determination of the _lamentous cyanobacteria planktothrix

7/27/2019 Determination of the _lamentous Cyanobacteria Planktothrix

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JournalofMicrobiologicalELSEVIER Journal of Microbiological Methods 26 (1996) 11-20 Methods

Measurement of filamentous cyanobacteria by image analysisAnthony E. Walsby*, Avril Avery

School of Biol ogical Sciences, Uni versit y of Bristol , Woodland Road, Bristol , BSS IU G, UKReceived 8 June 1995; accepted 5 October 1995

AbstractA method of image analysis is described for measuring total filament lengths of cyanobacteria collected on membrane

filters from samples of natural populations or cultures. Images of autofluorescent filaments viewed by epifluorescencemicroscopy were transferred to a computer screen by using a high resolution television camera and an image integrator toenhance sensitivity. The digitised images, saved as 0.4 Mbyte bitmap computer files, were analysed with an image analysisprogram. An evaluation is made of procedures for determining the total length of filaments from the detected area orperimeter of their skeletonised images. Methods are described for correcting errors arising from the orientation, crossing andoverlapping of filaments.Keywords: Image analysis; Cyanobacteria; Filaments

1. IntroductionLight microscopy provides a means of distinguish-

ing and enumerating different microorganisms innatural populations. The biomass of unicellular or-ganisms can be estimated by counting and measure-ments of cell volume but there are problems inapplying these methods to filamentous organisms,which exhibit large variations in length. It is difficultto measure the lengths of filaments directly withmicroscope graticules because the filaments are oftencurved and oriented at all angles. Olson [l] describeda method of estimating filament length that is basedon the number (11) of intersections that filamentsmake with an overlying grid: the filament length isgiven by nid4, where i is the mesh interval on thegrid. The method assumes that filaments are random-

*Corresponding author.

ly oriented, so that all angles are equally representedin large samples. Olsons method has been usedquite widely for measuring the filament length ofalgae and cyanobacteria in cultures [2-41 or naturalpopulations [5,6] and its application to such systemshas been checked empirically by Bott and Brock [7].

Another method based on a grid was described byBailey-Watts and Kirika [S] who emphasized that thesize of the grid squares should be small in relation tothe length of the image of the filament. This require-ment is fulfilled by using video images, whichcomprise a fine grid of pixels that can be analysed bycomputer. Sheath et al. [9] described a system thatinvolved making measurements on video-imagesfrom photographs of individual filaments of Bat-rachospermum sp. with the cursor of a digitisingtablet (see also [lo]). Hoogveld and Moed [l l] useda computer to determine the lengths of individualfilaments of Oscillatoria sp. traced with the image ofa cursor on a digitising tablet projected with a

0167-7012/96/$15.00 0 1996 Elsevier Science B.V. All rights reservedPII SO167-7012(96)00816-O


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12 A.E. Walsby, A. Avery I Journal of Microbiological Methods 26 (1996) 11-20drawing tube into the image plane of the microscope.Each of these methods requires manual interaction ofthe cursor with the images of individual filaments;this impairs the precision and limits the speed withwhich images can be analysed.

We describe an automated method of determiningfilament length by computer image analysis. Itentails transferring microscope images of filamentarrays from a video camera to a computer with aframegrabber system. The system incorporates anintegrator that increases image brightness and con-trast; this obviates the need to use intermediatephotographic images even when analysing faintobjects illuminated by epifluorescence. The positionsof filaments are located with a computer softwaresystem that distinguishes lines of pixels withinselected grey levels. Images of spurious objects canbe eliminated by editing functions. The lengths offilaments can then be determined from measurementsmade on the selected arrays of pixels, but to do thisit is necessary to understand the principles andpotential errors of the image analysis system.

