Algoritmi za prepoznavanje lica

master's thesis

• Title (english): Algorithms for face recognition
• Author: Dino Drmić
• Mentor: Matija Kazalicki (mentor)
• Committee member: Matija Kazalicki (predsjednik povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Tema ovog diplomskog rada je prepoznavanje lica algoritmima PCA i Tensorfaces. Rad prikazuje primjenu bitnih teorema o singularnim dekompozicijama matrice i tenzora u algoritmima za prepoznavanje lica. U početku su prikazani osnovni pojmovi i rezultati iz linearne algebre i vjerojatnosti. Nakon toga slijedi iskaz singularne dekompozicije matrice i opis poznate metode za redukciju prostora, PCA, u kontekstu prepoznavanja lica, kao i primjena samog algoritma na određenom skupu slika. U sljedećem poglavlju uvedeni su pojam tenzora, osnovne tenzorske operacije i singularna dekompozicija tenzora. Nakon toga slijedi opis metode Tensorfaces i primjena algoritma na istom skupu slika. Kodovi samih algoritama napisani su u programskom jeziku MATLAB.

Abstract (english)

The topic of this thesis is the Face Recognition using PCA and Tensorfaces algorithms. This thesis shows the application of important theorems of singular matrix and tensor decompositions in face recognition algorithms. The introduction contains basic terms and results in the field of linear algebra and probability. It is followed by the statement of the matrix singular value decomposition theorem, the description of the PCA algorithm in the context of face recognition and its application on the image dataset. Next chapter introduces tensors, basic tensor operations and the singular decomposition of a tensor. It is followed by the description of the Tensorfaces method and the application of the algorithm on the same image dataset. All of the algorithm codes are written in MATLAB programming language.

• Keywords: algoritam PCA; algoritam Tensorfaces; singularna dekompozicija matrice; tenzorske operacije; singularna dekompozicija tenzora; MATLAB
• Keywords (english): PCA algorithms; Tensorfaces algorithms; matrix singular value decomposition theorem; tensor operations; singular decomposition of a tensor; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:752982
• Study programme: Title: Mathematical Statistics; 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: 2022-09-13 10:14:10