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undergraduate thesis
Primjena SVD dekompozicije na kompresiju slike
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:149250
Šanić, Lucija-Katarina
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Šanić, L. K. (2024). Primjena SVD dekompozicije na kompresiju slike (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:149250

Šanić, Lucija Katarina. "Primjena SVD dekompozicije na kompresiju slike." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:149250

Šanić, Lucija Katarina. "Primjena SVD dekompozicije na kompresiju slike." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:149250

Šanić, L. K. (2024). 'Primjena SVD dekompozicije na kompresiju slike', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:149250

Šanić LK. Primjena SVD dekompozicije na kompresiju slike [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:149250

L. K. Šanić, "Primjena SVD dekompozicije na kompresiju slike", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:149250

Metadata
TitlePrimjena SVD dekompozicije na kompresiju slike
Title (english)Application of SVD Decomposition to Image Compression
AuthorLucija-Katarina Šanić
MentorKristian Sabo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-08-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Ovaj rad istražuje primjenu SVD dekompozicije matrice na problem kompresije slike, s posebnim naglaskom na grayscale slike i slike u boji. SVD je moćan alat koji omogućuje dekompoziciju matrice slike u tri komponente: U, Σ i \(V^{T}\) , gdje U i \(V^{T}\) predstavljaju ortogonalne matrice, a Σ je dijagonalna matrica koja sadrži singularne vrijednosti. Za grayscale slike, SVD omogućuje kompresiju uklanjanjem manjih singularnih vrijednosti koje doprinose manje značajno u rekonstruiranju slike dok za slike u boji, proces kompresije slike proširujemo na tri kanala: crveni, zeleni i plavi. Svaki se kanal tretira kao zasebna grayscale slika i primjenjuje se SVD dekompozicija.
Abstract (english)
This paper explores the application of SVD decomposition to the problem of image compression, with a particular focus on grayscale images and color images. SVD is a powerful tool that enables the decomposition of an image matrix into three components: U, Σ, and \(V^{T}\), where U and \(V^{T}\) are orthogonal matrices, and Σ is a diagonal matrix which contains singular values. For grayscale images, SVD enables compression by removing smaller singular values that contribute less significantly to the reconstruction of the image. For RGB format images, the compression process is extended to three channels: red, green, and blue. Each channel is treated as a separate grayscale image and SVD decomposition is applied to each one.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:149250
Study programmeTitle: Bachelor of Mathematics and Computer Science
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike i računarstva)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-09-12 10:51:55