This method is much faster than previous methodsand more accurate than Olsons grid intersectionmethod. We have used it for determining the totallength of Anabaena filaments from cultures andOscillutoriu filaments in samples of known volumesof lake water. We used an epifluorescence micro-scope system in which cyanobacteria fluorescedstrongly, so that these organisms could be distin-guished in the presence of other algae, which auto-fluoresce only weakly. The method can be applied toother phytoplankton by rendering them fluorescentwith primuline yellow [12] or used with bright fieldillumination.

2. Materials and methods2.1. Cultures

Cultures of cyanobacteria were grown in in-cubators at 20C under a photon irradiance of 20pm01 me2 s-. Filament length analyses were madeof the undifferentiated filaments of Oscillutoriurubescens BC 9303 and the heterocystous filaments

of Anubuena Jlos-uquue CCAP strain(PCC 9332).2.2. Filtration

1403f 13f

Samples of cultures and of lake water were filteredwith cellulose acetate membrane filters (which re-main flat on drying) of pore size 8 pm and 50 mmdiameter (Filter AE 99, Schleicher and Schuell). Themembrane filters were air dried overnight and thenwrapped in aluminium foil envelopes. Filamentswere fragmented if subjected to undue contactpressure but they were undamaged by contact withthe foil and during storage over several years.Because some of the light fluoresced by filaments isreflected from white membrane filters, producinghalos around the filament images, black-stainedfilters are recommended for epifluorescence micro-scopy [ 13,141. The halos are easily removed, how-ever, from the saved images by procedures of imageenhancement and adjustment of grey-level thres-holds, and they caused no problem in subsequentimage analysis.2.3. Epijkorescence microscopy, video camera andintegrator

Membrane filters containing cyanobacterial fila-ments were observed under epifluorescent illumina-tion with a Leitz Orthoplan microscope using a 2.5Xobjective. The filaments were illuminated through aPloemopak M2 filter block, which allowed an excita-tion beam of wavelength 546 nm through the bandpass filter and a fluorescent beam of wavelength>580 nm through the reflection short pass filter.

A Cohu high performance CCD camera mountedon the camera column of the microscope wasconnected via a Synoptics integration circuit to aDell 486 PC with 8 MB RAM (66 Mhz 486 DX2CPU) and 430 Mb hard drive. The 768 X 512 pixel256 grey level images were displayed on a section ofa Sony SVGA 1024 X 768 pixel 17 monitor. Thebrightness of the image was enhanced using theintegrator until filaments appeared as white linesagainst a dark ground (Fig. 1). The image wascaptured with a Synoptics (Cambridge Science Park)Synapse Grabber, version 1.3, and stored as a 0.39


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A.E. Walsby, . Av ery Journal of M i crobiol ogical ethods 6 (1996) 11-20

Fig. 1. Micrograph of a region of a filter sh owing the distribution of fluorescent filaments.

Mbyte BMP (bitmap) computer file. Images wereobtained from at li:ast 5 different fields across thediameter of each membrane filter.

3.

2.4. Anal ysing the images 4.2.4.1. Measuring tot al fi lament l ength

The recalled images were subsequently analysedwith PC-Image for VGA and Windows software,version 1.3 (Foster Findlay Associates, Newcastle).The images were edited and analysed with steps l-7of the following procedure using program commandsfrom pull-down menus. (Similar commands are used

5.

other image analysis software).

The image was inverted to display the fluorescentfilaments as dark lines against a light background(Process; Look up tables; Invert ).The contrast of the image was enhanced (Process;Convolutions; Sharpen; Gaussian smoothing).

6.

7.

The images of filaments, comprising pixels withincertain grey-level limits, were selected and high-lighted in blue (Process; Threshold, maximumand minimum limits selected).The highlighted lines over the filaments werethinned to single rows of pixels (Binari es; M or-phological; Skeleton) and then thickened to 3-pixel widths to render them more visible forsubsequent editing (Mor phological; Thi cken).The highlighting on spurious objects was re-moved (Binaries; Binary editor; Erase). Regionsof filaments below the threshold were highlightedby drawing with the cursor (Binary Editor;Draw). Where filaments overlapped, additionallines were drawn parallel to the overlap.The highlighted lines over the filaments wereagain thinned to single rows of pixels (Binaries;M orphol ogical; Skeleton).The total length, in pixels, of each of the high-lighted filament images was measured and thensummed (M easures; M easure al l ). The PC-Image


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14 A.E. Wal sby, A. Avery I Journal of Mi crobiological M ethods 26 (1996) II -20

software calculates several parameters for eachseparate highlighted object; for our procedureDetected area and Perimeter were selected (Mea-sures; Data Analysis; Classify Objects, Statisticson Data; select Detected area, Perimeter).

