Russ J.C. Image Analysis of Food Microstructure

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thresholded binary image relaxes the requirements for thresholding. In Figure 3.59

the thresholded red channel (Figure 3.57b) is skeletonized to thin lines whose total

length is related stereologically to the surface area of the cells. Since the skeleton-

ization (discussed in the next chapter) is used to thin down the cell walls, the setting

of the threshold (which controls to some extent the apparent thickness of the stained

tissue) can be varied over a considerable range without affecting the ﬁnal result.

Of course, not all images contain just two populations of pixels. The statistical

tests can be extended to deal with more groups, provided that the actual number of

distinguishable structures is known. Figure 3.60 shows an example. The original

image has visually distinguishable regions that have the same brightness values (both

mean and distribution), but the texture has an orientation. Applying a Sobel orien-

tation ﬁlter as described above assigns grey scale values from 0 to 255 as the direction

of the brightness gradient vector varies from 0 to 360 degrees. By using a color

lookup table (CLUT) as described previously, the pairs of direction values that are

180 degrees apart in Figure 3.60(b) can be mapped to the same value, and the 0- to

360-degree range of directions converted to 0 to 180 degrees, as shown in Figure

3.60(c). This image has a histogram with three well-deﬁned peaks. Generalization

of the student’s t-test described above to more than two populations results in the

familiar analysis of variance (ANOVA) statistical test. Applying that with the

assumption of three populations of pixels calculates threshold values that separate

the regions.

This example is also a reminder that the thresholding step generally occurs after

various stages of image processing. If nonuniform illumination is present, or exces-

sive image noise, or other image acquisition defects, thresholding cannot be suc-

cessfully accomplished until those problems have been corrected. If enhancement

is required to convert some characteristic of the image that can be visually distinguished

to a brightness difference so that thresholding is possible, that must be done ﬁrst.

(a) (b)

FIGURE 3.59 Thinning after thresholding: (a) thresholded red channel from Figure 3.57(b);

skeletonized (and short branch segments discarded).

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(a) (b)

FIGURE 3.60 Example of thresholding three populations of pixels: (a) test image containing

three orientations of texture; (b) application of Sobel orientation ﬁlter; (c) conversion of 0 to

360° angle values to 0 to 180° values; (d) boundary lines between regions obtained by

automatic thresholding using an ANOVA test; (e) histogram showing three well-separated

peaks, and the threshold settings calculated using an ANOVA statistical test used to produce

the boundaries shown in image (d).

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AUTOMATIC THRESHOLDING USING THE IMAGE

All of the methods described above use the image histogram as a starting point,

and treat the pixel values as individual and independent bits of information. In

particular, they ignore the relationship between a pixel and its neighborhood. Most

pixels in an image represent the same structure as their neighbors, and have similar

brightness values. Only a few lie adjacent to the boundaries between one structure

and another, or between feature and background. When we perform manual threshold

adjustment, rather than observing the histogram, most of the attention is directed

toward the appearance of the resulting image. The boundaries of the thresholded

binary representation of the structure must agree with what is seen and what is

known about the structures.

One of the most commonly encountered situations is images in which the feature

boundaries are locally smooth. For liquids, such as the images in Figures 3.55 and

3.56, surface tension creates a force that makes the droplets more-or-less spherical

and makes the surfaces locally smooth. In tissue, cell membranes do the same. Many

structures that form by slow growth have locally smooth boundaries because diffu-

sion along the boundary tends to ﬁll in any irregularities. Wear on surfaces can also

result in smooth shapes, as can local melting. When it is expected that the boundaries

should be smooth, the process of adjusting a threshold setting involves watching the

image and moving the slider so that the irregularities along the boundary are min-

imized. An algorithm that ﬁnds the threshold setting such that minor changes in

threshold produce the least change in the total length of the perimeter can automate

the process.

(e)

FIGURE 3.60 (continued)

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Figure 3.61 shows an image of bubbles in a whipped foam food product (the

full image was shown in Chapter 2, Figure 2.19). Setting an accurate threshold is

difﬁcult because of the intermediate grey values that lie around the periphery of the

bubbles (due to the penetration of light into the foam so that the image represents

a signiﬁcant depth in the material). It is reasonable to expect the bubbles to have

smooth borders, due to surface tension. Thresholding this using the smoothest

perimeter criterion produces a setting of 121 on the 0 to 255 scale. Changing that

setting even slightly (a value of 125 is shown in the ﬁgure) makes the borders of

the bubbles signiﬁcantly more irregular.

(a)

(b) (c)

FIGURE 3.61 Smooth boundary thresholding: (a) detail of image of bubbles in a whipped

food product (courtesy of Allen Foegeding, North Carolina State University, Department of

Food Science); (b) binary image resulting from automatic threshold setting for smoothest

perimeter; (c) binary image resulting from changing the threshold setting from 121 to 125.

