This lecture describes the author's approach to the representation of color spaces and their use for color image processing. The lecture starts with a precise formulation of the space of physical stimuli (light). The model includes both continuous spectra and monochromatic spectra in the form of Dirac deltas. The spectral densities are considered to be functions of a continuous wavelength variable. This leads into the formulation of color space as a three-dimensional vector space, with all the associated structure. The approach is to start with the axioms of color matching for normal human viewers, often called Grassmann's laws, and developing the resulting vector space formulation. However, once the essential defining element of this vector space is identified, it can be extended to other color spaces, perhaps for different creatures and devices, and dimensions other than three. The CIE spaces are presented as main examples of color spaces. Many properties of the color space are examined. Once the vector space formulation is established, various useful decompositions of the space can be established. The first such decomposition is based on luminance, a measure of the relative brightness of a color. This leads to a direct-sum decomposition of color space where a two-dimensional subspace identifies the chromatic attribute, and a third coordinate provides the luminance. A different decomposition involving a projective space of chromaticity classes is then presented. Finally, it is shown how the three types of color deficiencies present in some groups of humans leads to a direct-sum decomposition of three one-dimensional subspaces that are associated with the three types of cone photoreceptors in the human retina. Next, a few specific linear and nonlinear color representations are presented. The color spaces of two digital cameras are also described. Then the issue of transformations between \emph{different} color spaces is addressed.
Author(s): Eric Dubois, Alan C. Bovik
Series: Synthesis Lectures on Image, Video, and Multimedia Processing
Edition: 1
Publisher: Morgan & Claypool Publishers
Year: 2009
Language: English
Pages: 130
Cover
......Page 1
Notation......Page 14
Semigroups and Groups......Page 20
Equivalence Relations......Page 22
The Set P of Physical Light Stimuli......Page 23
Algebraic Structure of the Set P......Page 25
Embedding of P in a Vector Space A......Page 27
Metric on A......Page 29
Discrete Representation of Elements of A......Page 30
Vector Spaces......Page 32
Extension of Metameric Properties to A......Page 35
Proofs of Propositions and Theorems of Section 3.3......Page 37
Definition and Properties of the Color Vector Space......Page 39
The Mapping from A to C: Computing Tristimulus Values......Page 42
Black space and the canonical decomposition of the stimulus space......Page 44
Change of Primaries......Page 47
The Visual Subspace and General Color Spaces......Page 49
The CIE Color Spaces......Page 52
The Cone of Physically Realizable Colors......Page 55
Additive Reproduction of Colors......Page 57
New Primaries Specified in Terms of Existing Primaries......Page 58
Matrix for Transformation of Tristimulus Values Specified......Page 59
Color Matching Functions of New Primaries Specified......Page 60
Lattices......Page 64
Chromaticity Classes......Page 69
Determination of Tristimulus Values from Luminance and Chromaticities......Page 70
Additive Reproduction of Colors Revisited......Page 71
Decomposition of Color Space Corresponding to Certain Color Deficiencies......Page 73
Linear Color Space Representations......Page 80
Digital Camera Color Spaces......Page 82
Non-linear Color Coordinates......Page 83
Perceptually Uniform Spaces......Page 84
Device-dependent Coordinates......Page 85
Transformation between Color Spaces......Page 86
Continuous-domain Systems for Color Images......Page 92
Frequency Response and Fourier Transform......Page 94
Discrete-domain Color Images......Page 98
Color Signals with all Components on the Same Lattice......Page 99
Color Signals with Different Components on Different Sampling Structures......Page 101
Analysis of Color Mosaic Displays......Page 108
Concluding Remarks......Page 112
Author's Biography......Page 123
