Russ J.C. Image Analysis of Food Microstructure

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the distances between them, and that the background variation is gradual, as it usually

is for illumination nonuniformities. In the example of Figure 2.37b this technique

is marginally successful, but irregularities in the background remain because the

features are too close together for their complete elimination.

A superior method for removing the features to leave just the background uses

the rank ﬁlter. Rather than averaging the values from the pixels within the features

into the background, replacing each pixel with its darkest (or lightest) neighbor will

(a) (b)

FIGURE 2.37 Removing features to create a background: (a) original image of rice grains

dispersed for length measurement (note nonuniform illumination); (b) background generated

by Gaussian smoothing with 15 pixel radius standard deviation; (c) background generated by

replacing each pixel with its darkest neighbor in a 9 pixel neighborhood); (d) subtracting

image (c) from image (a) produces uniform background.

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erase light (or dark) features and insert values from the nearby background. This

technique uses much the same computation as the median ﬁlter, described above,

and is another example of ranking pixels in a moving neighborhood. As shown in

Figure 2.37c, this method works very well if the features are narrow in at least one

direction. It assumes that the features may vary in brightness but are always darker

(or lighter) than the local background.

This method can handle rather abrupt changes in brightness, such as can result

from shadows, folds in sections, or changes in surface slope. In the example of

Figure 2.38, the droplets on a glass surface are illuminated from behind and there

is considerable shading, which is not gradual and prevents thresholding to measure

their size distribution and spatial arrangement. In this case the contrast around the

edges of the droplets is darker than the interior or the background. Replacing each

pixel with its brightest neighbor produces a background. Dividing it pixel-by-pixel

into the original image produces a image with uniform contrast, which can be

measured.

In some cases, it is not sufﬁcient to simply replace pixels by their brighter or

darker neighbors, because it can alter the underlying background structure. A more

general solution is to ﬁrst replace the feature pixels with those from the background

(e.g., replace dark pixels with lighter ones) and then, when the features are gone,

perform the opposite procedure (e.g., replace light pixels with darker ones) using

the same neighborhood size. This restores the background structure so that it can

be successfully removed, as shown in Figure 2.39. For reasons that will become

clear in the next chapters, these procedures are often called erosion and dilation,

and the combinations are openings and closings.

Another method that can be used either manually or automatically is to ﬁt a

smooth polynomial function to selected background regions dispersed throughout

the image. Expressing brightness as a quadratic or cubic function of position in the

image requires coefﬁcients that can be determined by least-squares ﬁtting to a

number of selected locations. In some cases it is practical to select these by hand,

choosing either features or background regions as reference locations that should

all have the same brightness value. Figure 2.40 illustrates the result.

If the reference regions are well distributed throughout the image and are either

the brightest or darkest pixels present, then they can be located automatically and

the polynomial ﬁt performed. The polynomial method requires the variation in

brightness to be gradual, but does not require that the features be small or well

separated as the rank ﬁltering method does. Figure 2.41 shows an example.

The polynomial ﬁtting technique can be extended to deal with variations in

contrast that can result from nonuniform section thickness. Fitting two polynomials,

one to the brightest points in the image and a second to the darkest points, provides

an envelope that can be used to locally stretch the contrast to a uniform maximum

throughout the image as shown in Figure 2.42.

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(a)

(b)

(c)

FIGURE 2.38 Removal of a bright background: (a) original image (liquid droplets on glass);

(b) background produced by replacing each pixel with its brightest neighbor in a 7-pixel wide

neighborhood; (c) dividing image (b) into image (a) produces a leveled image with dark

outlines for the droplets.

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(a) (b)

FIGURE 2.39 Removal of a structured background: (a) original image (gold particles bound

to cell organelles); (b) erosion of the dark gold particles also reduces the size of the organelles;

from image (c) into the original image (a) produces a leveled imaged in which the gold

particles can be counted.

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(a)

(b)

FIGURE 2.40 Selecting background points: (a) original image with nonuniform illumination

(2-mm-thick peanut section stained with toluidine blue to mark protein bodies, see Color

Figure 1.12; see color insert following page 150); the cell walls (marked by the dashed lines)

have been manually selected using the Adobe Photoshop

wand tool as features that should

all have the same brightness; (b) removing the polynomial ﬁt to the pixels in the selected

area from the entire image levels the contrast.

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(a)

(b)

FIGURE 2.41 Automatic background correction: (a) original image (courtesy of Diana Kit-

tleson, General Mills) with nonuniform illumination (the blue channel was selected with the

best detail from an image originally acquired in color); (b) automatically leveled by removing

a polynomial ﬁt to the darkest pixel values.

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(a)

(b)

FIGURE 2.42 Automatic contrast adjustment using two polynomials, one ﬁt to the dark and

one to the light pixels: (a) original (TEM image of latex spheres); (b) processed.