Once established, the above procedures wereautomated by recording them to the Windows 3.1Macro recorder; the program then operated throughthe 7 consecutive steps with pauses only after step 3(to adjust the threshold) and step 5 (to edit theimage).2.4.2. Enumerating and measuring lengths ofindividual jilamentsThe numbers and dimensions (Detected areas,Perimeters, etc.) of individual filaments can beretrieved from the data file established at the last step(7) of the image analysis procedure, and copied to aMicrosoft Excel spreadsheet, for data analysis, but itis important for these purposes to modify the pro-cedure in the following way.

1. A microscope objective should be chosen thatgives a field of view exceeding the length of thelongest filaments.

2. Low concentrations should be used to reduce thenumber of touching filaments.

3. The highlighting on filaments contacting the edgeof the screen should be eliminated (Measures;Remove edge objects) after step 3 above.

4. The highlighting on touching filaments (treated assingle objects) should be eliminated (step 5above) and the length of the remaining separatefilaments analysed (step 7).

5. The analysis should then be repeated, makingindividual measurements (Measures; Measureobject) on each of the touching filaments aftererasing connections to neighbouring filaments.

2.5. Calibrating the imagesThe dimensions represented by a pixel were

determined by calibration with the images of a stagemicrometer, oriented parallel to the horizontal (X)and vertical (Y) axes of the screen, using the samemicroscope objective. Pixels are approximately

square; in our system the average dimensions repre-sented p, = 2.60 pm and p,, = 2.65 pm (a differ-ence of


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A.E. Walsby, A. Avery / Journal of Microbiological Methods 26 (1996) 11-20 15

cyanobacteria; their images were eliminated from thecomputer image by setting the upper grey-levelthreshold at an intermediate value (usually between90 and 160, depending on the image brightness).3.2. Determining filament length

The length of a filament can be calculated fromthe highlighted array of pixels (the Object) in theimage. The PC-Image software contains facilitiesthat will calculate a number of parameters from thenumber and arrangement of the pixels, but none thatwill calculate length directly. (A facility namedLength is inappropriate as it measures the maximumchord length, e.g. the major axis of an ellipse or aC-shaped line). We describe the use of Detected areaand Perimeter for measuring filament length, andcomplications that arise in each case.3.3. Detected area method

The Skeleton function in Binary Editor is used toerode the highlighmd band of pixels over a filamentto a single unbroken line of pixels. If each pixel is a

square of side p, the area of a straight line of npixels oriented either in a row on the X axis or in acolumn on the Y axis is rips, and the length is1 = np,. The length of a line oriented at an angle, 19,between 0 and n/4 radians (4.5) to the X or Y axis,is1, = np,lcos0 (1)

The value of 1 /cos6 varies from 1.0 (at 13 = 0) tod2 = 1.414 (at 8 = r/4). This error is illustrated inFig. 2, which shows the lengths of straight lines of 1pixel width drawn (by using the facility Binaryeditor, Draw segment) at different angles across theimage of a 360 protractor. The measured pixel areasof these lines showed a minimum at angles of 7r/4(45) from the X or Y axes; multiplying the pixelareas by 1 lcos8 gave corrected line lengths that wereall within 2% of the mean diameter of the circle (Fig.2). (An additional minor correction for pixelasymmetry, described below, is also included in Fig.2). For a large array of lines oriented at all angles theaverage correction is therefore obtained by integra-tion,

450

50c0 15 30 45 60 75 90 105 120 135 150 165 180

Angle I degreesFig. 2. Estimates of the length of images of lines of approximately the same length drawn at different angles (0) and skeletonised to files of1 pixel width from measurements made by: (m) Perimeterl2; (A) Detected area/p; and (0) Detected area/p co& (see text for precisedetails).


