Implementation of Gaussian Convolution for Edge Detection in Gray-scale Images

Overview

This project investigates one of the core techniques in digital image processing — edge detection using Gaussian convolution. The focus is on implementing convolution-based Gaussian smoothing and edge detection for a grayscale image, combining step-by-step manual convolution calculations with a Python-based implementation. The project demonstrates how Gaussian kernels reduce noise while enhancing edges, and highlights the transition from raw convolution results to normalized grayscale outputs.

It serves as an educational introduction to convolution-based filtering, bridging applied linear algebra, matrix operations, and practical image processing. The project emphasizes the role of Gaussian convolution in feature extraction, segmentation, and computer vision applications.

Suitable For

• BS Mathematics – applied linear algebra, convolution, matrix transformations

• BS Computer Science – introduction to digital image processing and computer vision

• BS Statistics – application of normalization and data scaling in visualization

Technologies Used

• Programming Language: Python

• Libraries & Tools: NumPy, Matplotlib, SciPy

• Techniques: 2D Convolution, Gaussian Smoothing, Zero-Padding, Normalization

• Visualization: Original grayscale images, raw convolution matrices, normalized outputs

Features

• Step-by-step manual convolution with a Gaussian kernel

• Python-based automation of convolution and normalization for validation

• Clear visualization of:

  • Original grayscale image

  • Raw convolution output matrix

  • Normalized edge-detected image

• Explanation of how Gaussian kernels preserve intensity while reducing noise

• Extendable methodology for larger and real-world image datasets

Deliverables

• Complete Python source code for Gaussian convolution edge detection

• Project documentation (setup guide, methodology, step-by-step explanation)

• Presentation slides (objectives, methods, and results with figures)

• Visual assets (comparative images: original, raw convolution, normalized edges)

• Support for running, modifying, or extending the project

Benefits for Students

• Gain hands-on experience with convolution and Gaussian smoothing

• Understand the mathematical foundation of Gaussian-based edge detection

• Learn to bridge theory (manual calculations) and practice (Python implementation)

• Acquire skills in data normalization and visualization using Python libraries

• Strong capstone project choice for portfolios, academic presentations, and research preparation