undergraduate thesis
Fast Fourier transform and application in image processing

Denis Pejić (2015)
Metadata
TitleBrza Fourierova tranformacija i njezina primjena u obradi slike
AuthorDenis Pejić
Mentor(s)Irena Galić (thesis advisor)
Abstract
U ovom radu je primjenjena brza Fourierova transformacija u obradi slike pomoću programa matlab. Vremenska diskretna Fourierova transformacija predstavlja Fourierovu transformaciju za vremenske diskretne signale. U obradi digitalne slike vremenska diskretna Fourierova transformacija se proširila na 2D vremensku diskretnu Fourierovu transformaciju, zato što je digitalna slika dvodimenzionalna. Primjenom 2D vremenske diskretne Fourierove transformacije na matricu slike, pretvorba slike se vrši iz prostorne domene u frekvencijsku domenu. U obradi slike razlikuje se prostorno i frekvencijsko područje. Slike su filtrirane u frekvencijskoj domeni. Filtriranje u frekvencijskoj domeni zahtjeva manju računsku složenost. Prevođenjem frekvencijskog filtera u konvolucijsku masku dobije se aproksimacija najmanje kvadratne greške[35]. Ako je frekvencijski filtar realan i simetričan, tada će konvolucijska maska biti također realna i simetrična. U slučaju nemogućnosti određivanja dovoljno dobre maske za aproksimaciju filtra ili ako aproksimacijom filtra dobivamo veliku konvolucijsku masku, tada se filtriranje provodi u frekvencijskom području. Iz tog razloga filtriranje u frekvencijskoj domeni zahtjeva manju računsku složenost za razliku sa konvolucijom s velikim maskama.
KeywordsFT DTFT 2D DTFT FFT algorithm spatial domain frequency domain FR digital image
Parallel title (English)Fast Fourier transform and application in image processing
Committee MembersIrena Galić (committee chairperson)
Hrvoje Glavaš (committee member)
Mario Vranješ (committee member)
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Fakultet elektrotehnike, računarstva i informacijskih tehnologija Osijek
Lower level organizational unitsZavod za programsko inženjerstvo
Katedra za vizualno računarstvo
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineTECHNICAL SCIENCES
Electrical Engineering
Electronics
Study programme typeuniversity
Study levelundergraduate
Study programmeUndergraduate University Study Programme; branch Electrical Engineering
Academic title abbreviationuniv.bacc.ing.el.
Genreundergraduate thesis
Language Croatian
Defense date2015-09-24
Parallel abstract (English)
In this work was applied fast Fourier transformation in picture processing with program matlab. Time discrete Fourier transform presents Fourier transform of discrete-time signals. In digital image processing time discrete Fourier transform expands to two-dimensional time discrete Fourier transform, because the digital image is two-dimensional. By applying the twodimensional discrete-time Fourier transform on the matrix image, image conversion is made from the spatial domain to the frequency domain. In image processing it differs spatial and frequency domain. Pictures are filtered in frequency domain. Filtering in frequency domain require lower calculation complexity. By transfering frequency filter in convolution mask it gets approximation of least square mistake. If the frequency filter is realistic and simetric, then convolution mask will also be realistic and simetric. In cases where determination of mask for approximation filter isn't good enough or if with approximation of filter results with large convolution mask, then filtering is carried out in frequency domain. Because of that reason filtering in frequency domain requests lower calculation complexity compared to convolution with large masks.
Parallel keywords (Croatian)FT DTFT 2D DTFT FFT algoritam prostorna domena frekvencijska domena FR digitalna slika
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:200:853097
CommitterAnka Ovničević