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16 A.E. Walsby, A. Avery I Journal of Microbiological Methods 26 (1996) 11-209714

r = (4/%-) I 1 /cost d0= (4/r) ;-lntan(7r/X), = 1.1222 (2)This factor of 1.1222 can be used to provide an

average correction term for randomly oriented arraysof filaments. In theory applying this correction couldcause errors of between + 0.1222 (all lines horizontalor vertical) and -0.2920 (all lines at 45). Inpractice, the lines are usually oriented at a range ofangles and the errors are much less (see Fig. 3).3.3.1. A minor correction for pixel asymmetry 3.4. Perimeter method

Because the pixels are not exactly square, thelength of a straight line of n pixels oriented in a rowon the X axis is I, = np,, and that in a column onthe Y axis is 1, = np,. A straight line of n pixels atan angle 13 between 0 and tan-(p,/p,) (= 45.5 inour system) to the X axis crosses n columns of pixelsand therefore has a length of np,lcostY; a line atgreater angles (between 45.5 and 90) has a lengthof np,lsint? These additional corrections were usedin calculating the line lengths from measurements ofDetected area in Fig. 2.

An alternative method of determining total fila-ment length is to use the facility Perimeter, whichdetermines the length of the edge of a highlightedobject. The software in PC-Image calculates thelength of a smoothed line along the edge. Measure-ments made on diameters drawn on a circle atdifferent angles indicate that the mean error of thecalculation is only 0.65% for lines over all angles,with the greatest error being 1.1% for lines at anglesof 10 from the vertical or horizontal axes (see Fig.2). The length of the skeletonised line is half theperimeter; the measurement needs no additionalcorrection for orientation and in this respect ispreferable to the Detected area method. (In systemsthat do not provide this smoothing facility a correc-tion must be applied; see below).

/

y=o.976&Rz=0.998

old0 locm 2oc4 3GQo 4cm 5ooo 6ocu 7!mdetected are a x 1.1222 I pixels

Fig. 3. Comparison of measurements made of the length ofOscillatoria filaments by Perimeterl2, corrected by addition of0.619 for each filament end, and Detected area/p (multiplied by1.1222, the average value of 1 /cost?, to correct for angle oforientation).

This type of correction cannot be automated formaking measurements on an array of lines by theDetected area method. Measurements are thereforebased on the geometric mean value, p = (pxpy)o.5,which in our system would generate an error with amaximum of 1% (all lines vertical and/or horizontal)and usually much less.

In summary, to calculate the total line length, thetotal detected area of the skeletonised objects isdivided by the geometric mean of p, and pY andmultiplied by 1.1222. Corrections for overlappinglines are discussed below.

The Perimeter method incurs a problem, however,when crossing filaments enclose islands of space: thepixel edges bordering the enclosed space are notmeasured. The solution is to erase a highlighted pixelin one of the bordering lines. The number of pixelslost in the erasures (given by the difference inDetected area before and after the erasures) shouldbe noted and added to the final perimeter value.

In practice there is an upper limit to the maximumfilament concentration that can be analysed by thePerimeter method. It is difficult to keep track ofmore than 30 erasures and the smaller enclosedspaces that occur at high concentrations are easilyoverlooked. We investigated the relationship betweenthe number of enclosed spaces and total filamentlength: the numbers were negligible at concentrationsbelow 3000 pixels (= 9 mm) per image, but rose


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400

300

200

100

00 5000 10000 15000

total filament length / pixels20000 25000

Fig. 4. The relation between number of filament (line) intersections (m) and the number of islands of space isolated by filaments (0) inrelation to the total filament length (number of pixels) on the screen. The formula of the line for the curve (n = n + [nl 1005].75 + [nl10 000]5 ) can be used to correct for the pixels counted only once at the intersections.

steeply to about 60 at total filament lengths of 15 000pixels (= 45 mm), and to 300 at lengths of 25 000pixels (= 75 mm) (Fig. 4).