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For images in which the boundary is sharp and has good contrast to begin with,

this method usually produces results that agree closely with what a skilled and

knowledgeable human operator determines. The ability to produce reasonable results

as the image quality degrades is a strong plus for this method. But its use depends

on knowing a priori that the boundaries should be smooth, and this is by no means

a universal condition. Figure 3.62, for instance, shows an example of particles that

have very rough boundaries. In general, objects produced by fracture and some forms

of agglomeration have rough, even fractal borders. In some cases using a criterion

of maximum, rather than minimum, perimeter change with threshold setting can

successfully produce automatic threshold values.

Many other criteria can be used to generate automatic thresholding algorithms,

but all require independent knowledge about the nature of the sample, which in most

cases must come from information external to the image. It is often useful to try to

make such knowledge explicit by forcing yourself to write down every detail you

can think of about the specimen, its preparation, and the imaging process. If this

information is sufﬁcient to allow someone else to obtain the same images, results,

and understanding that you have, then probably the list contains the information that

would enable successful thresholding of the features.

Figure 3.63 shows an example in which it can be anticipated that the features

(nuclei in frog red blood cells) should all be about the same size. Applying that

criterion to the thresholding process produces the threshold setting shown). It has

no obvious relationship to the shape of the histogram.

FIGURE 3.62 SEM image of pregelatinized cornstarch. Brittle fracture has produced highly

variable, irregular shapes.

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OTHER THRESHOLDING APPROACHES

There are many other techniques that are used, particularly in specialized appli-

cations, to separate the features of interest in an image from each other or from the

background. One of these, often used in robotics and machine vision, is a split-and-

merge strategy. Starting with the entire image, the histogram is examined. If statistical

(a) (b)

(c)

FIGURE 3.63 Threshold setting based on size uniformity: (a) original (frog red blood cells);

(b) thresholded binary result; (c) histogram with threshold setting.

Pixel Brightness Value

Frequency

064128

192 255

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tests indicate that it is not composed of a single class of pixels, the image is split,

usually into four parts (from which the name “quadtree” is also taken to apply to

this method). The same uniformity test is repeated on each part, so that any regions

that are not homogeneous are ultimately split down to the individual pixels. At the

same time, after each iteration of splitting, regions are compared to their neighbors

and joined (merged) if the same statistical test indicates similarity. The method is

reasonably efﬁcient, but depends critically on the ability to detect the presence of

inhomogeneity within a region from the histogram. If the inhomogeneity represents

only a small fraction of the area, it is unlikely to be detected.

Another approach that is complementary to traditional thresholding draws con-

tour or iso-brightness lines on the image. Instead of using the logic that a peak in

the histogram indicates the similarity of the pixels represented, this method examines

the valleys in the histogram as indicators of boundaries between regions. Contour

lines have several advantages for separating the structures in an image. For one

thing, they are continuous lines that close on themselves (or run off the edge of the

image). For another, it is not necessary for a pixel to have any particular value to

locate the contour line. It follows a path between values that are greater and ones that

are smaller than a given threshold value. Finally, the contour lines very often correspond

to the visually detected boundaries in images, even for rather complex structures.

Figure 3.64 shows a simple contour line applied to a scanned-probe image of a

coin. In this case, the brightness of each pixel represents a physical elevation.

Consequently, the contour line really is a line of constant elevation and as such can

mark the boundaries of the raised ﬁgure on the surface.

It is easy to extend this method to draw multiple contour lines, converting the

image to a contour map in which the lines have exactly the same meaning as on a

conventional topographic map. In the example of Figure 3.65, a set of ten lines

equally spaced in brightness or elevation are drawn using a scanned probe image of

the tip of a ball point pen. The irregularities of the lines show clearly the roughness

of the ball, their spacing can be used to measure its curvature, and the elongation

of the circles into ellipses measures the out-of-roundness of the ball. All of this same

information is, of course, present in the original image, but it is much more visible

and more easily accessed for measurement purposes in the contour map.

One of the most useful attributes of the contour method is the outlining of

boundaries around features, which facilitates measurements of structure or features.

In Figure 3.66 a typical image of bread shows a variety of pore sizes and shapes.

Drawing a single contour line on this image produces an outline of the pores. The

same logic for determining the optimum threshold setting was used as for binary

thresholding (in this example the Shannon algorithm). As discussed in Chapter 1,

the resulting lines provide a direct measure of the total surface area of the pores (the

surface area per unit volume of the bread, which is a major factor in the mouth-feel

and texture of the bread, is equal to 4/π times the total length of the contour lines

divided by the area of the image).

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(a) (b)

(c)

FIGURE 3.64 Drawing a contour line on an image: (a) scanned probe image of a coin; (b)

contour line drawn to outline the raised head; (c) histogram of image (a) with the brightness

value used for the contour line marked.

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(a)

(b)

FIGURE 3.65 Drawing a contour map: (a) scanned probe image of a ball point pen; (b)

contour map drawn from the image.

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(a)

(b)

FIGURE 3.66 Contour lines for structure measurement: (a) image of pores in bread; (b)

contour line drawn to mark the edges of the pores.

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