AUTOMATED COUNTING OF YEAST COLONIES USING

THE FAST RADIAL TRANSFORM ALGORITHM

Jan Schier and Bohumil Kov

Institute of Information Theory and Automation of the ASCR, Pod vod

arenskou v

ı 4

CZ-182 08 Prague 8, Czech Republic

Keywords:

Colony counter, Yeast colonies, Image segmentation, Fast radial transform.

Abstract:

A method for counting yeast colonies in images of Petri dishes, based on the fast radial transform by Loy

and Zelinsky, is introduced and evaluated in the paper. The paper focuses on processing images produced

by a general-purpose imaging setup. The characteristic properties of the images, as produced by the setup

used in the cooperating genetics research laboratory, are described. The performance of the method has been

evaluated with a test set of 245 images. The images, included in this set, typically contained between 10 and

70 colonies per dish, with relative coverage of the dish less than 10% of the area. The average counting error

(missed colonies) on this set was under 4%.

A tool, implementing the method, has been developed in Matlab. The tool provides a batch mode for pro-

cessing of larger image sets prepared beforehand in the darkroom and it automates the process of counting as

much as possible. It is available for download or can be requested from the authors of the paper, in both cases

free on charge.

1 INTRODUCTION

Yeast, namely Saccharomyces cerevisiae, is often

used as a model organism in biological research. This

is mainly due to its many favourable properties, such

as the short generation time, easy genetical manipula-

tion, as well as thanks to its established use in indus-

try.

When performing experiments with S. Cerevisiae

yeast, part of the process is growing the yeast colonies

in Petri dishes, and evaluating the growth parame-

ters, such as the coverage of the dish and the num-

ber of colonies. Traditionally, the colonies have

been counted manually, using either manual colony

counter or a counting raster. Examples of the man-

ual counters are the Colony counter SC6 by Stu-

art (www.stuart-equipment.com) or the EW-14211-02

Hand-Held Electronic Colony Counter from Cole-

Parmer (www.coleparmer.com). However, the hand

counting is considered rather laborious and time-

consuming process, error prone due to the fatigue and

eye-strain of the laboratorian. Also, it does not pro-

vide any ﬁgures on the coverage of the dish or the

radii of the colonies.

There are also a number of automated colony

counters available – it is of interest that such sys-

tem has been described as early as in 1974 (Goss

et al., 1974). Such system usually consists of a single-

purpose chamber with the illumination and camera

system, where the dishes are placed one-by-one, or of

an automated plate-handler, and a computer running

an image-processing program that performs thresh-

olding and segmentation of the image.

While an automated counter is deﬁnitely the

system-of-choice for a commercial lab, in our case,

the requirement was to reuse the imaging equipment

already available in the lab (to achieve a low-cost so-

lution) and to provide an off-line batch processing of a

set of images taken beforehand in the darkroom. Also,

the goal was that the system performs adequately for

typical image variations, as described in the next sec-

tion, with minimum possible manual intervention of

operator. At the same time, it should allow for man-

ual correction of the counting errors (multiple detec-

tions of a single colony or missed colonies). Finally,

it should provide not only the count of colonies, but

also evaluate the total coverage of the dish.

In this paper, we focus on the counting algorithm

used in the system and present the performance data

that we have achieved. The paper is structured in the

following way: in the next section, the characteristics

of typical images are reviewed. Then, the methods for

Schier J. and Ková

r B..

AUTOMATED COUNTING OF YEAST COLONIES USING THE FAST RADIAL TRANSFORM ALGORITHM.

DOI: 10.5220/0003129000220027

In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2011), pages 22-27

ISBN: 978-989-8425-36-2

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

(a) Fluffy and touching colonies, di-

verse radii, dish centered

(b) Smooth colonies, dish touching

edge of image

Figure 1: Examples of typical images of yeast colonies.

detecting round or symmetrical objects are surveyed

in brief and the fast radial transform algorithm is de-

scribed. The paper is concluded by description of the

properties of the test data set and by discussion of the

achieved results.

2 CHARACTERISTICS OF

TYPICAL IMAGES

As has been stated, the requirement on the system de-

scribed in this paper was that it would be able to pro-

cess batches of images taken with a simple general-

purpose imaging system; the laboratory is using a

camera/copy stand with lightning units by Kaiser Fo-

totechnik (see www.kaiser-fototechnik.de). The dishes

are manually placed roughly into the center of the im-

age, on a matt black background. No dish holder or

stopper is used.