3.4.1. An average correction for unsmoothedPerimeter methods

In some image analysis systems the length ofpixels at the edge of an object may be measuredeither as length p or pd2/2, depending on whetherthey contact the edge or the corner of the nextadjacent pixel. These give exact lengths of lines thatare horizontal, vertical or at 45 (or, more precisely,at tan- (p,/p,), ,45.5 in our system), but giveoverestimates at other angles. Consider an image of astraight line of length z at an angle 8 to thehorizontal rows of pixels. The skeletonised file ofpixels will cross y rows and x columns of pixels inwhich$ = x2 + y2 (3)y = xtant? (4)

The skeletonised line will contain y pixels thatmake comer contacts to pixels in the next row and(x - y) pixels that make straight contacts. Ignoringthe end pixels, the total length of the line wouldtherefore be calculated by Perimeter12 asI = yV2 + (X - y)l = x + y(V2 - 1) (5)Substituting from Eq. (4), the calculated length is1 = x + Man&2 - 1) (6)while the true length, from Eq. (3) and Eq. (4), isz = (x2 + (xtanf9)2)05 (7)

Putting x = 1, the relative difference (A) betweenI and z is calculated asA = (2 -2)/z

= [l + tan@2 - 1) - (1 + tan20)0.5]l(1+ tan26))0.5 (8)The value of A rises from 0 (at 0) to a maximum


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18 A.E. Walsby, A. Aveq I Journal of Microbiological Methods 26 (1996) I1 -20

of 0.0824 at r/8 radians (22.5) and then falls backto 0 at 7~14 (45). The user is advised to check thesystem by comparing the length of images of a scaleline (e.g. a stage graticule) oriented at differentangles by the perimeter method. If the line at 22.5 isabout 8% longer, then a correction should be applied.The average overestimate for lines at all angles isgiven by integration of Eq. (8) between angles of 0and ~14 (45).

7rl4

d = f i {[1 + tan&2 - 1)0

- (1 + tan20)0-5]l(1 + tan28)0.5}dB= 0.0548 (9)In such systems the values given by Perimeter12

should therefore be corrected by multiplying by l/1.0548 = 0.948.

3.5. Comparison of the Detected area andPerimeter methods

For straight lines of 1 pixel width drawn parallelto either the X or Y axes the measurement given bythe Perimeter-12 was always 1.382 pixels less thanthe measurement given by Detected area, i.e. theterminal pixels are each measured as (2 - 1.382) =0.618 pixels by Perimeter. For straight lines drawn

at other angles we found that the measurement givenby Perimeter-12 agreed closely with that given byDetected area/co@ when the small correction de-scribed above for the difference in p, and py wasapplied (see Fig. 2).

We also compared measurements, by the twomethods, of filament lengths from 20 images ofOscillatoria rubescens filaments in which the totalfilament length ranged between 150 and 7000 pixels(= 0.4 and 18 mm). The measurement of Perimeter/2 was corrected by addition of 1.382012 where D isthe number of ends; Detected area was multiplied by1.1222, the correction for angle. The Detected areamethod gave measurements that were on average2.4% higher than the Perimeter method (Fig. 3). Athigher filament concentrations the discrepancy in-creased, probably due to the difficulty in locatingenclosed spaces.

