Russ J.C. Image Analysis of Food Microstructure

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The method of successive erosion and counting is iterative and slow, and can

be replaced by an equivalent procedure using the EDM. In the example in Figure

4.8(c), the peaks of the mountains correspond to the various features present, and

the height of each mountain (the value of the EDM at the maximum point) measures

the radius of an inscribed circle in the feature. It is not necessary to actually perform

the watershed segmentation to measure this size distribution. Simply ﬁnding each

local maximum in the EDM and recording their values provides a measurement of

(a)

(b)

FIGURE 4.10

Measurement of particle size by counting successive erosions. The images

here show four stages of successive grey scale erosion of the features (each image has the

particles reduced in radius by four pixels). Overlapped and touching features separate before

their ﬁnal disappearance. Counting the number of features that disappear after each iteration

provides a size distribution.

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the size (speciﬁcally, the radius of an inscribed circle) for each touching or over-

lapped feature. These local maxima in the EDM are called the “ultimate eroded

points” to emphasize that they are the same points that would be the last pixels

within each feature to remain in the iterative erosion procedure shown above. How-

ever, they have the advantage that the EDM method is isotropic, whereas iterative

erosions, as noted above, can introduce directional bias. In Figure 4.11, the ultimate

eroded points are marked on the touching spherical particles from Figure 4.9.

Watershed segmentation cannot always successfully separate touching objects.

In Figure 4.12, thresholding the image of cells produces a binary image in which

the cells have holes within them, the result of low density vacuoles in the grey scale

image. Attempting to apply a watershed procedure to this image breaks the cells up

(c)

(d)

FIGURE 4.10 (continued)

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into pieces as watershed lines are drawn to the interior holes (Figure 4.12c). Simply

ﬁlling all of the holes will not correct the problem, because the image also contains

holes that lie between the cells. However, the size and shape of the interior holes

are different from those of the holes between cells: the latter are larger and/or cusp-

shaped while the interior holes are small and/or round. Selecting just the interior

holes and ﬁlling them in allows a watershed procedure to successfully separate the

touching cells (Figure 12e). The selection process is performed by measurement of

size and shape, as discussed in Chapter 5, after which a Boolean OR is used to

combine the image of the selected interior holes with the original binary image.

Angular features can also create difﬁculties for the watershed method. As shown

in Figure 4.13, when irregularly shaped particles touch the junctions are frequently

not simple. The watershed method sometimes draws the separation lines in ways

that alter the apparent shape of the features. It may also fail to draw some of the

lines where the width of the touching junction is greater than the perpendicular width

of the feature. An example is shown by the arrow in Figure 4.13(c). Another problem

with this particular image is that the size range of the features is too great for

measurement at a single magniﬁcation. The shapes of the smallest features (under

about 40 pixels) are not adequately represented in this image, and should be elim-

inated before measurement. Additional images at higher magniﬁcation can then be

FIGURE 4.11

The ultimate eroded points (UEP) are local maxima in the EDM, marked on

the original image from Figure 4.9. The value of the EDM at the ultimate point is a direct

measure of particle size without requiring watershed segmentation, corresponding to the radius

of an inscribed circle in each feature.

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used to measure the small features to include in the overall statistics. The removal

of features based on size, shape or other parameters is carried out as part of the

measurement process, not by erosion which would also alter the shapes of other

features present.

(a)

(b)

FIGURE 4.12

Segmentation of touching features containing holes: (a) original image of

cells; (b) thresholded; (c) watershed applied to image (b) cuts cells into fragments; (d) ﬁlling

holes within cells based on size and shape; (e) successful watershed segmentation of image

(d); (f) watershed segmented cell outlines superimposed on original image.

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Images of ﬁbers or other features with long lines of nearly constant width also

create a hazard for the watershed technique. Many programs implement the EDM

on which the watershed depends using integer representations of the distance values

for each pixel. Because of the aliasing of the pixel image, thin lines are often broken

into many small pieces by the watershed, which sees each indentation along the

(c)

(d)

FIGURE 4.12 (continued)

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edges of the feature (Figure 4.14c and 4.14d). But even a properly constructed EDM

in which the distance values have enough precision to accurately reﬂect the pixel

distances will cut ﬁbers where they cross, as shown in Figure 4.14(b). This may or

may not be useful. Other ways to segment and measure ﬁber images, based on the

feature skeleton, will be shown below.

(e)

(f)

FIGURE 4.12 (continued)

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(a)

(b)

FIGURE 4.13

Segmentation of angular particles: (a) freeze-dried coffee particles (see color

insert following page 150); (b) thresholded; (c) watershed segmentation (arrow marks a

location where the width of the touching junction is greater than the width of the smaller

feature, and no separation line is drawn); (d) removal of features with area less than 40 pixels.

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(c)

(d)

FIGURE 4.13 (continued)

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(a)

(b)

FIGURE 4.14

Watershed segmentation applied to an image of crossing ﬁbers: (a) thresholded

original; (b) watershed cuts features near crossing points; (c) Image Pro Plus result; (d) NIH-

Image result. These two widely used programs implement the EDM with integer arithmetic

which creates many erroneous cuts across the ﬁber images.

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(c)

(d)

FIGURE 4.14 (continued)

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