Examples of typical images of yeast colonies are

shown in Figure 1.

The images are characterized by the following

properties:

• dark background to increase image contrast

• illumination by two linear lights along the short

edges (this is not important for processing,

though)

Figure 2: Dish image after preprocessing.

• variations of dish position – cf. Figure 1(a) and

1(b)

• varying diameter of the dish in image

• varying intensity of the dish background

The colonies themselves are characterized by differ-

ent types of morphologies (both smooth and ﬂuffy),

different size and/or age and by colonies touching

each other.

3 SYSTEM DESCRIPTION

It follows from the image characteristics that the

counting of colonies includes image thresholding,

dish localization, and the counting itself. The process

can be divided into two basic parts:

• Image Preprocessing – includes the following op-

erations:

– Image quality check: faulty images are elimi-

nated to prevent system hangup

– Image thresholding

– Dish localization

– Dish background thresholding

As a result of preprocessing, we get a centered im-

age of the dish, with eliminated background. An

example of such image is given in Figure 2.

• Colony Counting – includes:

– colony diameter estimation

– colony center estimation

The description of the preprocessing part is out of

the scope of this paper. Interested reader may ﬁnd

some details in technical report (Schier, 2009b). The

method, however, has been simpliﬁed and made more

robust since the publication of this report.

AUTOMATED COUNTING OF YEAST COLONIES USING THE FAST RADIAL TRANSFORM ALGORITHM

3.1 Colony Counting

The simplest approach is to correlate the contour of

the colonies with a circular pattern, assuming that

the maxima of correlation is located at the centers

of colonies. This has been the ﬁrst method we have

tested (Schier, 2009a). During experiments, we have

experienced poor performance in the case of big clus-

ters and sensitivity to mismatch between the radius

of the circular pattern diameter and the radius of the

colony (and, hence, sensitivity to dispersion of colony

radii).

An interesting approach to the counting of bac-

teria colonies has been described in (Marotz et al.,

2001): to ﬁnd colonies, a number of shape and struc-

ture criteria are used on the image pixels, including

e.g. mean object radius, roundness of an object, com-

pactness and asymmetry, radial monotony of fall-off

in intensity, etc. These criteria are combined into

shape and structure quality parameters and evaluated

using fuzzy logic. The method works best under the

assumptions of well-deﬁned circular shape and mono-

tone intensity fall-off of the colonies, which are well

satisﬁed for bacteria (the case treated in the paper),

but not necessarily in our case of the yeast colonies.

A popular method to detect circular objects is the

circular Hough transform (for deﬁnition see e.g. (Bal-

lard and Brown, 2003)). Based on our experiments, if

multiple yeast colonies are overlapping or touching,

it tends to detect (incorrectly) adjacent colonies as a

single object. Also, following the results presented

in (Loy and Zelinsky, 2003), the output of the Hough

transform may be rather noisy.

Another possibility is to use the radial symme-

try-based methods: the radial symmetry transform

has been introduced in the work of Reisfeld (Reis-

feld et al., 1995). Fast radial transform – a modi-

ﬁed version of the radial symmetry transform with

improved computational complexity – has been pre-

sented in (Loy and Zelinsky, 2003). Since this trans-

form is the method that is currently employed in our

tool, it will be reviewed in the next section.

3.1.1 Fast Radial Transform

Fast Radial Transform is a transform that maps the

original image to the transformed image according to

its contribution to radial symmetry of the gradients at

distance n ∈ N (N is the set of radii) away from each

point. For full details of the method see the original

description in the paper of Loy and Zelinsky.

First, image gradient g

i,j

at each point (i, j) is cal-

culated. Then, the positively- and negatively-affected

pixels are determined:. The affected pixel is deﬁned as

the point in the direction of the gradient vector g

i, j

(for the positively-affected ones) or counter the direc-

tion of the gradient vector (for the negatively-affected

ones), at a distance n pixels away from the point at

coordinates (i, j). The coordinates of affected pixels

are given by

(i, j) = (i, j) + round



i, j



−

(i, j) = (i, j) − round



i, j



The gradient matrix g, together with the coordi-

nates of affected pixels, is used to determine the ori-

entation and magnitude projection images O

and M

for the given radius n:

(i, j)) = O

(i, j)) + 1,

−

(i, j)) = O

−

(i, j)) − 1,

(i, j)) = M

(i, j)) + kg

i, j

−

(i, j)) = M

−

(i, j)) − kg

i, j

The radial symmetry at radius n is deﬁned by con-

volution

= F

∗ A

where

(i, j) =

(i, j)



(i, j)|



and

(i, j) =

(

(i, j) i f O

(i, j) < k

otherwise.

is a two-dimensional Gaussian, α is the radial

strictness parameter and k

is a scaling factor used to

normalize M

and O

. Projection images M

and O

are initially set to zero.