In summary, the Detected area method is prefer-able to the Perimeter method as it requires no editingof bordering lines and is unaffected by errors associ-ated with this at higher filament concentrations.3.6. Crossing, overlapping and touching jilaments

If two filaments intersect, the total length of theskeletonised lines is underestimated by I pixel. Theproportion of intersections rises with the line density(in theory as a function of n2). An analysis of 33fields, containing skeletonised images of Oscillatoriarubescens filaments, indicated that the error rosefrom


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A.E. Wal sby, A. Av ery I Journal of M icrobi ologi cal M ethods 26 (1996) 11-20 19

80

y = 680 ho,46

0 5000 10000 15000 20000mean number of pixels per image

25000 30000

Fig. 5. The relationship between the standard deviation and total filament length per image. Each of the 141 points indicates the standarddeviation of measurements of images from 5 different areas of the same filter. The area analysed is 391 937 pixels (= 2.7 mm).

cyanobacteria collected on filters (A.E. Walsby andF. Schanz, in preparation). Fig. 5 shows the variationin standard deviation of the mean of 5 images fromeach sample, related to the mean filament length perimage. As expected, the standard error trend de-creases as a hyperbolic function of filament con-centration.

This data set draws attention to the large standarderrors associated with measurements on distributionsof filaments. For a random distribution of lines thestandard error depends on both the number andlength distribution of the line.

AcknowledgmentsWe wish to thank Dr. F. Schanz, University of

Zurich, for providing filtered samples for analysis,Mr Tim Colbum for assisting with drawing imagetemplates and photography, and Professor B. Silver-man for discussion of statistical methods. This workwas supported by grants GR9/1201 and GR3/8018from the Natural Environment Research Council.

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Olson, F.C.W. (1950) Quantitative estimates of tilamentousalgae. Trans. Am. Microsc. Sot. 59, 272-279.Gibson, C.E. (1975) Cyclomorphosis in natural populationsof Oscillaforia redekei Van Goor. Freshwater Biol. 5, 279-286.Booker, M.J. and Walsby, A.E. (1981) Bloom formation andstratification by a planktonic blue-green alga in an ex-perimental water column. Br. Phycol. J. 16, 411-421.Oliver, R.L. and Walsby, A.E. (1984) Direct evidence for therole of light-mediated gas vesicle collapse in the buoyancyregulation of Anabaenu jos-aquae (cyanobacteria). Limnol.Oceanogr. 29, 879-886.Konopka, A. (1982) Buoyancy regulation and vertical migra-tion by Oscill ator ia rubescens in Crooked Lake, Indiana. Br.Phycol. J. 17, 427-442.Konopka, A., Brock, T.D. and Walsby, A.E. (1978)Buoyancy regulation by planktonic blue-green algae in LakeMendota, Wisconsin. Arch. Hydrobiol. 83, 524-537.Bott, T.L. and Brock, T.D. (1970) Growth and metabolismof periphytic bacteria: methodology. Limnol. Oceanogr. 15,333-342.Bailey-Watts, A.E. and Kirika, A. (1981) The assessment ofsize variation in Loch Leven phytoplankton: methodologyand some of its uses in the study of factors influencing size.J. Plankton Res. 3. 261-282.


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191 Sheath, R.G., Morison, M.O., Cole, K.M. and Valanstyne,K.L. (1986) A new species of freshwater Rhodophyta,Bactrachospermum carpocontortum. Phycologia 25, 321-330.

[IO] Sheath, R.G. and Cole, K.M. (1990) Bactrachospermumheterocorticum sp. nov. and Polysiphonia subtilissima(Rhodophyta) from Florida spring-fed streams. J. Phycol. 26,563-568.

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[12] Brock, T.D. (1978) Use of fluorescence microscopy forquantifying phytoplankton, especially filamentous blue-greenalgae. Limnol. Oceanogr. 23, 158-160.[131 Daley, R.J. and Hobbie. J.E. (1975) Direct counts of aquaticbacteria by a modified epifluorescence technique. Limnol.Oceanogr. 20, 875-882.

[14] Waterbury, J.B., Watson, SW., Guillard, R.R.L. and Brand,L.E. (1979) Widespread occurrence of a unicellular marineplanktonic cyanobacterium. Nature (Land.) 277, 293-294.

determination of the _lamentous cyanobacteria planktothrix

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