A Quality Pre-processor for Biological Cell

Images

Adele P. Peskin1, Karen Kafadar2, and Alden Dima3

1 NIST, Boulder, CO 80305 2 Dept of Statistics and Physics, Indiana University, Bloomington, IN 47408-3725 3 NIST, Gaithersburg, MD 20899

Abstract. We have developed a method to rapidly test the quality of a

biological image, to identify appropriate segmentation methods that will

render high quality segmentations for cells within that image. The key

contribution is the development of a measure of the clarity of an individual biological cell within an image that can be quickly and directly

used to select a segmentation method during a high content screening

process. This method is based on the gradient of the pixel intensity field

at cell edges and on the distribution of pixel intensities just inside cell

edges. We have developed a technique to synthesize biological cell images

with varying qualities to create standardized images for testing segmentation methods. Differences in quality indices reflect observed differences

in resulting masks of the same cell imaged under a variety of conditions.

1 Introduction

High content screening (HCS) has become a critical method for large scale cell

biology and is often used for drug discovery. HCS is the automation of cell biological investigation using automated microscopes and sample preparation and

includes the acquisition and analysis of cellular images without human intervention. Quantitative fluorescent microscopy plays a key role in HCS as it does in

cell biology in general. Typical HCS-based experiments can involve the analysis

of more than a million cells [1][2][3][4][5].

Image segmentation is the most important part of analyzing biological image

data [4]. Consequently, many segmentation methods have been published, including histogram-based, edge-detection-based, watershed, morphological, and

stochastic techniques [4]. However, segmenting the same image with different

methods can lead to different masks for a given cell, and hence different estimates of cell characteristics (e.g, area, perimeter, etc.). We refer to a mask as

the set of pixels that are used to define an object within an image.

Accurate segmentation is one of the challenges facing high content screening

[5], given the large number of images and consequent impracticalities of human

supervision. Indeed, the handling and analysis of large image sets has been identified as an impediment to the wider use of HCS [4]. Therefore it is important to

This contribution of NIST, an agency of the U.S. government, is not subject to

copyright.

G. Bebis et al. (Eds.): ISVC 2009, Part II, LNCS 5876, pp. 1051–1062, 2009.

c Springer-Verlag Berlin Heidelberg 2009
1052 A.P. Peskin, K. Kafadar, and A. Dima

obtain a predictive, objective and efficient measure of the segmentation quality

resulting from a particular method, on a cell-by-cell basis. Not all cells in the

same image will lead to segmentations with the same accuracy. Certain clinically

relevant cell lines are also known to be particularly difficult to segment, making

the automated analysis of image data unreliable. In one study, the dose response

of morphological features varied significantly between well segmented and poorly

segmented cells taken from high content screening data [6].

The goal of this project is to provide a simple, yet reasonably faithful, measure of the quality of an individual cell in an image, to facilitate the choice of

segmentation method and focus setting for the image. This index is determined

on a cell-by-cell basis, by the characteristics of the edge of each cell, different

from other quality indices proposed previously that describe overall image noise

and distortion ([7] [8] [9] [10]). To define a quality index for each cell, we first

examine a series of images and their ranges in quality, revealing types of features

associated with low/high quality. Section 2 describes the data images considered

in this project. Examination of these images leads to the definition of the quality index in Section 3. We then illustrate in Section 4 our method of creating

synthetic images with a given quality index. While our measure is shown to behave as expected (i.e., poor images associated with low quality indices), a field

study is needed to validate this measure for more general cases. We propose the

investigation of this issue and others in the concluding Section 5.

