imaging particle analysis: the importance of image quality

Copyright © 2010 by Lew Brown, Fluid Imaging Technologies, Inc.1

I. What is “Image Quality”

Everyone has a basic understanding of the term “image quality” that is purely subjective, or “qualitative” in nature. We make qualitative judgements on image quality all the time, especially when it comes to our own pictures taken using consumer cameras, etc. Figure One shows an example of a simple landscape image where one version of the image is clearly of “higher quality” than the other. The lower image is perceived as poorer quality due to its lack of sharpness and improper color balance.

It is crucially important in any discussion of image quality to recognize that many factors that contribute to image quality can only be looked at from a “systems level”. As an example, the quality of an image produced by a digital camera is the sum of several parts, the lens’ ability to correctly transmit the information, the sensor’s resolution and the noise and processing characteristics of the camera electronics. Furthermore, if the image produced by this camera is being judged for quality by a human being, then the characteristics of the observer also come into play: what is the quality of the person’s eyesight (do they need corrective lenses, and if so, are they wearing them?), the distance to the image he/she

is viewing, the lighting conditions, etc. Last, but not least, in the case of a human observer, the situation becomes even muddier due to the fact that each person’s brain processes the visual information differently!

Some of the common descriptors used when discussing image quality include sharpness (amount of detail conveyed), dynamic range (range of light levels captured), contrast, distortion (usually caused by the optics), tonal mapping and artifacts (usually produced by the electronics or software processing of the image). Of all of these, the factor that has

Imaging Particle Analysis: The Importance of Image QualityLew Brown

Technical DirectorFluid Imaging Technologies, Inc.

Abstract: Imaging particle analysis systems can derive much more information about particles compared to classical “volumetric-based” systems (light obscuration, electrozone sensing, laser diffraction, etc.), which can only measure particle size in terms of the Equivalent Spherical Diameter (ESD) of a sphere corresponding to the derived volume of the particle. Imaging-based systems can also measure many different parameters for each particle which represent both shape and gray scale information. This gives these systems the capability to differentiate amongst non-similar particles contained in a heterogeneous mixture. These image-based systems can “classify” particles into different types where the volumetric systems can only report a “size” for each particle.

One drawback to imaging particle analysis systems is that they are limited in the lower end of the size range they can properly characterize (1). However, in applications within these systems' resolution range, they do offer significant advantages. This paper will discuss how the quality of the images directly affects the ability of the system to make proper measurements, and therefore affects the ability of the system to differentiate between different particle types. Using real-world data and examples, we come to the succinct (but rather unscientific) conclusion:

Fuzzy Images = Fuzzy Measurements = Fuzzy Classifications

Figure 1: Landscape Image with “good image quality” (top) and “bad image quality” (bottom).


the largest influence on perceived image quality is usually “sharpness”. Although this is sometimes simplified to “focus”, it really is a combination of many factors (focus being only one) that indicate the overall amount of spatial information captured by the image.

Due to the high degree of variability of subjective image quality, scientists have found it necessary to come up with “qualitative” measurements for image quality. Usually, these measurements are “systems level” as discussed above, except in some cases where a particular element of an optical system can be isolated, such as the lens only.

II. Qualitative Measures of Image Quality

As stated above, the most critical factor in image quality is “sharpness”, or the ability of the system to capture image detail. If an image is “blurry” or “out of focus” to begin with, other factors such as tonal mapping, color balance and dynamic range really do not have as much meaning because of the lack of information contained in the image to begin with.

“Sharpness” is most commonly equated to the term “resolution”, which can be a bit of a misnomer and cause for confusion, since there are many different kinds of resolution (sensor, spectral, display, etc.) . However, in general, the resolution of a system is defined as the ability to reproduce spatial detail in the object being imaged (2). In systems that include the human eye, resolution is a combination of “sharpness” and “acutance”. Acutance is a “perceived sharpness” caused by the changes in brightness on edge transitions (3). Those familiar with Photoshop use operations such as “unsharp masking” and “sharpening” frequently; these operations increase perceived sharpness through acutance changes only, the actual resolution of the image is unchanged. As an example, the lower image in Figure 1 was produced merely by applying a “blurring” filter and lowering the image acutance, but it still contains the same resolution (in pixels) as the original image!

