Russ J.C. Image Analysis of Food Microstructure

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(a)

(b)

FIGURE 3.27

Application of a maximum likelihood ﬁlter to the beef image from Figure

3.6(a) (detail enlarged to show individual pixels): (a) original; (b) processed.

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TEXTURE

Many structures are not distinguished from each other or from the surrounding

background by a difference in brightness or color, nor by a distinct boundary line

of separation. Yet visually they may be easily distinguished by a texture. This use

of the word “texture” may initially be confusing to food scientists who use it to

describe physical and sensory aspects of food; it is used in image analysis as a way

to describe the visual appearance of irregularities or variations in the image, which

may be related to structure. Texture does not have a simple or unique mathematical

deﬁnition, but refers in general terms to a characteristic variability in brightness (or

color) that may exist at very local scales, or vary in a predictable way with distance

or direction. Examples of a few visually different textures are shown in Figure 3.28.

These come from a book (P. Brodatz,

Textures: A Photographic Album for Artists

and Designers

, Dover Publications, New York, 1966) that presented a variety of

visual textures, which have subsequently been widely distributed via the Internet

and are used in many image processing examples of texture recognition.

Just as there are many different ways that texture can occur, so there are different

image processing tools that respond to it. Once the human viewer has determined

that texture is the distinguishing characteristic corresponding to the structural dif-

ferences that are to be enhanced or measured, selecting the appropriate tool to apply

to the image is often a matter of experience or trial-and-error. The goal is typically

to convert the textural difference to a difference in brightness that can be thresholded.

Figure 3.29 illustrates one of the simplest texture ﬁlters. The original image is

a light micrograph of a thin section of fat in cheese, showing considerable variation

in brightness from side to side (the result of varying slice thickness). Visually, the

smooth areas (fat) are easily distinguished from the highly textured protein network

around them, but there is no unique brightness value associated with the fat regions,

and they cannot be thresholded to separate them from the background for measure-

ment. The range operator, which was used above as an edge detector, can also be

useful for detecting texture. Instead of using a very small neighborhood to localize

the edge, a large enough region must be used to encompass the scale of the texture

(so that both light and dark regions will be covered). In the example, a neighborhood

radius of at least 2.5 pixels is sufﬁcient.

Many of the texture-detecting ﬁlters were originally developed for the applica-

tion of identifying different ﬁelds of planted crops in aerial photographs or satellite

images, but they work equally well when applied to microscope images. In Figure

3.30 a calculation of the local entropy isolates the mitochondria in a TEM image of

liver tissue.

Probably the most calculation-intensive texture operator in widespread use deter-

mines the local fractal dimension of the image brightness. This requires, for every

pixel in the image, constructing a plot of the range (difference between brightest

and darkest pixels) as a function of the radius of the neighborhood, out to a radius

of about 7 pixels. Plotted on log-log axes, this often shows a linear increase in

contrast with neighborhood size. Performing least-squares regression to determine

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the slope and intercept of the relationship measures the fractal parameters of the

image contrast (for a range image, as would be acquired from an AFM, it is the

actual surface fractal dimension; for an image in which the brightness is a function

of slope, as in the SEM, it is equal to the actual surface dimension plus a constant).

As shown in the example of Figure 3.31, these parameters also convert the

original image in which texture is the distinguishing feature to one in which bright-

ness can be used for thresholding. The fractal texture has the advantage that it does

not depend on any speciﬁc distance scale to encompass the bright and dark pixels

that make up the texture. It is also particularly useful because so many structures in

the real world are naturally fractal that human vision has apparently evolved to

recognize that characteristic, and many visually discerned textures have a fractal

mathematical relationship.

FIGURE 3.28

A selection of the Brodatz textures, which are characterized by variations in

brightness with distance and direction.

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(a)

(b)

FIGURE 3.29

Thresholding the fat in cheese: (a) original image; (b) texture converted to a

brightness difference using the range operator; (c) the fat regions outlined (using an automatic

thresholding procedure as described subsequently).

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Since fractal geometry has been mentioned in this context, it is an appropriate

place to insert a brief digression on the measurement of fractal dimension for

surfaces. These frequently arise in food products, especially ones that consist of an

aggregation of similar particles or components. For example, the images in Figure

3.32 show the surface of particulate whey protein isolate gels made with different

pH values. Visually, they have network structures of different complexity. This can

be measured by determining the surface fractal dimension (we will see in later

chapters other ways to measure the fractal dimension).