2 Data Description

We examined 16 sets of fixed cell images prepared by our biological collaborators

at NIST. These images consist of A10 rat smooth vascular muscle cells and 3T3

mouse fibroblasts stained with Texas Red cell body stain [11]. For each set, we

compared six different images for a total of 96 images. Each image comprises

multiple cells. Five of the six images are repeated acquisitions under five sets of

imaging conditions. The first three sets were acquired using three different exposure times with Chroma Technology’s Texas Red filter set (Excitation 555/28,

#32295; dichroic beamsplitter #84000; Emission 630/60, #41834). This filter

is matched to the cell body stain used and allows us to compare the effect of

exposure time on acquired cell images. We used non-optimal filters to reduce intensity signal to noise and introduce blurring: Chroma Technology’s GFP filter

set (Excitation 470/40, #51359; dichroic beamsplitter #84000; Emission 525/50,

#42345).1 The resulting images were blurred in a fashion similiar to the Gaussian

blurring operation found in many image processing systems. These five image

sets were acquired using 2x2 binning in which the output of four CCD image

elements are averaged to produce one image pixel. Binning is typically used to

trade image resolution for acquisition speed and sensitivity [2].

1 Certain trade names are identified in this report in order to specify the experimental

conditions used in obtaining the reported data. Mention of these products in no way

constitutes endorsement of them. Other manufacturers may have products of equal

or superior specifications.
A Quality Pre-processor for Biological Cell Images 1053

Table 1. The five sets of imaging conditions

Image Illumination Exposure Filter type

Level time(s)

1 low 0.015 optimal filter (Texas Red filter set)

2 medium 0.08 optimal filter (Texas Red filter set)

3 high 0.3 optimal filter (Texas Red filter set)

4 low 1.0 non-optimal filter (GFP filter set)

5 medium 5.0 non-optimal filter (GFP filter set)

6 (gold standard)

Fig. 1. Individual pixel intensities are color-coded over the range in each image, to

show differences in edge sharpness. The ground truth mask is shown for comparison.

The sixth image is a higher-resolution 1x1 binned image, using the full image

range to define pixel intensities. We use this image to create a ground truth mask

for each cell, via expert manual segmentation to assure a “gold standard” image.

The five sets of imaging conditions are a combination of filter type (optimal or

non-optimal) and illumination level (low, medium, high), and are given in Table

1. We visualize the quality of each cell by color-coding the pixels. Figure 1

provides a visual rendition of the five conditions for cell number 4 from image

set 1, revealing differences in the implied masks. Cell edges vary widely in clarity

and sharpness. In particular, the images vary in terms of the number of pixel

lengths (distance between pixels) needed to represent the thickness of the edge

of the cells. We will attempt to quantify this feature in the next section.

3 Quality Calculation

For each cell in an image, we look at pixel intensities within an isolated region

containing the cell. We fit this distribution using a 3-component Gaussian mixture via the EM (Expectation-Maximization) algorithm. A 2-component mixture

model, with a cell component and a background component, resulted in estimates

for means, standard deviations, and component fractions significantly different

from the actual data. Thus we reasoned that the edge pixels, whose intensities

span a wide range of pixels, form their own third distribution. The 3-component

model is illustrated in Figure 2 for the second and fifth cells of Figure 1 and better reflects the actual data. We provide the equations for fitting the 3-component

model (described in general terms in [12] [13]) in [14]. As illumination is increased,
1054 A.P. Peskin, K. Kafadar, and A. Dima

Fig. 2. Normalized curves of the 3 components of pixel intensities, as an example, for

the second and fifth cells of Figure 1, background(blue), edge(green), and cell(purple)

the overall range of pixel intensities increases, giving a better separation of the

background and edge peaks. At high illumination, however, the center of the cell

is flooded with light, and the edge distribution is very thin and pushed back towards the background distribution. In the discussion below, xp and sp denote the

estimated mean and standard deviation, respectively, of the intensities from pixels

of type p from the EM algorithm, where p corresponds to B (background pixels),

E (edge pixels), or C (cell interior pixels).

