Spaces Of Representation

The Structure and Properties of Color Spaces and the Representation of Color Images

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 different color spaces is addressed. Finally, these ideas are applied to signal and system theory for color images. This is done using a vector signal approach where a general linear system is represented by a three-by-three system matrix. The formulation is applied to both continuous and discrete space images, and specific problems in color filter array sampling and displays are presented for illustration. The book is mainly targeted to researchers and graduate students in fields of signal processing related to any aspect of color imaging.

Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization

MPEG-7 is the first international standard which contains a number of key techniques from Computer Vision and Image Processing. The Curvature Scale Space technique was selected as a contour shape descriptor for MPEG-7 after substantial and comprehensive testing, which demonstrated the superior performance of the CSS-based descriptor. Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization is based on key publications on the CSS technique, as well as its multiple applications and generalizations. The goal was to ensure that the reader will have access to the most fundamental results concerning the CSS method in one volume. These results have been categorized into a number of chapters to reflect their focus as well as content. The book also includes a chapter on the development of the CSS technique within MPEG standardization, including details of the MPEG-7 testing and evaluation processes which led to the selection of the CSS shape descriptor for the standard. The book can be used as a supplementary textbook by any university or institution offering courses in computer and information science.

Body Representations, Peripersonal Space, and the Self: Humans, Animals, Robots