Since imaging particle analysis involves measurements made on images by a computer, we need not worry about acutance in this discussion, as it is a “perceived-only” (via the human eye) characteristic. However, it is important to remember that when any of these images are viewed by the human eye, the subjectivity of vision and acutance can cause confusion!

Quantitative measurement of image sharpness is typically expressed in terms of the ability of the system to distinguish closely-spaced, high contrast pairs of lines in a given distance, most typically as “line pairs per millimeter” or lp/mm (4). In order to measure this, the system being evaluated is used to

image a standardized test target consisting of groups of bars of increasing numbers of line pairs/millimeter, and the largest bars that the imaging system can not discern are considered the limit of the system’s resolving power. One of the most commonly used targets is the 1951 USAF Resolution test Target (Figure 2).

The problem with merely using lp/mm to measure sharpness is that there is still a subjective judgment left in terms of the word “discern” in the definition above. To overcome this limitation, a measurement called “Modulation Transfer Function” (MTF) was introduced that measures the ability of the system to transfer contrast in the frequency domain (5). The modulation (or variance) of contrast transmitted by the system from target to image, ranging from 100% (unattenuated) to 0% (completely attenuated), is measured over a varying range of spatial frequencies and plotted (5). A typical graph of MTF is shown in Figure 3.

The modulation of contrast is measured by using the system to image a target such as the USAF target above, or more commonly a sinusoidal (in intensity) target of varying frequency, and measuring the transmitted contrast versus the original on the target. The commonly accepted modulation representing the “limit” of a system’s ability to transfer information is 9%, which is also known as the Rayleigh diffraction limit (5).

Figure 2: USAF 1951 Resolution Test Target

Figure 3: Typical MTF Plot (6)


A final common, related descriptor for image sharpness is the Point Spread Function (PSF), which can be thought of as the spatial domain equivalent of MTF (7). The PSF is the intensity response of the system when it images a point light source at infinity (i.e. perfectly focused). If the system was "perfect", the image would also be a point. However, diffraction and other factors cause the image of the point to be "spread" out, and in fact diffraction will cause intensity "rings" to emanate from the center. This representation is also referred to as the "airy disk". A 3-D plot and 2-D intensity image of the airy disk is shown in Figure 4 (8).

III. Variation in Image Measurements Caused by Varying Image Quality

In imaging particle analysis, the measurements made on the particles are done on a thresholded binary image rather than the original gray-scale image (9). This is done by choosing a gray-scale threshold value and then declaring each pixel as “particle” or “not particle” based upon the actual particle image pixel gray-scale value compared to the threshold. Figure 5 shows two particle images of a 10µm calibration bead, one in focus and the other out of focus. It is important to note that these images have "artificial blur" in this diagram caused by having to upsample the original 72ppi screen image to a print resolution of 300ppi. An “intensity profile” can be generated for each by making a line across the particle (passing through the center) and then plotting distance versus intensity. Figure 6 shows the result of doing this for the two particles in Figure 5.

As can be seen in Table 1, based on information from Figure 6, if both images are thresholded identically at an intensity value of 150, the “sharp” particle would have a diameter of 10.13µm, whereas the “blurry” particle would have a diameter of 10.96µm. Table 1 shows how the diameter for each particle would vary based upon a different threshold value. Note that the ESD varies by a total of 12.86µm between a threshold value of 100 and 200 for the blurry image, whereas the ESD only varies by a total of 1.67µm over the same range.

Figure 4: Airy disk representation of Point Spread Function (PSF)showing 3-D and 2-D intensity plots. (8)

Figure 5: Particle images of 10µm calibrated beads, "sharp" focus (left) and "blurry" focus (right). (NOTE: both images have extra blur

caused by pixel-replicated zoom necessary to display for print).

Threshold Value

Equivalent Spherical Diameter (ESD in µm)

"Sharp" Image "Blurry" Image100 9.33 4.69125 9.72 7.80150 10.13 10.96175 10.49 14.64200 11.00 17.55

Figure 6: "Intensity profile plots" for the two images in Figure 5. Upper plot is for the "sharp" image, lower plot is for the "blurred"

image.

Table 1: ESD value for varying threshold levels on the two particles shown in Figure 5.


Figure 5: Comparison of bead images and corresponding summary statistics from lower peak (left) and upper peak (right). The mean Equivalent Spherical Diameter (ESD) for the in-focus beads was 9.81µm, whereas the mean ESD for the out-of-focus beads was 15.64µm.