We examined 16 sets of data in detail. For each set of imaging conditions in

Table 1, we find a consistent background distribution. Data for the background

Table 2. Background and Edge values for all low illumination, optimal filter images

Set Cell number Background Background Edge Edge

Mean, xB SD, sB Mean, xE SD, sE

1 1 115 4 141 19

2 5 119 4 193 42

3 2 117 4 178 36

4 1 115 4 188 50

5 2 116 4 238 85

6 1 119 4 195 40

7 1 119 4 202 38

8 2 116 3 131 12

9 1 119 5 152 24

10 1 113 4 156 33

11 1 115 4 141 20

12 1 116 3 158 31

13 1 113 3 152 25

14 1 117 5 190 59

15 1 114 4 178 48

16 1 117 4 171 31

Mean 116 3.94 173 37

SD 0.51 0.14 7.0 4.45

N.B. Pooled sB = 3.98 (mean(sB) = 3.94); pooled sE = 40.87 (mean(sE) = 37.06)
A Quality Pre-processor for Biological Cell Images 1055

mean, xB, and standard deviation, sB, as well as for the edge pixel mean, xE ,

and standard deviation, sE, for each image taken at low illumination with the

optimal filter (set 1 in Table 1), are given in Table 2. There is less variation

in the background than the edge distributions. A single cell chosen from each

image provides the data for Table 2, using the first cell of each image unless a

particular cell in the image was used consistently in another part of this analysis.

For each pixel intensity between xB and xE (i.e., between the mean of the

background distribution and the mean of the edge distribution), we also calculate

an average value for the magnitude of the gradient at that intensity. We look at

the gridded data within a bounding box on the image that contains a single cell.

At each pixel location, pij , with pixel intensity, Iij , we find a local derivative

of that intensity and its magnitude, using a Sobel mask. In the i direction, a

numerical estimate for the directional derivative at each pij is:

∂I/∂i|pij = [2 · I(i+1)j − 2 · I(i−1)j + I(i+1)(j−1) − I(i−1)(j−1)

+ I(i+1)(j+1) − I(i−1)(j+1)]/8. (1)

In the j direction, we find the numerical estimate at each pij :

∂I/∂j|pij = [2 · Ii(j+1) − 2 · Ii(j−1) + I(i−1)(j+1) − I(i−1)(j−1)

+ I(i+1)(j+1) − I(i+1)(j−1)]/8. (2)

The total derivative gives the magnitude of the gradient of the intensity at pij ,

which we denote by g(i, j):

g(i, j) ≡ dI(i, j) = 

(∂I/∂i)2|pij + (∂I/∂j)2|pij . (3)

We find a gradient magnitude value g(i, j) at each location pij . The average

value of the gradient magnitude at those locations where the measured intensity

level is a given value, say I∗, is given by:

G(I∗) = ave{g(i, j) : I(i, j) = I∗}. (4)

If, for example, a particular intensity value, Iv, occurs 3 times within the bounding box, at positions pab, pcd, and pef , the average magnitude of the gradient at

intensity = Iv is:

G(Iν ) ≡ Gv = (gab + gcd + gef )/3. (5)

We will refer to this average gradient function as G(I), where I is an intensity

in the region of the edge. We use G(I) as a way of smoothing this otherwise

noisy estimate of the gradient curve. Values of I near the edge likely lie between

xB and xE + 2sE. We denote by A the intensity for which G(I) is largest for

xB ≤ I ≤ xE; i.e., A = argmaxxB≤I≤xE G(I). In Figure 3, we show the locations

of the pixels, pij , whose intensities are equal to Intensity A. We see that these

pixels lie within one or two pixel lengths of the apparent edge of the cell, which we

see in accompanying images of more detailed contouring of the pixel intensities.
1056 A.P. Peskin, K. Kafadar, and A. Dima

Fig. 3. Cell 2, set 1, imaging conditions 1-5: pixel intensities above Intensity A are

red, Intensity A (+/- 1 unit), green, and below A, blue. Green pixels fall close to the

apparent cell edge. Below, each cell is color-coded in 40 equally-spaced pixel ranges.

