(1012) The magnitude of in Software

Encoding UPCA in Software (1012) The magnitude of

lip - wll Since Pr = (1,0,0)

= v(r - 1/3)2 + (g - 1/3)2 + (b - 1/3)2

(1013)

= V2/3

1/3) - (b - 1/3)

(1014)

The dot product between P - wand Pr - w is (1015) ~ Divide this dot product by lip - wll and IIPr- wll, substitute Equations 109 through 1011, and simplify to get the formula for computing the hue from the R, G, and B values: cas H = 2R - G - B 2(r - 1/3) - (g (p _ w) (Pr _ w) =

(R - B)(G - B)

(1016)

In order to have the value for hue in the range from 0 to 360 degrees, it is necessary to subtract H from 360 when B / I > G / I Even though this derivation began with normalized RGB values, the formula in Equation 1016 will work with RGB values on any scale since the scale factors in the numerator and denominator will cancel The saturation is the distance on the triangle in the rgb-space from white relative to the distance from white to the fully saturated color with the same hue Fully saturated colors are on the edges of the triangle Let dp be the distance from point W at the center of the triangle to point P for some color, and let dq be the distance to point Q at the edge of the triangle along the line from W to Q passing through P The saturation is the ratio of the distances, dp/ dq The formula for the saturation is R+ ~ + B The derivation is provided by Gonzalez and Woods [91] S

min(R, G, B)

(1017)

Equations 1016, 1017, and 1018 can be used to convert the RGB image from a color image acquisition system to the HSI representation for further processing The hue is not defined when the saturation is zero, that is, for any colors along the axis of the HSI solid Saturation is not defined when the intensity I = O The transformation from RGB to HSI is used to convert color images into a form appropriate for machine vision Gray-level algorithms can be performed on the I component of the HSI representation Segmentation can be performed on the H component to discriminate between objects with different hues However, hue is not reliable for discrimination when the saturation is low, so the segmentation algorithms must be modified to leave pixels with low saturation unassigned Region growing algorithms can use thresholds on hue to form core regions, leaving unassigned any pixels that have low saturation or are outside the threshold boundaries The algorithms for growing core regions by assigning neighboring pixels are unchanged More general algorithms can divide the HSI solid into regions using thresholds on hue, saturation, and intensity These thresholds are easier to formulate and apply in the HSI representation than in the RGB representation provided by the imaging system

The color content of outdoor light varies considerably, yet people are able to correctly perceive the colors of objects in the scene independent, for the most part, from the color of the ambient illumination This phenomenon is called color constancy Ambient light has the spectral distribution E(>"), which describes the power at each wavelength Assume that scene surfaces are opaque, so that scene coordinates can be specified using the coordinates of the corresponding point (x, y) on the image plane The fraction of light at wavelength>" reflected from the surface point at location (x, y) is S(x, y, >) The light arriving at each location in the image is determined by the spectral distribution of the ambient light that falls on the scene surfaces and the fraction of light reflected at various wavelengths: S(x, y, >")E(>") (1018)