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Spaces of Spectral Distributions and Their Natural Geometry

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It is well-known that the knowledge of the natural geometry of a problem is often crucial in finding solutions. Problems involving functions on a circle are, for example, often solved using the theory of Fourier series. This is the mathematical explanation of the enormous success of the DFT, FFT and DCT-based methods. Another example is the relation between scaling properties and wavelet theory.

In this paper we show that spaces of spectral distributions, like color stimuli, have a natural cone-like structure. We use the framework of the Karhunen-LoƩve transform in a Hilbert space context to describe this cone-like structure and demonstrate how to compute natural coordinate systems from empirical data, like multi-spectral measurements and images. We will illustrate the theoretical findings with databases consisting of collections of multispectral measurements of color chips from color systems like Munsell, NCS and Pantone, multi-channel images of natural scenes, satellite data and daylight spectra.

We will also comment on the possible application of group theoretical methods in color science based on those findings.
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Document Type: Research Article

Publication date: January 1, 2002

More about this publication?
  • Started in 2002 and merged with the Color and Imaging Conference (CIC) in 2014, CGIV covered a wide range of topics related to colour and visual information, including color science, computational color, color in computer graphics, color reproduction, volor vision/psychophysics, color image quality, color image processing, and multispectral color science. Drawing papers from researchers, scientists, and engineers worldwide, DGIV offered attendees a unique experience to share with colleagues in industry and academic, and on national and international standards committees. Held every year in Europe, DGIV papers were more academic in their focus and had high student participation rates.

    Please note: For purposes of its Digital Library content, IS&T defines Open Access as papers that will be downloadable in their entirety for free in perpetuity. Copyright restrictions on papers vary; see individual papers for details.

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