delo diplomskega seminarja
Anamari Oštarijaš (Author), Marjetka Krajnc (Mentor)

Abstract

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.

Keywords

matematika;razpoznavanje obrazov;multilinearna algebra;tenzorji;singularni razcep višjega reda;numerične metode;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [A. Oštarijaš]
UDC: 519.6
COBISS: 18740825 Link will open in a new window
Views: 1320
Downloads: 198
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Other data

Secondary language: English
Secondary title: Face Recognition Using Singular Value Decomposition
Secondary 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.
Secondary keywords: mathematics;face recognition;multilinear algebra;tensors;higher order singular value decomposition;numerical methods;
Type (COBISS): Final seminar paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages: 26 str.
ID: 11221128