Prepoznavanje lica pomoću tenzorske dekompozicije singularnih vrijednosti

master's thesis

• Author: Ivan Zirdum
• Mentor: Nela Bosner (mentor)
• Committee member: Nela Bosner (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-11-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu opisani su automatski postupci za prepoznavanje lica na fotografijama koji ne ovise o variranju uvjeta poput osvjetljenja, kuta gledanja ili izraza lica. U zadnje vrijeme proučavaju se metode za multilinearnu analizu skupine slika. Posebno se za problem prepoznavanja slika razmatra korištenje tenzorskog modela. U tom slučaju modovi tenzora predstavljaju različite uvjete gledanja kao što su osvjetljenje i izrazi lica, i time se povećava preciznost algoritma za prepoznavanje. U radnji ćemo se fokusirati na tenzorsku metodu za prepoznavanje lica. Budući da se bavimo fotografijama koje su spremljene kao \(m \times n\) polja, postupci računanja za identifikaciju lica na svakoj slici bili bi prezahtjevni. Tenzorska dekompozicija singularnih vrijednosti (HOSVD) može se koristiti za smanjenje dimenzionalnosti i redukciju broja operacija kod računanja. Na kraju je teorija ilustrirana konkretnim primjerima izraženim u MATLABu.

Abstract (english)

This paper describes automatic face recognition procedures for images that do not depend on variations in conditions such as brightness, angle of view, or facial expression. Lately, the methods for multilinear analysis of a group of images are being studied. When it comes to the problem of image recognition, the use of the tensor model has especially been taken into account. In this case, the modes of the tensors represent different viewing conditions such as illumination and facial expressions, thereby increasing the accuracy of the recognition algorithm. The paper focuses on the tensor method for facial recognition. Since we are dealing with images saved as \(m \times n\)fields, counting procedures for face identification in each image would be overwhelming. Tensor decomposition of singular values (HOSVD) can be used to reduce dimensionality and reduce number of operations in computing. In the end of the paper, the theory is illustrated by concrete examples expressed in MATLAB.

• Keywords: prepoznavanje lica; multilinearna analiza; tenzorski model; tenzorska dekompozicija singularnih vrijednosti; HOSVD; MATLAB
• Keywords (english): face recognition; multilinear analysis; tensor model; tensor decomposition of singular values; HOSVD; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:788907
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-07-05 10:25:41