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.
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.
KEYWORDS: Positron emission tomography, Data acquisition, Clocks, Calibration, Signal processing, Digital signal processing, Crystals, Field programmable gate arrays, Sensors, Signal detection
Positron emission tomography~(PET) systems employ mixed-signal front-end to carry out relatively simple, and ad hoc, processing of the charge pulses generated upon event detection. To obtain, and maintain over time, proper calibrations of the mixed-signal circuitry for generating accurate event information is a challenging task due to the simplicity of the event processing, and the huge number of channels and multiplexing of the input signals found in modern PET systems. It is also difficult to modify or extend the event-processing technologies when needs arise because it would involve making changes to the circuitry. These limitations can be circumvented by applying digital signal-processing technologies for analyzing event pulses generated in PET. With digital technologies, optimized event-processing algorithms can be implemented and they can be modified or extended with ease when needed. The resulting PET data-acquisition (DAQ) system is easier to calibrate and maintain, can generate more accurate event information, and has better extendibility. In this paper, we present our work toward developing a scalable all-digital DAQ system for PET, built upon a personal-computer platform for reducing cost. We will present the overall architecture of this digital DAQ system, and describe our implementations of several components of the system.
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