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Linnaeus University

1. Qamar, Aamir; Din, Islamud. Analysis of Spherical Harmonics and Singular Value Decomposition as Compression Tools in Image Processing.

Degree: Physics and Mathematics, 2012, Linnaeus University

Spherical Harmonics (SPHARM) and Singular Value Decomposition (SVD) utilize the orthogonal relations of its parameters to represent and process images. The process involve mapping of the image from its original parameter domain to a new domain where the processing is performed. This process induces distortion and smoothing is required. The image now mapped to the new parameter domain is descripted using SPHARM and SVD using one at a time. The least significant values for the SPHARM coefficients and singular values of SVD are truncated which induces compression in the reconstructed image keeping the memory allocation in view. In this thesis, we have applied SPHARM and SVD tools to represent and reconstruct an image. The image is first mapped to the unit sphere (a sphere with unit radius). The image gets distorted that is maximum at the north and south poles, for which smoothing is approached by leaving 0.15*π space blank at each pole where no mapping is done. Sampling is performed for the θ and φ parameters and the image is represented using spherical harmonics and its coefficients are calculated. The same is then repeated for the SVD and singular values are computed. Reconstruction is performed using the calculated parameters, but defined over some finite domain, which is done by truncating the SPHARM coefficients and the singular values inducing image compression. Results are formulated for the various truncation choices and analyzed and finally it is concluded that SPHARM is better as compared with SVD as compression tool as there is not much difference in the quality of the reconstructed image with both tools, though SVD seem better quality wise, but with much higher memory allocation than SPHARM.

Subjects/Keywords: Spherical Harmonics and Singular Value Decomposition; Signal Processing; Signalbehandling

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Qamar, Aamir; Din, I. (2012). Analysis of Spherical Harmonics and Singular Value Decomposition as Compression Tools in Image Processing. (Thesis). Linnaeus University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-18608

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Qamar, Aamir; Din, Islamud. “Analysis of Spherical Harmonics and Singular Value Decomposition as Compression Tools in Image Processing.” 2012. Thesis, Linnaeus University. Accessed July 09, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-18608.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Qamar, Aamir; Din, Islamud. “Analysis of Spherical Harmonics and Singular Value Decomposition as Compression Tools in Image Processing.” 2012. Web. 09 Jul 2020.

Vancouver:

Qamar, Aamir; Din I. Analysis of Spherical Harmonics and Singular Value Decomposition as Compression Tools in Image Processing. [Internet] [Thesis]. Linnaeus University; 2012. [cited 2020 Jul 09]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-18608.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Qamar, Aamir; Din I. Analysis of Spherical Harmonics and Singular Value Decomposition as Compression Tools in Image Processing. [Thesis]. Linnaeus University; 2012. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-18608

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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