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IMAGE DISTORTION AND FOCUS

Another assumption in subsequent chapters on processing and measurement is

that dimensions in an image are uniform in all locations and directions. When images

are acquired from digital or ﬁlm cameras on light microscopes, or from scanners,

that condition is generally met. Digitized video images often suffer from non-square

pixels because different crystal oscillators control the timing of the camera and the

digitizer. Atomic force microscopes compound problems of different scales in the

slow- and fast-scan direction with nonlinearities due to creep in the piezo drives.

Macro cameras may have lens distortions (either pincushion or barrel distortion;

short focal length lenses are particularly prone to ﬁsh-eye distortion) that can create

difﬁculties.

Electron microscopes have a large depth-of-ﬁeld that allows in-focus imaging

of tilted specimens. This produces a trapezoidal distortion that alters the shape and

size of features at different locations in the image. Photography with cameras (either

ﬁlm or digital) under situations that view structures at an angle produces the same

foreshortening difﬁculties. If some known ﬁducial marks are present, they can be

used to rectify the image as shown in Figure 2.43, but this correction applies only

to features on the corrected surface.

Distortions in images become particularly noticeable when multiple images of

large specimens are acquired and an attempt is made to tile them together to produce

a single mosaic image. This may be desired because, as mentioned in the discussion

of image resolution, acquiring an image with a large number of pixels allows

measurement of features covering a large size range. But even small changes in

magniﬁcation or alignment make it very difﬁcult to ﬁt the pieces together.

This should not be confused with software that constructs panoramas from a

series of images taken with a camera on a tripod. Automatic matching of features

along the image edges, and sometimes knowledge about the lens focal length and

distortion, is used to distort the images gradually to create seamless joins. Such

images are intended for visual effect, not measurement or photogrammetry, and

consequently the distortions are acceptable. There are a few cases in which tiling

of mosaics is used for image analysis, but in most cases this is accomplished by

having automatic microscope stages of sufﬁcient precision that translation produces

correct alignment, and the individual images are not distorted.

Light microscope images typically do not have foreshortening distortion because

the depth of ﬁeld of high magniﬁcation optics is small. It is possible, however, to

acquire a high magniﬁcation light microscope image of a sample that has a large

amount of relief. No single image can capture the entire depth of the sample, but if

a series of pictures is taken that cover the full z-depth of the sample, they can be

combined to produce a single extended-focus image as shown in Figure 2.44.

The automatic combining of multiple images to keep the best-focused pixel

value at each location requires that the images be aligned and at the same magniﬁ-

cation, which makes it ideal for microscope applications but much more difﬁcult to

use with macro photography (shift the camera, do not refocus the lens). The software

uses the variance of the pixel values in a small neighborhood at each location to

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select the best focus. For color images, this can be done separately for the red, green,

and blue channels to deal with slight focus differences as a function of wavelength.

When an entire image is imperfectly focused, it is sometimes practical to correct

the problem by deconvolution. This operation is performed using the Fourier trans-

form of the image, and also requires the Fourier transform of the point spread

function (psf). This is the image of a perfect point with the same out-of-focus

(a)

(b)

FIGURE 2.43 Example of correction for trapezoidal distortion: (a) original foreshortened

image; (b) calculated rectiﬁed view; note that the screen and the edges of the computer, which

do not lie in the plane of the keyboard, are still distorted.

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condition as the image of interest. In a few cases it is practical to measure it directly,

as shown in Figure 2.45. In astronomy, an image of a single star taken through the

same optics becomes the point spread function. In ﬂuorescence microscopy, a single

microbead may serve the same function. It is slightly more complicated to obtain

the psf by obtaining a blurred image of a known structure or test pattern, deconvolve

it with the ideal image to obtain the psf, and then use that to deconvolve other

images. That technique is used with the AFM to characterize the shape of the tip

(which causes blurs and distortion in the image).

In many cases the most straightforward way to perform deconvolution is to

estimate the point spread function, either interactively or iteratively. The two most

common types of blur are defocus blur in which the optics are imperfectly adjusted,

and motion blur in which the camera or sample are moving, usually in a straight

line (Figure 2.46). These produce point spread functions that are adequately modeled

in most cases by a Gaussian or by a line, respectively. Adjusting the standard

deviation of the Gaussian or the length and orientation of the line produces the point

spread function and the deconvolution of the image.

Deconvolution is hampered by the presence of random noise in the image. It is

very important to start with the lowest noise, highest bit depth image possible. The

noise in the deconvolved result will be much greater than in the original because

(a) (b)

FIGURE 2.44 Example of extended focus: (a, b, c) images of the leg and wing of a fruit ﬂy

at different focal depths; (d) combination keeping the in-focus detail from each image.

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