Haar Wavelet Transform for Edge Detection — Python & Vivado HLS Implementation

A Python and Vivado HLS implementation of the 2D Haar Wavelet Transform for image edge detection. The project bridges software prototyping and hardware design, offering visual and quantitative comparisons between the two approaches.

Table of Contents

1. Overview
2. What is the Haar Wavelet Transform?
3. Python Implementation
4. Vivado HLS Implementation
5. Experimental Results
6. Implementation Workflow
7. Project Structure
8. Contributing
9. License

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Overview

This repository presents a complete implementation of the 2D Haar Wavelet Transform — both in Python (software) and C++ using Vivado HLS (hardware).
This project aims to compare results between floating-point and integer synthesis versions and visualize differences.

Key Features

• Full 2D Haar Wavelet Transform (LL, LH, HL, HH)
• Python + NumPy implementation (from scratch)
• Synthesizable C++ implementation
• Floating-point vs Integer performance comparison
• Visualization and analysis notebooks

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What is the Haar Wavelet Transform?

The Haar Wavelet Transform is one of the simplest and most computationally efficient wavelet transforms, widely used in image compression, signal analysis, and edge detection.

Subband	Meaning	Description
LL	Low-Low	Approximation — coarse version of the image
LH	Low-High	Horizontal details — vertical edges
HL	High-Low	Vertical details — horizontal edges
HH	High-High	Diagonal details — fine edges

Mathematical Formulation

At its core, the Haar transform computes pairwise averages and differences of pixels.

The same process is applied first across each row (horizontal transform), and then across each column (vertical transform).

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Python Implementation

Notebook: notebooks/Haar_Wavelet_Transform.ipynb

Features

• Pure Numpy implementation of 1D and 2D Haar transforms
• Visualization of LL, LH, HL, HH components
• Validation via PyWavelets (pywt)
• Conversion of the image into pixels.txt for HLS input
• Comparison between software and HLS results

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Vivado HLS Implementation

Core Files

File	Description
wavelet.h	Constants, type definitions, function prototypes
wavelet_process.cpp	Core Haar Transform logic
wavelet_top.cpp	Top-level function for synthesis
main.cpp	Testbench for simulation and I/O

Supported Features

• Works on any even-sized image (non-square supported)
• Synthesizable with Vivado HLS 2019.1+
• Handles both float and int pixel types
• AXI-stream compatible for hardware acceleration

Visualization and Analysis

The notebook Visualize_HLS_Results.ipynb compares:

• HLS Floating-point results
• HLS Integer results

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Experimental Results

The following results compare Python software and Vivado HLS hardware implementations:

Implementation	Description	Result
Python (float)	Software baseline using NumPy
HLS (float)	Hardware-equivalent floating-point
HLS (int)	Integer arithmetic optimized for synthesis

Quantitative Comparison

• Floating-point version maintains higher accuracy but consumes more FPGA resources.
• Integer version offers lower resource utilization with minimal loss of precision.

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Implementation Workflow

Step	Description
1. Algorithm Study	Compared edge detection techniques (Sobel, Wavelet, etc.) and chose Haar for simplicity & hardware suitability
2. Python Prototype	Built from scratch with validation against PyWavelets
3. HLS Translation	Converted Python logic to synthesizable C++ and verified through testbench
4. Synthesis & Co-simulation	Generated VHDL/Verilog and compared floating vs integer results
5. Visualization	Python notebooks used for graphical result comparison

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Project Structure

haar-wavelet-edge-detection/
│
├── src/
│   ├── wavelet.h
│   ├── wavelet_process.cpp
│   ├── wavelet_top.cpp
│   └── main.cpp
│
├── notebooks/
│   ├── Haar_Wavelet_Transform.ipynb     
│   └── Visualize_HLS_Results.ipynb      
│
├── data/
│   ├── image.png
│   └── pixels.txt               
│
├── results/
│   ├── Comparison_plot.png
│   ├── Haar_img.png
│   ├── Haar_Wavelet_Transform_Sub-bands.png
│   ├── HLS-float.png
│   ├── HLS-int.png
│   ├── Python-float.png
│   ├── wavelet_float_results.txt
│   └── wavelet_int_results.txt
│
├── .gitignore
├── LICENSE
├── README.md 
└── requirements.txt                

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Contributing

Contributions are welcome!
If you have suggestions or improvements, feel free to fork the repository and create a pull request.

Steps to Contribute:

1. Fork the repository.
2. Create a new branch:

   git checkout -b feature-name

3. Commit your changes:

   git commit -m "Description of changes"

4. Push the changes and open a pull request.

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License

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