An example of a symmetry map for a dish with

yeast colonies is given in Figure 3.

To estimate the colony centers, the transform must

be completed with two additional procedures: esti-

mation of the set of radii N to be tested, and by a

procedure to ﬁnd local maxima (corresponding to the

centers) in the symmetry map S (map S is a weighted

sum of all symmetry maps S

). Both procedures will

be discussed in the following sections.

3.1.2 Colony Radius Estimation

To estimate the range of radii of the objects contained

in the image, the following steps are used:

• the equivalent diameter d and eccentricity ε of all

objects in the image is computed. The diameter

is computed from area A (number of pixels) of an

BIOINFORMATICS 2011 - International Conference on Bioinformatics Models, Methods and Algorithms

(a) Preprocessed image of colonies

(b) Symmetry map S with the centers of

colonies

Figure 3: Illustration of function of the radial symmetry al-

gorithm.

object. The eccentricity equals to the eccentricity

of an ellipse with the same second-moments as the

object. It equals to ε = 0 for a circle and to ε = 1

for a line segment.

• Nearly circular objects (with eccentricity ε < θ

is the eccentricity threshold), are selected.

• Min and max diameter d

min

and d

max

of the ob-

jects in the set of circular objects are determined.

The interval between them is divided to ν equidis-

tant subintervals. The set of radii N for the fast

radial transform is then given by:

∆ = d

max

− d

min

N = {d

min

+ [0,...,ν] · ∆/ν}/2

3.1.3 Estimation of Colony Centers

The centers of the colonies are represented by local

maxima of the symmetry matrix S. To ﬁnd these

maxima, the nonmaxsuppts() function for Matlab

(Kovesi, 2005) is used. It performs grey scale dilation

of the input image and ﬁnds the points in the dilated

image that match the original and that are greater than

the threshold. Finally, it returns the row and column

coordinates of these points.

4 EXPERIMENTS AND RESULTS

To test system recognition performance, it was evalu-

ated using 245 images, containing colonies with dif-

ferent morphology and relative coverage of the dish.

The distribution of the test set in the terms of fre-

quencies of the number of colonies in the dish is

shown in Figure 4. Figure 5 shows the distribution

of relative coverage of the dish and mean diameter of

colonies (marker size) in comparison with the number

of colonies in the dish. It can be seen that the typical

dish contains less than 70 colonies, with relative cov-

erage less than some 10%.

The illustrative counting results for typical images

used in these tests are shown in Figure 6 on the next

page.

10 20 30 40 50 60 70 80 90 100

Occurrences

Number of colonies

Figure 4: Petri dishes with the same number of yeast

colonies.

0 10 20 30 40 50 60 70 80 90 100

Relative area [%]

Number of colonies

Figure 5: Distribution of the test set – relative dish coverage

in comparison with the number of colonies. Diameter of

markers represents mean radius of the colonies in the dish.

4.1 Counting Tool

The algorithms, as described in Section 3, have been

implemented in a counting tool. In the background,

this tool performs fully automatic thresholding of

the image, localization of the dish and counting of

colonies. It provides an environment for selecting the

directory tree with images to process, the ﬁle to store

AUTOMATED COUNTING OF YEAST COLONIES USING THE FAST RADIAL TRANSFORM ALGORITHM

(a) (b)

Figure 6: Examples of algorithm detection and counting re-

sults. Figures (a) - (b) illustrate dishes with high coverage,

the counting results, and the counting mode: in the

semi-automatic mode, a simple point-and-click editor

can be used for manual correction of the output of the

counting algorithm, in the fully-automatic mode, the

output of algorithm is directly stored into the result

ﬁle.

This tool was used also to obtain the reference re-

sults used in this paper: using manual correction, we

obtained the correct counts of colonies in Petri dishes,

which were used to evaluate counting error rates.