The average gradient magnitude curve, G(I) vs. intensity I, reflects two cell

characteristics. The initial slope of the curve directly indicates the sharpness of

the edge: the steeper the slope, the sharper the edge. The shape of this curve

also indicates a feature of the cell edges. For very sharp edges, the average

gradient magnitude increases monotonically across the range from the mean of

the background, xB, to the mean of the edge distribution, xE, as is seen for all

high illumination images (type 3 in Table 1; rightmost curve in Fig 4a). For the

low and medium illumination images, the gradient increases from xB, reaches

a maximum, and then falls. The graphs for the gradient magnitude for cell 5,

image set 2, under low, medium, and high illumination with the optimal filter

are shown in Figure 4a, and for low illumination for both filters in Figure 4b.

For the type 3, high illumination images, the gradient magnitude continually

increases between xB and xE , so we set the maximum gradient value in this

region, Intensity A, to be the magnitude of the gradient at xE . The edge distribution is very close to the background distribution for these images, and we do

not expect a rise and fall in the plot of the gradient magnitude within this small

part of the curve (see the purple curve of Figure 4).

Fig. 4. Cell 5, set 2: a.)Averaged magnitudes of the pixel gradient for imaging conditions 1(red), 2(blue), 3(purple); b.)for imaging conditions 1(red), 4(blue)
A Quality Pre-processor for Biological Cell Images 1057

Fig. 5. The mask for cell 5 of set 2, and enlarged pictures of the lower right hand

marked section, in order of decreasing quality index, imaging conditions 3,2,1,5,4

We measure the quality of an image in terms of an index that measures how

rapidly the pixel intensities fall from the intensity at the maximum gradient at

the edge (Intensity A) to the background mean value (xB). In particular, we

calculate the expected fraction of this range that should lie on the image within

two physical pixel lengths of intensity A = argmaxxB≤I≤xE G(I).

Consider the set of images from cell 5 in set 2, which yielded the gradient

curves in Figure 4. The intensity range between xB and Intensity A is divided

into 10 equal-pixel-length ranges, and each range is displayed in Figure 5, enlarged pictures of the lower right corner of each of the five images in the region

containing the cell pseudopodia. This example is chosen because the pseudopodia

are connected to the rest of the cell over a very narrow region, of approximately

the same size as the boundary edge region we use to define the quality measure.

From the magnitude of the gradient, we calculate the expected fraction of the

cell edge that lies within two pixel lengths of the maximum gradient at the edge.

We use the following sequence of steps:

1. Find the 3-component pixel intensity distribution; denote means of the components by xB, xE , xC .

2. Find the average gradient magnitude at each intensity between xB and xE .

3. Smooth the gradient in this region to fill in any gaps, and denote the resulting

function by G(Intensity).

4. Find the intensity, Intensity A, at which the smoothed gradient magnitude

is maximized.

5. G(A) represents the maximum change in intensity among the edge pixels:

find Intensity B, the intensity that is expected at one pixel unit away from

A; i.e., B = A − G(A)·(1 pixel unit).

6. Find Intensity C, the intensity expected at one pixel unit away from B; i.e.,

C = B − G(B)·(1 pixel unit)

7. Compute the quality index as QI = (A - C)/(A - xB).

We perform the above calculations for the five different images of cell 5, image

set 2. The results of each of the steps are given in Table 3. The quality index

appears to describe how well the very thinnest geometry of the cell, the place

where the pseudopodia are attached, appears in the image. For the optimal filter

images, increasing the illumination increases the range of pixel intensities in the

image, separating the background and edge distributions from each other and

from the pixel intensity distribution that represents the cell and its pseudopodia.
1058 A.P. Peskin, K. Kafadar, and A. Dima

