The paper introduces a new approach to tone correction of color images through a spherical color model. Although color changes more smoothly under the spherical model, some colors of the model cannot be displayed in the RGB color cube. The paper demonstrates the disadvantage does not affect the applications of the general techniques of tone correction in the spherical model. The achromatic component defined by the spherical model is separated from a given image with tonal imbalance, and then a tone correction function is performed on the component. The resulting achromatic component is combined with the original chromaticity to produce a tone corrected image. In the spherical color model, tone correction functions can be designed such that the corrected colors are within the RGB color cube for display. Technical requirements of the tone correction functions are discussed, and comparisons are made between the spherical color model and other similar color models including the commonly used HSV and HSL. Empirically, the effects of the general tone correction techniques in the spherical color model are close to those in the HSV color model.
KEYWORDS: RGB color model, Spherical lenses, Mathematical modeling, Visual process modeling, Systems modeling, Human vision and color perception, Mathematics, Roads, Computing systems, Computer science
The paper introduces a spherical coordinate system-based color model and studies the color change in the model. A circular cone with a spherical top tightly circumscribing the RGB color cube is equipped with a properly rotated spherical coordinate system. Similar to the commonly used color models with a hue component such as the HSV model, the spherical model specifies color by describing the color attributes recognized by human vision, using the components of the spherical coordinate system. The formulas of conversions between the spherical model and the RGB color model are provided, which are mathematically simpler and more intuitively understandable than those for commonly used models with a hue component. Most importantly, color changes are perceptually smoother in the spherical model. Comparisons between the spherical model and the HSV model on color changes are made in the paper.
Proc. SPIE. 8652, Color Imaging XVIII: Displaying, Processing, Hardcopy, and Applications
KEYWORDS: RGB color model, Mathematical modeling, Spherical lenses, Visual process modeling, 3D modeling, Distance measurement, Systems modeling, Human vision and color perception, Mathematics, Computer science
The paper introduces a transformed spherical model to represent the color space. A circular cone with a spherical top
tightly circumscribing the RGB color cube is equipped with a spherical coordinate system. Every point in the color cube
is represented by three spherical coordinates, with the radius ρ measuring the distance to the origin, indicating the
brightness attribute of the color, the azimuthal angle Θ measuring the angle on the horizontal plane, indicating the hue
attribute of the color, and the polar angle θ measuring the opening of the circular cone with the vertical axis as its center,
indicating the saturation attribute of the color. Similar to the commonly used perceptual color models including the HSV
model, the spherical model specifies color by describing the color attributes recognized by human vision. The
conversions between the spherical model and the RGB color model are mathematically simpler than that of the HSV
model, and the interpretation of the model is more intuitive too. Most importantly, color changes perceptually smoother
in the spherical color model than in the existing perceptual color models.
Gradient operators are commonly used in edge detection. Usually, proper smoothing processing is performed on the
original image when a gradient operator is applied. Generally, the smoothing processing is embedded in the gradient
operator, such that each component of the gradient operator can be decomposed into some smoothing processing and a
discrete derivative operator, which is defined as the difference of two adjacent values or the difference between the two
values on the two sides of the position under check. When the image is smoothed, the edges of the main objects are also
smoothed such that the differences of the adjacent pixels across edges are lowered down. In this paper, we define the
derivative of f at a point x as f'(x)=g(x+Δx)-g(x-Δx), where g is the result of smoothing f with a smoothing filter, and Δx is an increment of x and it is properly selected to work with the filter. When Δx=2, sixteen gradient directions can be obtained and they provide a finer measurement than usual for gradient operators.
Edges can be characterized through the evolution of a wavelet transformation at different scale levels. A two-dimensional wavelet transformation of a given image is proportional to the gradient of a corresponding smoothed image. Each component of a normal two-dimensional wavelet transformation is in fact a one-dimensional wavelet transformation in one variable followed by a smoothing process in the other variable. The modified wavelet transformation of the given image gets rid of the smoothing process in each component since the magnitude of the wavelet transformation in the center part of a linear object may be increased by the big magnitudes of the wavelet transformation along the edges if the smoothing process is adopted, which makes it hard to isolate the centerline of the linear object. The modified wavelet transformation gives high magnitudes along the edges and low magnitudes in the center part of the linear objects in the wavelet-transformed image. In the image showing the magnitude of the wavelet transformation, there are high ridges along the edges of the linear objects and low grey level valleys bounded by the ridges. A suitable threshold can be used to extract the low grey level part of the image, such that the center parts of the linear objects are included. Since they are separated from other objects, they can be easily extracted in a post-processing.
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