20.500.12556/RUL-184577 Singularni razcep matrik s kvaternionskimi koeficienti in njihova uporaba pri procesiranju slik delo diplomskega seminarja Singular value decomposition of quaternion-valued matrices and its application to image processing V diplomskem delu je obravnavana uporaba singularnega razcepa matrik s kvaternionskimi koeficienti pri procesiranju barvnih slik. Kvaternionski zapis omogoča, da so barvne komponente slike obravnavane skupaj, kar je naravna razširitev običajnega matričnega zapisa slik. Po predstavitvi osnov kvaternionov in matrik s kvaternionskimi koeficienti, je uvedena kompleksna pridruženka, s katero je mogoče izračun singularnega razcepa prenesti na kompleksne matrike. Obravnavana sta dva algoritma za izračun singularnega razcepa kvaternionskih matrik. Prvi temelji na izračunu singularnega razcepa kompleksne pridruženke, drugi pa uporablja Givensove rotacije in Householderjeva zrcaljenja. Oba algoritma sta implementirana v MATLAB-u in uporabljena na primerih procesiranja slik. Zaključni del je namenjen primerjavi algoritmov ter interpretaciji dobljenih rezultatov. In this diploma thesis, the use of the singular value decomposition of matrices with quaternion coefficients in colour image processing is studied. The quaternion representation enables the colour components of an image to be treated jointly, which is a natural extension of the usual matrix representation of images. After introducing the basics of quaternions and matrices with quaternion coefficients, the complex adjoint matrix is introduced, allowing the computation of the singular value decomposition to be transferred to complex matrices. Two algorithms for computing the singular value decomposition of quaternion matrices are considered. The first is based on singular value decomposition of the complex adjoint matrix, while the second one employs Givens rotations and Householder reflections. Both algorithms are implemented in MATLAB and applied to examples of image processing. The final part is devoted to a comparison of the algorithms and an interpretation of the obtained results. singularni razcep kvaternioni procesiranje slik singular value decomposition quaternions image processing true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2026-07-10 08:15:19 2026-07-10 08:15:22 2026-07-16 09:04:52 0000-00-00 00:00:00 2026 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512:519.6 160638 285007107 22041.pdf 22041.pdf 1 9C48D5AE2777BF38573CA53E4898ACE6 d08f851b1d28856afdff8ecca9f237a1770ae546bf937efb4dbafc7fd489a05f 9a6788ec-7c26-11f1-9b0d-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=237468 Fakulteta za matematiko in fiziko 0 0 0