-to-Noise Ratio)
   • SSIM (Structural Similarity Index)
   • % of zeroed coefficients
   • Compression ratio (original/compressed)

6. Results visualization

   • Comparative plots between original and reconstructed images.
   • Boxplots, scatter plots, and violin plots for statistical analysis.

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🧰 Technologies Used

• Python 3 – Main language for algorithm implementation and analysis scripts.
• NumPy – Matrix operations, array manipulation, and numerical computation.
• OpenCV – Image reading, writing, resizing, and color conversion.
• Matplotlib – Visualization of images and comparative plots.
• SciPy – Implementation of DCT/IDCT and Fourier transforms.
• PyWavelets – Wavelet (Haar) transforms for full-frame compression.
• Scikit-Image – Computation of image quality metrics such as PSNR and SSIM.
• Pandas – Storage and manipulation of results in DataFrames for analysis.
• Seaborn – Generation of aesthetic statistical plots (boxplot, violin, scatter).

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🖼️ Image Dataset

Images must be placed in the ./img/ directory.
During execution, each image is automatically resized to 512x512.

• Image datasets include:
  • SIPI Image Database (link)
  • ImageNet Sample Images (link)

There are 210 images from each dataset, totaling 420 images tested.

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⚙️ How the Algorithm Works

1. 🔁 Batch Processing

The script automatically iterates through all images in the ./img/ folder and applies the configured transforms or quantization tables.

2. 📥 Compression and Reconstruction

For each image:

• It is divided into 8x8 blocks.
• The chosen transform is applied.
• Coefficients are quantized.
• The image is reconstructed for quality evaluation.

3. 🧪 Metric Calculation

After reconstruction, the following are computed:

• PSNR (Peak Signal-to-Noise Ratio)
• SSIM (Structural Similarity Index)
• % of zeroed coefficients after quantization
• Original vs. compressed size (via Huffman encoding)
• Compression ratio

4. 📦 Huffman Compression

• Quantized coefficients are concatenated.
• A Huffman tree is generated.
• The compressed size (in bytes) is estimated.
• The compression ratio (original/compressed) is computed.

5. 🖼️ Visualization

For selected images (img_comparativo), the script displays comparisons between:

• Original image
• Reconstructed images for each quantization table or transform
• Quality metrics shown in figure titles

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📊 Outputs

📈 Example Output from JPEG_Algorithm_Quantization.py

Comparative Plot

BoxPlot

Scatter Plot

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📈 Example Output from JPEG_Algorithm_Transform.py

Comparative Plot

BoxPlot

Scatter Plot