Table 3. Quality calculation for cell 5 of image set 2 for the five test images

Type xB A G(A) B G(B) C Quality

1 119 146 16.06 130 7.91 122 0.852

2 165 319 109.13 210 45.23 165 1.000

3 321 799 480.50 319 5.38 314 1.015

4 192 222 7.87 215 7.02 208 0.467

5 524 692 39.92 653 33.67 620 0.429

The sharper the edge, the higher the quality index. The thin connection (2 to 3

pixel lengths) between the main part of the cell and the pseudopodia is clearly

seen for the medium and high illumination figures, and pixel intensities between

the two parts of the pseudopodia decrease to levels near xB. For the images taken

with the non-optimal filter, the connection between the main part of the cell and

the pseudopodia is lost in the images, and the pixel intensities between the two

parts of the pseudopodia do not approach xB. It is clear from these figures that

the decrease in pixel intensity between the inside of the cell and the background

covers much more than two pixel lengths. In the medium illumination, nonoptimal filter image, type 5, much less noise appears than in the corresponding

low illumination image, type 4, but the edge of the cell covers, on average, about

4 to 5 pixel lengths, so no connection appears between the lower portion of the

pseudopodia and the main portion of the cell.

4 Data Creation

To compare cell segmentation techniques with one another, we use the quality

index we defined above to create sets of test images over a specified range of

qualities. We assume that a given segmentation method will have some quality

range over which the segmentation provides a given measure of accuracy. A

quality index permits a quick assessment of the accuracy of the cell area from

a particular segmentation method. To illustrate the creation of sets of synthetic

cells with a specified range of qualities, we describe and show a set created from

a ground truth mask of one of the cells in the 16 sets described above, cell 2

from set 10.

The five images of the cell of interest from that set have qualities equal to

0.842, 0.910, 1.137, 0.563, and 0.636. The images of those cells are shown in

Figure 6. To test our method, we will construct a cell with pixel distributions

and gradients that correspond with the second image, and compare its quality

index to the index for that cell, 0.910. We now construct the new cell from

the mask, such that its distribution has three components whose means and

standard deviations agree with those of the original cell. Then we use the other

characteristics of that cell, namely the intensity of maximum gradient at the edge

and the cell quality, to compare with the new cell to ensure a match between the

set values and the calculated values on the synthetic image. To begin, we read

in the mask from Figure 6, and assign each pixel of the new image to be either
A Quality Pre-processor for Biological Cell Images 1059

Fig. 6. The five different images of the cell whose mask is used for the cell synthesis

and the corresponding mask

on the cell boundary, inside, or outside of the cell based on the mask. We build

our cell edge starting from those pixels at the edge of the mask.

We assemble a pixel distribution for the new cell using the three components

of the original cell. For cell 2 of image 10, the type 2 image, xB, xE, and xC

respectively are 132, 225, and 826, and the sB, sE, and sC values are 5, 80, and

817. The fractional components are 0.800, 0.103, and 0.096. We calculate the

expected number of pixels at each intensity by adding the contributions of each

component at each intensity. If the total number of pixels in this region is T,

then the expected number of pixels with intensity I is:

pE = 0.800T ; pB = 0.103T ; pC = 0.096T ; (6)

#pixels(I) = pBφ(I; xB , sB) + pEφ(I; xE , sE) + pC φ(I; xC , sC), (7)

where φ(I; μ, σ) denotes the Gaussian density function with mean μ and standard

deviation σ at a particular value of the intensity, I. For each pixel intensity, we

compute the difference between the raw data and the data computed from the

3-component distribution above to determine the standard deviation in the raw

data. We compute the standard deviation over different pixel intensity ranges.

We collect two sets of pixel intensities from the 3-component distribution. One

set contains intensities at or below Intensity A, the intensity where the gradient

is maximized. One set lies above Intensity A. We modify each pixel intensity by

changing it to its Gaussian variate determined by N(xp,s2

p), where p corresponds

to B (background), E (edge), or C (cell interior) pixels. The pixels in the first

set are placed outside of the mask according to their distances from the edge of

the mask. The pixels in the second set are placed inside of the mask in the same

way. Figure 7b shows the resulting new cell alongside the original cell, 7a, from

which it is made. We then test the new image by recalculating the 3-component

analysis, pixel intensity gradient, and quality to ensure that it retained the same

features. The 3-component analysis is only slightly different, as would be expected

by imposing random noise: xB = 134, xE = 214, and xC = 770. The intensity of

maximum gradient at the edge occurs at Intensity A = 181, and the quality is

0.915. The new cell has the same basic features as the original.

Now we can change some of the characteristics of this synthetic cell and monitor the corresponding change in quality. First, we create a set of cells in the

same way as the cell above, but change the standard deviation of the background
1060 A.P. Peskin, K. Kafadar, and A. Dima

