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Application of Principal Component Analysis to Image Compression

In: Statistics - Growing Data Sets and Growing Demand for Statistics

Author

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  • Wilmar Hernandez
  • Alfredo Mendez

Abstract

In this chapter, an introduction to the basics of principal component analysis (PCA) is given, aimed at presenting PCA applications to image compression. Here, concepts of linear algebra used in PCA are introduced, and PCA theoretical foundations are explained in connection with those concepts. Next, an image is compressed by using different principal components, and concepts such as image dimension reduction and image reconstruction quality are explained. Also, using the almost periodicity of the first principal component, a quality comparative analysis of a compressed image using two and eight principal components is carried out. Finally, a novel construction of principal components by periodicity of principal components has been included, in order to reduce the computational cost for their calculation, although decreasing the accuracy.

Suggested Citation

  • Wilmar Hernandez & Alfredo Mendez, 2018. "Application of Principal Component Analysis to Image Compression," Chapters, in: Turkmen Goksel (ed.), Statistics - Growing Data Sets and Growing Demand for Statistics, IntechOpen.
    • Handle: RePEc:ito:pchaps:143689
    DOI: 10.5772/intechopen.75007
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    File URL: https://www.intechopen.com/chapters/59936
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    Cited by:

    1. Singh, Manav Mahan & Singaravel, Sundaravelpandian & Geyer, Philipp, 2021. "Machine learning for early stage building energy prediction: Increment and enrichment," Applied Energy, Elsevier, vol. 304(C).

    More about this item

    Keywords

    principal component analysis; population principal components; sample principal components; image compression; image dimension reduction; image reconstruction quality;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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