Linear Algebra Applications in Digital Image Processing for Security Systems in Nigerian Airports

This study examines the application of linear algebra methods in digital image processing for security system applications at Nigerian international airports, with focus on the mathematical operations underpinning image enhancement, noise reduction, and facial recognition as implemented in automated security screening technologies. Nigerian airports, including Murtala Muhammed International Airport in Lagos, Nnamdi Azikiwe International Airport in Abuja, and Mallam Aminu Kano International Airport in Kano, have been the subject of significant security investment in recent years, including the deployment of advanced imaging and biometric systems. The study provides a rigorous mathematical treatment of image representation as matrices, linear transformations for geometric image operations, eigenvector decomposition for principal component analysis-based dimensionality reduction, and singular value decomposition for image compression and noise filtering. The performance of Gaussian low-pass filtering, Laplacian edge enhancement, and morphological operations is analysed in terms of their linear algebra formulations, and computational complexity is assessed for implementation in real-time security screening contexts. Case analysis of face recognition pipeline architecture, including eigenface computation via singular value decomposition, is conducted using a publicly available face image database. The study evaluates the accuracy-speed tradeoff for various decomposition strategies relevant to immigration control throughput requirements. Keywords: linear algebra, image processing, singular value decomposition, facial recognition, airport security