IV. Example of the Effect of Image Quality on Particle Measurements

In order to concretely demonstrate how varying image quality affects measurements in imaging particle analysis, a simple experiment was run. Fluid Imaging Technologies FlowCAM® was used to perform the experiment, where NIST traceable calibrated size beads were imaged by the system. The system was set up to use the 10X objective lens (which yields an overall system magnification ≈ 100X), and 10µm diameter beads. For these parameters, the FlowCAM would normally be set up using a 100µm (depth) flow cell in order to keep the particles in sharp focus. However, in this instance, a 300µm (depth) flow cell was used to insure that some of the particles imaged would be out of focus.

One of the many measurements made by the FlowCAM’s VisualSpreadsheet™ software is “edge gradient”. Edge gradient essentially measures the “sharpness” of edges in the image by looking at the slope of the gray scale change on an edge. High edge gradients indicate “sharp” edges, while low edge gradients indicate “fuzzy” edges. If the target is a high-contrast

object, such as the beads in this experiment, then the particles with high edge gradient are seen as being in “sharp focus” whereas the ones with low edge gradient are seen as “blurry”. So the edge gradient measurement can be used to quickly separate high quality (sharp) bead images from low quality (blurry) bead images.

After running the beads through the FlowCAM several times in this configuration, the diameter versus frequency graphs clearly showed a bimodal distribution for size: one peak at 10µm representing the beads in sharp focus, and another (wider) peak centered around 16µm representing the out-of-focus beads.

Using the VisualSpreadsheet software, one can quickly isolate the best quality images from each peak by merely selecting each peak and then sorting based upon edge gradient. Figure 5 shows the results from doing this, and clearly demonstrates the measurement change that occurs when the beads are not in sharp focus. The mean Equivalent Spherical Diameter (ESD) for the in-focus beads was 9.81µm, whereas the mean ESD for the out-of-focus beads was 15.64µm.


One might make the argument that this result is somewhat "rigged", since the FlowCAM's distance calibration was based upon sharply focused beads. However, one only needs to look at the standard deviation and coefficient of variability (CV) for the two data sets to see that the mean is only part of the story. The out-of-focus particles exhibit a significantly higher standard deviation (0.56µm versus 0.14µm) and CV (3.57% versus 1.46%) than do the in-focus particles. To put this in rather succinct (but unscientific) terms:

Fuzzy Images = Fuzzy Measurements

V. How Particle Measurements Affect Particle Classification

As shown in the example above, image quality (in this case specifically, “sharpness”) has a direct relationship to the quality and precision of measurements made on these particles from the images. The efficacy of any type of particle classification, whether value or statistical based (9), is going to be dependent on the quality of the measurements, and therefore directly dependent upon the original image quality produced by the system. In either type of classification, the measurements are used for the basis of characterizing the particle images. So, if we take the above example to its next logical step, we can assume that image quality will directly affect the ability for pattern recognition software to properly classify particles.

To demonstrate this, another experiment was run using the FlowCAM. This time, rather than using beads, we wanted to use a”real world” sample containing non-spherical particles that vary slightly in shape, size, transparency and other attributes. A culture of the phytoplankton species Cosmarium

was used. This species has a fairly distinctive shape as can be seen from the sample images in Figure 7. The average size of these particles is around 50µm, so they are normally run in the FlowCAM using the 4X objective (approximately 40X overall magnification) with a 300µm (depth) flow cell. As before, in order to get particles both in and out of focus, the flow cell used was larger than normal (600µm in depth). After the sample had been run, two image libraries were built by selecting 8 Cosmarium algae images that represented typical “in-focus” images (Figure 7) and 8 that represented

Figure 8: Typical out-of-focus images of Cosmarium algae as captured by the FlowCAM.

Figure 6: Close up view of 2 bead image sets (left), and with binary overlay (right). Note the higher degree of variability,both in size and in shape on the out-of-focus beads (right hand side of each screen shot).

Figure 7: Typical in-focus images of Cosmarium algae as captured by the FlowCAM.


“blurry” images (Figure 8). These library images are then used as the basis for a statistical pattern recognition algorithm (9) whereby each particle in the run is compared statistically against the library particles to determine how closely they “match” the target particles.