4.2 Algorithm Settings

The following settings were used in our experiments:

• Parameters of the fast radial transform:

= 6, α = 4

• Parameters of non-maxima suppression:

threshold = 4, radius = 0.8 · min(N),

where N is the set of radii for the fast radial trans-

form.

• Construction of N:

eccentricity threshold θ

(see Section 3.1.2) is ini-

tially set to θ

= 0.25. The number of equidistant

intervals ν is set to ν = 4. At least ﬁve colonies of

given eccentricity must be in the image, else the

eccentricity is increased by 0.1.

4.3 Typical Detection Errors

Figure 7 illustrates typical detection errors of fast ra-

dial transform. A colony may be missed if it touches

other colony or, rather, multiple colonies, so that they

form a cluster. This detection error is almost absent if

the colonies touch only at one point and thus creates

a structure similar to a chain. If more colonies are

touching each other, they form a structure in which

their shape is distorted and internal colonies cease to

be circular. The circular outer border of colony lo-

cated in such cluster could be too short for the pro-

posed method to work properly.

(a) (b)

Figure 7: Example of typical detection error of fast radial

transform.

The counting errors for various number of

colonies are summarized in the Table 1. The relatively

high counting error for the dishes with the colony

counts greater than 60 is given by two factors. First,

with the increasing number of colonies increases also

the probability that there will be colonies touching

each others (Figure 7a). Second, the number of sam-

ples with this high density of coverage was relatively

low, thus increasing the evaluation error (Figure 4).

Table 1: Dependence of the counting errors on the number

of colonies in the dish. The system average counting error

is under 4%

] colonies samples missed [%] false [%]

0 – 17 21 1.47 0

18 – 20 19 2.99 0

21 – 23 25 3.31 0

24 – 26 29 4.00 0

27 – 29 27 3.28 0

30 – 40 35 4.17 0

41 – 49 30 4.00 0

50 – 60 29 3.87 2.00

> 60 30 5.36 3.22

Figure 8 shows the recognition performance re-

lated to the number of colonies in the dish. A typical

dish used in our experiments contains from 10 to 40

yeast colonies. The ﬁgure also shows the recognition

performance of the fast radial transform for the de-

tection of circular objects. The dishes, where some

colonies have not been detected are shown below the

dashed line.

Another view on the algorithm performance is

provided by Figure 9, which presents a box-whisker

BIOINFORMATICS 2011 - International Conference on Bioinformatics Models, Methods and Algorithms

100

20 40 60 80 100

Number of detected colonies

Number of colonies

Figure 8: Algorithm recognition performance regarding to

number of colonies.

plot of relative counting error (missed colonies) in

several groups of the colony counts. The numbers of

samples in each group are given in the table, included

with this plot.

0-20 20-40 40-60 >60

Missed colonies (normalized) [%]

Number of colonies

# colonies samples

0–20 40

20–40 123

40–60 52

>60 30

Figure 9: Relative number of missed colonies dependent on

the number of colonies.

5 CONCLUSIONS

In the paper, we have presented the method for count-

ing of yeast colonies, based on fast radial transform.

The method has been tested on a set of 245 images

with different degrees of coverage. The distribution

of the data in the test set and the performance of the

counter is discussed. It should be noted that the av-

erage counting error is below 4%. It is difﬁcult to

compare the performance with the commercial solu-

tions, since the performance data of these systems are

not available.

The algorithm has been implemented in a

Matlab-based tool which provides environment

for automatic or semi-automatic processing of

batches of images. This tool has been suc-

cessfully deployed in the cooperating biology

research laboratory and is available for download at

http://zs.utia.cz/index.php?ids=results&id=yeastcolco

unt&lang=enghttp://zs.utia.cz/index.php?ids=results&

id=yeastcolcount&lang=eng.

ACKNOWLEDGEMENTS

This research has been supported from the 1M0567

”Centre for Applied Cybernetics” project of the Min-

istry of Education, Youth and Sports, the Czech Re-

public.

We would like to thank the staff of the Yeast

Colony Group, Department of Genetics and Micro-

biology, Faculty of Sciences, Charles University, who

have introduced us into the problem and provided us

with the sample images from their experiments.

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AUTOMATED COUNTING OF YEAST COLONIES USING THE FAST RADIAL TRANSFORM ALGORITHM