Rekonstrukcija položaja 3D objekta iz kontinuiranog izvora 2D fotografija

master's thesis

• Title (english): Reconstruction of the position of a 3D object from a continuous source of 2D photographs
• Author: Ena Škopelja
• Mentor: Goranka Nogo (mentor)
• Committee member: Goranka Nogo (predsjednik povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu analiziran je problem rekonstrukcije položaja statičnog, pravokutnog objekta u trodimenzionalnom prostoru na temelju niza njegovih fotografija. Pravokutnik je opisan svojim vrhovima u 3D prostoru, a položaj njegovih vrhova na fotografiji (u 2D prostoru) se procjenjuje pomoću modela dubokog učenja. Opisani algoritam kao ulaz uzima skup procjena položaja objekta na fotografijama zajedno s parametrima koji definiraju kameru koja je proizvela odgovarajuće fotografije i vraća procjenu položaja objekta od interesa u trodimenzionalnom prostoru. Prezentiran je pregled teorijske pozadine i predstavljene su dvije standardne metode rješavanja zadanog problema, nehomogena metoda i Loewenberg-Marquardtova metoda. Dodatno, predložena je nova metoda koja se temelji na gradijentnom spustu i kojom je osigurano da je rekonstruirani objekt zaista pravokutnog oblika. To je ostvareno tako da se pretraga vrši u prostoru parametara jedne od četiriju odabranih parametrizacija pravokutnika u trodimenzionalnom prostoru. Rezultat nehomogene metode uzet je kao početna procjena za preostale dvije metode, kojima je radena daljnja optimizacija. Promatrane su dvije metrike, reprojekcijska pogreška (m1) i poslovna metrika (m2). Pošto je za poznavanje rezultata poslovne metrike nužno poznavati i stvarnu poziciju traženog objekta u trodimenzionalnom prostoru, u algoritmu se promatra m1. Međutim, pokazalo se da rezultati ove dvije metrike ne slijede nužno isti trend. Bez obzira na to, kako je i očekivano, pokazalo se da predložena metoda u ovom području zaista unaprijeduje dosadašnje. Cjeloviti sustav implementiran je u biblioteci Tensorflow.

Abstract (english)

This thesis analyzes the problem of reconstructing the position of a static, rectangular object in three-dimensional space based on a series of its photographs. The rectangle is described by its vertices in 3D space and the position of its vertices in the photograph (in 2D space) is estimated using a deep learning model. The algorithm takes in a set of estimates along with parameters defining the camera that produced the corresponding images and produces an estimate of the 3D position of the object of interest. An overview of the theoretical background is presented and two standard methods for solving the given problem, the inhomogeneous method and the Loewenberg-Marquardt method, are introduced. Additionally, a new method, based on gradient descent, is proposed. The method ensures that the reconstructed object is indeed rectangular in shape by searching the parameter space of one of the four selected rectangle parameterizations in three-dimensional space. The result of the inhomogeneous method was taken as the initial estimate for the remaining two methods, with which a further optimization was performed. Two metrics were monitored, the reprojection error (m1) and a business metric (m2). Since, to calculate the results of the business metrics, one has to know the true position of the desired object in three-dimensional space, the algorithm monitors m1. However, it was shown that the results of these two metrics do not necessarily follow the same trend. Regardless of that, as expected, it has been shown that the proposed method, in this domain, improves the previous ones. The entire system was implemented in the Tensorflow library.

• Keywords: model dubokog učenja; nehomogena metoda; Loewenberg-Marquardtova metoda; Tensorflow
• Keywords (english): deep learning model; inhomogeneous method; Loewenberg-Marquardt method; Tensorflow library
• Language: croatian
• URN:NBN: urn:nbn:hr:217:859204
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2023-09-14
• Created on: 2022-09-14 12:32:34