Figure 9 shows the overall results for one of the FlowCAM runs made with the Cosmarium algae culture. The left side window shows the summary statistics for the run: 4,500 particle images were collected and stored yielding a mean volume-weighted ESD of 52.91µm and a mean aspect ratio (width/length) of 0.69. The right side window shows a random sampling of the particle images themselves; you can clearly see the variations in shape and size caused both by the organic variation of the species itself and due to the variation in focus through the flow cell depth.

Figure 9: Summary results of FlowCAM run using Cosmarium culture.

Figure 10: Typical images and summary statistics for particles found with the "sharp" image library.

Figure 11: Typical images and summary statistics for particles found with the "blurry" image library.


At this point, the two statistical filters created from the libraries show in Figures 7 and 8 were run against the entire run of data (separately, not at the same time). Figure 10 shows some of the particle images found using the “sharp” library, along with the summary statistics for the filter. Figure 11 shows the same results when using the “blurry” library. Out of the 4,500 original particles, the “sharp” filter found 230 “like” particles representing a concentration of 1,029 particles/ml, whereas the “blurry” filter only found 44 “like” particles representing a concentration of only 197 particles/ml. So, the “sharp” filter found an order of magnitude more particles than the “blurry” filter. This is due to the fact that the “sharp” library has tighter measurements, forming a tighter cluster in the n-dimensional pattern recognition space (9), thereby more specifically defining the shape and gray-scale attributes of the desired particles. The “blurry” library has a much “looser”, more ambiguous cluster to it due to the larger variance in all the measurements.

This particular case shows a very simplistic situation where only a single particle type is present in the sample. In the real world, such as when studying a water sample with multiple algal species present, or a protein sample containing agglomerated proteins, silicone droplets and other foreign matter, the importance of sharp images in the libraries becomes greater. In these applications, the filters will be run at the same time and be mutually exclusive (a particle should not belong to two different “types”). Not only will “blurry” filter images cause undercounting as in the example just shown, but they also will lead to “false positives” and “false negatives” in each class, thereby making the classification less accurate and less repeatable. To further expound on the succinct (but unscientific) conclusion found in section IV:


VI. Conclusions

While “image quality” can sometimes be a rather fleeting concept in the realm of the qualitative (subjective), digital image processing does not suffer from any ambiguity in this arena. This is because digital images are purely mathematical constructs, and thus can be evaluated in mathematical, quantitative terms. Since imaging particle analysis often deals with microscopic particles, it frequently will run into limitations based purely on resolution (1). Even when the particles are within the range that a particular imaging particle analysis system can resolve well, the quality of the image still greatly affects the ability of a system to classify particles of different types (let alone properly measure them!). Through two real-world examples, this paper has shown that image quality, in particular “sharpness”, greatly affects measurement

quality and therefore the system’s ability to properly classify particles of different types. Since the true strength of imaging particle analysis systems over volumetric-based systems (which can only measure particle size) is their ability to differentiate particles based upon shape and gray-scale, image quality is paramount to the value of one of these systems. As previously summarized:


VII. References

1.) "Imaging Particle Analysis: Resolution and Sampling Considerations", Lew Brown, Fluid Imaging Technologies Web Site: http://fluidimaging.com/imaging-particle-analysis-white-papers.aspx

2.) Wikipedia entry on Optical Resolution:http://en.wikipedia.org/wiki/Optical_resolution

3.) Wikipedia entry on Acutance:http://en.wikipedia.org/wiki/Acutance

4.) "Understanding Sharpness", Michael Reichmann, Luminous Landscape Web Site: http://www.luminous-landscape.com/tutorials/sharpness.shtml

5.) "Understanding image sharpness part 1: Introduction to resolution and MTF curves", Norman Koran, tutorial on web site: http://www.normankoren.com/Tutorials/MTF.html

6.) MTF Plot from: http://www.edmundoptics.com/technical-support/optics/modulation-transfer-function/

7.) Wikipedia entry on Point Spread Function: http://en.wikipedia.org/wiki/Point_spread_function

8.) Wikipedia entry on Airy Disk: http://en.wikipedia.org/wiki/Airy_disk

9.) "Particle Image Understanding - A Primer", Lew Brown, Fluid Imaging Technologies Web Site: http://fluidimaging.com/imaging-particle-analysis-white-papers.aspx

http://fluidimaging.com/imaging-particle-analysis-white-papers.aspx

imaging particle analysis: the importance of image quality

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