The most efﬁcient way to determine a fractal dimension for a surface is to

calculate the Fourier transform power spectrum, and to plot (on the usual log-log

axes) the amplitude as a function of frequency. As shown in Figure 3.33, the plot is

a straight line for a fractal, and the dimension is proportional to the slope. If the

surface is not isotropic, the dimension or the intercept of the plot will vary with

direction and can be used for measurement as well.

(c)

FIGURE 3.29 (continued)

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(a)

(b)

FIGURE 3.30

A TEM image of liver tissue (a) and the result of calculating the entropy

within a neighborhood with radius of 4 pixels and representing it with a grey scale value (b).

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(a)

(b)

FIGURE 3.31

The slope (a) and intercept (b) from calculation of the fractal texture in the

image in Figure 3.29(a).

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(a)

(b)

FIGURE 3.32 Surface images of particulate whey protein isolate gel networks showing a

change in fractal dimension vs. pH. (a) pH 5.4, fractal dimension 2.17; (b) pH 5.63, fractal

dimension 2.45. (Courtesy of Allen Foegeding, North Carolina State University, Department

of Food Science. Magniﬁcation bars are 0.5 µm)

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(a)

(b)

FIGURE 3.33 Analysis of the fractal gel structure shown in Figure 3.32a: (a) the Fourier

transform power spectrum; (b) its analysis, showing the phase values which must be random-

ized and a plot of the log magnitude vs. log frequency which must be linear. The slope of

the plot is proportional to fractal dimension; the slope and intercept of the plot are uniform

in all directions, as shown, for an isotropic surface.

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DIRECTIONALITY

Many structures are composed of multiple identical components, which have

the same composition, brightness, and texture, but different orientations. This is true

for woven or ﬁber materials, muscles, and some types of packaging. Figure 3.34

shows an egg shell membrane. Visually, the ﬁbers seem to be oriented in all directions

and there is no obvious predominant direction. The Sobel vector of the brightness

gradient can be used to convert the local orientation to a grey scale value at each

pixel, which in turn can be used to measure direction information. Previously, the

magnitude of the vector was used to delineate boundaries. Now, the angle as shown

in Figure 3.23 is measured and values from 0 to 360 degrees are assigned grey scale

values of 0 to 255. A histogram of the processed image shows that the ﬁbers are

not isotropic, but that more of them are oriented in a near-horizontal direction in

this region.

This method can also be used with features that are not straight. Figure 3.35

shows an example of collagen ﬁbers, which seem not to be random, but to have a

predominant orientation in the vertical direction. The direction of the brightness

gradient calculated from the Sobel operator measures orientation at each pixel

location, so for a curved feature each portion of the ﬁber is measured and the

histogram reﬂects the amount of ﬁber length that is oriented in each direction.

Note that the brightness gradient vector points at right angles to the orientation

of the ﬁber, but half of the pixels have vectors that point toward one side of the ﬁber

and half toward the other. Consequently the resulting histogram plots show two

peaks, 128 grey scale values or 180 degrees apart. It is possible to convert the grey

scale values in the image to remove the 180 degree duplication, by assigning a color

look up table (CLUT) that varies from black to white over the ﬁrst 128 values, and

then repeats that for the second 128 values. This simpliﬁes some thresholding

procedures as will be shown below.

The images in the preceding examples are entirely ﬁlled with ﬁbers. This is not

always the case. Figure 3.36 shows discrete ﬁbers, and again the question is whether

they are isotropically oriented or have a preferential directionality. The measurement

is performed in the same way, but the image processing requires an extra step. A

duplicate of the image is thresholded to select only the ﬁbers and not the background.

This image is then used as a mask to select only the pixels within the ﬁbers for

measurement. The random orientation values that are present in the non-ﬁber area

represent gradient vectors whose magnitude is very small, but which still show up

in the orientation image and must be excluded from the measurement procedure.

The thresholded binary image of the ﬁbers is combined with the direction values

keeping whichever pixel is brighter, which replaces the black pixels of the ﬁbers

with the direction information.

The 0 to 360 degree range of the orientation values is often represented in color

images by the 0 to 360 degree values for hue. Like most false-color or pseudocolor

displays, this makes a pretty image (Figure 3.37) and helps to communicate one

piece of information to the viewer (the orientation of the ﬁber), but adds no new

information to the measurement process.

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