Razpoznavanje obrazov z uporabo singularnega razcepa : delo diplomskega seminarja

Oštarijaš, Anamari (author), Knez, Marjetka (mentor)

Razpoznavanje obrazov se uporablja na različnih področjih in je zahteven problem zaradi različnih faktorjev, kot so osvetljava, zorni kot, izraz na obrazu, ki ključno vplivajo na klasifikacijo izbrane slike. Multilinearna algebra nam omogoča slike razvrstiti v objekt na podlagi več kategorij in nam poda matematični okvir za analizo teh objektov (tenzorjev). V delu pregledamo idejo razpoznavanja obrazov z linearno algebro in singularnim razcepom. Definiramo osnove multilinearne algebre in predstavimo singularni razcep višjega reda, posplošitev matričnega singularnega razcepa na tenzorje ter uporabnost le-tega za podatkovno rudarjenje. Razložimo uporabo tega razcepa za razpoznavanje obrazov na tenzorju, v katerem so slike obrazov razvrščene na podlagi treh kategorij, in prikažemo rezultate uporabljenega razcepa na bazi obrazov Extended Yale Face Database B.

• Language: Slovenian
• Keywords: razpoznavanje obrazov, multilinearna algebra, tenzor, singularni razcep višjega reda, numerične metode
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-109973
• UDC: 519.6
• COBISS.SI-ID: 18740825
• Publication date in RUL: 11.09.2019

OŠTARIJAŠ, Anamari, 2019, Razpoznavanje obrazov z uporabo singularnega razcepa : delo diplomskega seminarja [online]. Bachelor’s thesis. [Accessed 2 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=109973

Secondary language

• Language: English
• Title: Face Recognition Using Singular Value Decomposition

Abstract

Face recognition is used in different fields and is considered as a difficult problem due to different factors, such as lighting, image angle, face expression, which significantly affect clasification process of an image. Multilinear algebra enables us to sort images in an object considering multiple categories and offers mathematical framework for dealing with these objects (tensors). We present the idea of face recognition with linear algebra using singular value decomposition. Further, we define basics of multilinear algebra, describe higher order singular value decomposition, extension of the matrix singular value decomposition, and usefulness of this decomposition in data mining. We explain how to use higher order singular value decomposition on a tensor that is constructed of face images considering three categories, and show results on an example using the Extended Yale Face Database B database.

• Keywords: face recognition, multilinear algebra, tensor, higher order singular value decomposition, numerical methods