. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. COLOR MICROSCOPY 103 Green. White --Red -- 0° 24(f Figure 4. Cylindrical color space. Intensity is added as the axial variable. Every color plots to a position in this space. based on experimental data from color-matching experi- ments conducted on human observers. Color coordinate conversion Some image processing techniques are intrinsically more successful when carried out in rectangular RGB- space, whereas others work best in cylindrical HSI-space. Thus it is useful to be able to convert color digital images from RGB to H
. The Biological bulletin. Biology; Zoology; Biology; Marine Biology. COLOR MICROSCOPY 103 Green. White --Red -- 0° 24(f Figure 4. Cylindrical color space. Intensity is added as the axial variable. Every color plots to a position in this space. based on experimental data from color-matching experi- ments conducted on human observers. Color coordinate conversion Some image processing techniques are intrinsically more successful when carried out in rectangular RGB- space, whereas others work best in cylindrical HSI-space. Thus it is useful to be able to convert color digital images from RGB to HSl color coordinates and back again. RGB to HSI conversion The conversion from RGB to HSI format can be ap- proached as follows. Recall that the gray line is the diago- nal of the color cube in RGB-space, and it is the vertical axis in cylindrical HSI-space. Thus we can begin by rotat- ing the RGB cube in .v, y. c-space so that its diagonal lies along the ;-axis, and its R-a\is lies in the x-z plane (Ledley et 1990; Castleman. 1996). This is given by "Te'" G - B] z = ^[R + G + B] (1) The latter of these gives the HSI intensity parameter. We can convert to cylindrical coordinates by defining polar coordinates in the .v-y plane. Then we normalize the radial variable so that the fully saturated colors (those having no more than two of the primary colors present) fall on a unit-radius circle in the x-y plane. This leads to the formula for saturation V3 5=1 min (/?, G. 5) We compute the angle '/,[(/? - G) + {R - B)] = cos and the hue is H V(/? - G)- + (R - B)(G - B) f). G > B 2tt - e. G s B (2) (3) (4) Notice that black { [R. G. B] = [0. 0. 0]) creates a problem for Eq. (3). We can assign black to [H, S, f] = [0, 0. 0]. HSI to RGB conversion The formulas for converting from HSI to RGB coordi- nates take on slightly different form for different sectors of the color circle (Castleman, 1996). For0° < // < 120°, -5 / I -I- S cos (//) cos (60° - H) while
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