Aplicações da álgebra linear em processamento de imagens digitais

Abstract

This work clearly presents how Linear Algebra is fundamental in digital image processing, an area that emerged along with technological advances and image transmission techniques to facilitate their visualization and analysis. With the increase in the number of digitally generated and processed images in various areas, from medicine to the automotive industry, Linear Algebra has become even more important, allowing the representation and manipulation of images as numerical matrices. To understand how the relationship between Linear Algebra and digital images works, it was necessary to study the history and essential concepts of this area. In addition, we will explore the applications of matrix operations in digital image processing, with examples to illustrate the development of techniques in images. A practical application of Linear Algebra in Decomposition by singular values will also be presented, which is a technique that facilitates the compression and reconstruction of images, in addition to helping with transportation. This work aims to present the basic techniques of digital image processing, to provide a solid basis for future studies and, finally, to explore the geometric part of Linear Algebra in the context of digital image processing.