Fig. 7. a.) The original cell imaged with medium illumination, optimal filter. b.) Synthesized cell of the same type as (a), made as a test case. c,d.) Two cells identical except

for the spread of the background pixels: standard deviations are 10 and 12 compared

to original 5. e,f) Two cells identical except that the edge distribution has been shifted

from a mean of 225 to a mean of 215 and 205.

Fig. 8. Original cell imaged with medium illumination, non-optimal filter; cell synthesized with the same characteristics, starting from the ground truth mask

peak. The original background peak has a standard deviation of 5, and we create

two new cells with backgrounds of mean xB = 132 as before, but with standard

deviations, sB equal to 10 and 12 instead of 5 (see Figure 7c,d). The quality

indices of these new cells change from 0.910 to 0.766 and 0.667, respectively.

Next we modify the edge distribution without changing the magnitude of the

pixel intensity gradient. We shift the value of xE from its original value of 225

to either 215 or 205, so that the modified edge distribution overlaps more closely

with the background distribution. The results for these two examples are shown

in Figure 7e,f. The image qualities for these two examples change from 0.910 to

0.878 and 0.825, respectively. As one would expect, the quality index decreases

as the overlap between the background and edge distributions increases.

We can use these techniques to look at the effect of using a less optimal filter

for cell imaging. We focus on the type 5 images from Table 1 of this same cell.

If we try to reconstruct this cell, using the original cell’s 3-component mean

and standard deviation values, the same pixel gradient, and the same value

of pixel intensity for the maximum gradient at the cell edge, we create a cell

with basically the same quality as the original cell (0.59 compared with 0.58

for the original), but a different shape, shown in Figure 8. Clearly the precise

shape of the cell is influenced by the optical effects introduced with different

filter sets, leading to different segmentation results, and hence the masks for the

two cells in Figure 8 will be different. Thus this index appears to describe only

the clarity of the cell edge, which will differ from the true mask as the quality

decreases.
A Quality Pre-processor for Biological Cell Images 1061

5 Conclusions and Future Work

The features of a biological cell image are complex. The accuracy of a cell segmentation by any given method can depend on many different factors: the magnitude

of the pixel gradient at the cell edges, the background pixel intensity distribution: the overlap between the background pixel intensity distribution and the

edge pixel intensity distribution, and spreads in these distributions. It can also

depend upon other geometric features of a cell, such as roundness of the cell and

jaggedness of the edges of the cell.

The goal of this quality index is to provide an indication of the segmentation

method that should be used to yield the highest accuracy in derived cell quantities (e.g., area, perimeter, etc.). Ideally, we would like to be able to distinguish

between those segmentation methods that over- or under-estimate cell area from

those that provide unbiased estimates of cell area, based on the quality of the

edge of the cell. Because our quality index as defined here measures only edge

clarity, we may need to modify it to better capture cell image features. Our future work includes a more thorough investigation of the properties of this quality

index, particularly its relation to accuracy of cell area. We plan to create sets of

images with a very wide range of quality indices and cell geometries, to use as

test images for a wide variety of segmentation methods. From them we hope to

use this quality index (possibly modified) to choose segmentation techniques for

very rapid analysis of large numbers of biological images.

Acknowledgements

Kafadar’s support from Army Research Office Grant Number W911NF-05-1-

0490 awarded to University of Colorado-Denver, and National Science Foundation Grant Number DMS 0802295 awarded to Indiana University is gratefully

acknowledged. James Filliben of NIST’s Statistical Engineering Division and

John Elliott of NIST’s Biochemical Science Division (BSD) designed the experiment that John performed to produce the cell images used in this study. Anne

Plant and Michael Halter, of BSD, provided helpful discussion and input.

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