Convolution-Based Edge Detection in Gray-scale Images Using the Laplacian Kernel

Overview:

This project explores one of the fundamental tasks in digital image processing — edge detection — using the Laplacian operator. The focus is on implementing convolution-based Laplacian edge detection for a grayscale image, demonstrating both manual mathematical calculations and automated execution in Python. A comparative analysis is carried out between step-by-step manual convolution of selected pixels and programmatic results, reinforcing the concepts of 2D convolution, zero-padding, normalization, and visualization.

The project serves as an educational introduction to convolution-based filtering in image processing while highlighting the importance of edges in object recognition, segmentation, and computer vision applications.

Suitable For:

• BS Mathematics – applied linear algebra, convolution, and discrete transformations

• BS Computer Science – foundational concepts in digital image processing

• BS Statistics – application of matrix operations and transformations in data visualization

Technologies Used:

• Programming Language: Python

• Libraries & Tools: NumPy, Matplotlib, SciPy

• Techniques: 2D Convolution, Laplacian Operator, Zero-Padding, Normalization

• Visualization: Grayscale images, convolution matrices, and edge-detected outputs

Features:

• Step-by-step manual convolution demonstration with a Laplacian kernel

• Python-based automation of convolution and normalization for validation

• Visualization of the original image, raw convolution matrix, and normalized edge-detected image

• Educational explanation of convolution and image normalization in practice

• Extendable methodology for larger, real-world images

Deliverables:

• Complete Python source code for Laplacian edge detection

• Project Documentation: Setup guide, methodology, and step-by-step explanation

• Presentation Slides (PPT): Objectives, methods, and results with figures

• Visual Assets: Comparative images (original, raw convolution, normalized edges)

• Support: Guidance for running, modifying, or extending the project

Benefits for Students:

• Gain hands-on experience in image processing and convolution operations

• Understand the mathematics behind edge detection using the Laplacian operator

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

• Acquire data visualization and analysis skills with Python libraries

• Excellent capstone project choice for portfolios, academic demos, and research preparation