AREA 1-y

EDGE PIXEL BRIGHTNESS

AREA 1-y AREA 1-y

I back

AREA y lobj < !back

ledge = Y lobj + ( 1-y) lback

Figure 3.8: Example of effect of edge threshold setting on perceived object size. Percentages shown are for fraction of edge pixel occupied by object included in digital

representation. Numbers below objects are number of pixels included in object.

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Several physical phenomena influenced edge pixel brightness:

1) Fluctuating illumination intensity: Line voltage variations on the order of± 2 percent produced intensity fluctuations in the tungsten lamp illuminating the objects. Varying lamp intensity altered background pixel brightness relative to object pixel

brightness (discussed in Section 3a below). Edge pixels containing both object and background would have fluctuating grey-level

values that varied with changes in background brightness and might oscillate above and below the preset threshold value at the

moment the image is digitized. If edge pixels were below the threshold value, they were included in the object. They were excluded from the object if above the threshold value. The

magnitude of the error introduced by this process depended on the number of perimeter pixels relative to total pixels in the object.

The perimeter-area ratio declines as 4/D for circular and square objects, where Dis the characteristic diameter of the object. The relative magnitude of errors arising from edge effects might be expected to decline with increasing object size. When single polystyrene latex spheres of known size (Dow Chemical Company, Indianapolis, IN.) were repeatedly digitized in fluctuating light using constant threshold values, relative errors of 0.2-3.0

percent were obtained (Figure 3.9). Error initiaily declined with increasing object size, then became constant. Experimental error was much lower than the worst-case estimate of a shift in area caused by loss or gain of a one pixel-wide "ring" along the entire

Figure 3.9: Experimental precision of 10 repeated digitizations of single spheres.

Top: Standard deviation in pixels vs. mean sphere area.·

Bottom: Coefficient of variation vs. mean sphere area. Line is error for change in edge position by± 1 pixel around entire object.

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object boundary. It is possible to conclude that at least for high contrast objects, a small proportion of available edge pixels were fluctuating in and out of the analysis.

2) Fluctuation in apparent size of object that is due to random positioning in field of view. The net gain or loss of edge pixels around an object as it is moved over the digitizing grid may not sum to zero for irregular objects that are small relative to pixel size. Error resulting from repeated measurements of randomly

positioned objects was roughly twice the error caused by illumination fluctuations alone (Figure 3.9). Relative error

generally declined with increasing object size, and was never more than 3 percent of "true" object size.

3) Interaction between image contrast and threshold levels set by the experimenter:

a) Influence of illumination intensity: Assume Lambert-Beer extinction of light within an object:

1₀ = lb exp (-kz), where lb background light intensity

1₀ light intensity transmitted through object

k extinction coefficient z = thickness of object.

(3.6)

The intensity difference between object and background will be:

Idiff = lb - Io.

Substituting from 6),

Idiff = lb ( 1 - exp (-kz) ).

From Equation (8), intensity differences between object and background should increase proportionately with incident

(3. 7)

(3.8)

illumination intensity (Figure 3.10). In practice, contrast differences between object and background increased to a maximum value as illumination intensity increased, then declined as the video imager became light-saturated (detector output voltages reached maximum values) and contrast was lost.

b) Influence of spatially varying light extinction on object intensity: If the extinction coefficient or thickness in

Equation (8) varies with (x,y) position within an object, then intensity differences between background and object will vary with location inside the object. Extinction coefficient and thickness act similarly to determine the light extinction at any point within the object. Optical density is defined as the logarithm of

the ratio of incident to transmitted light, which for Lambert-Beer extinction is the product of extinction coefficient and thickness, kz (McGraw-Hill, 1977). High contrast occurs when an object has high optical density (the product, kz, is large). Background illumination intensity and varying optical density interact to determine variability in light intensity transmitted through the object (Figure 3.11). Coefficients of variation (standard devia- tions divided by respective means) computed for this one dimen- sional case declined with increasing optical density (Fig. 3.12).

c) Interaction between contrast difference and threshold setting:

The impact of threshold selection on measured object size is shown in Figure 3.13 for the simple models described above.

Thresholds set to include only a portion of object intensities resulted in inaccurate size determinations. Error in object area

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Figure 3.10: Effect illumination intensity on contrast difference.

between object and background .

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Figure 3.11: Effect spatially varying object optical density on transmitted light intensity. Hatched regions in lower figure

simulate cell walls with higher extinction coefficient (k-0.25) than surroundings. Upper figure is resulting transmitted intensity for light with background intensity - 1

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