Image analysis in nonlinear microscopy

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Hagmar et al. Vol. 25, No. 9 /September 2008 /J. Opt. Soc. Am. A 2195

Image analysis in nonlinear microscopy

Jonas Hagmar,1,2 Christian Brackmann,1 Tomas Gustavsson,3 and Annika Enejder1,*1Department of Chemical and Biological Engineering, Chalmers University of Technology, Fysikgränd 3,

S-412 96 Göteborg, Sweden2The Fraunhofer–Chalmers Research Centre for Industrial Mathematics, Chalmers Science Park,

SE-412 88 Göteborg, Sweden3Department of Signals and Systems, Chalmers University of Technology, S-412 96 Göteborg, Sweden

*Corresponding author: [email protected]

Received March 17, 2008; revised June 21, 2008; accepted June 24, 2008;posted July 3, 2008 (Doc. ID 93928); published August 6, 2008

The ability to automatically extract quantitative data from nonlinear microscopy images is here explored, tak-ing nonlinear and coherent effects into account. Objects of different degrees of complexity were investigated:theoretical images of spherical objects, experimentally collected coherent anti-Stokes Raman scattering imagesof polystyrene spheres in background-generating agar, well-separated lipid droplets in living yeast cells, andconglomerations of lipid droplets in living C. elegans nematodes. The in linear microscopy useful measure offull width at half-maximum (FWHM) was shown to provide inadequate measures of object size due to the non-linear density dependence of the signal. Instead, the capability of four state-of-the-art image analysis algo-rithms was evaluated. Among these, local thresholding was found to be the widest applicable segmentationalgorithm. © 2008 Optical Society of America

OCIS codes: 180.4315, 100.2960.

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. INTRODUCTIONight microscopy images are formed by collecting trans-itted, reflected, or emitted photons from the object, usu-

lly following linear interaction processes such as absorp-ion, fluorescence emission, and elastic and inelasticcattering. The object points act here as independentoint sources, and image formation can be described ashe convolution of each object point with a point-spreadunction (PSF) [1]. With the knowledge of the PSF, therue contours of the object can be deduced from the image.he simplest and most commonly used approximation ofbject size is the parameter of full width at half-maximumFWHM). In addition, a wide range of more advanced im-ge analysis routines are being explored [2–4], driven byhe desire to exploit more than the pure visual informa-ion in the microscopy images, allowing for quantitativend reproducible evaluation of larger data sets with highccuracy and minimal user interaction. These analysisoutines have all been developed for images formedhrough linear optical processes. However, within themerging field of microscopy techniques based on coher-nt, nonlinear interaction processes, such as coherentnti-Stokes Raman scattering (CARS) and second- andhird-harmonic generation (SHG and THG), respectively,icroscopy, image formation follows completely different

ules. The emitted light is here a result of a coherent su-erposition of phase-related radiation fields from vibrat-ng molecular bonds or electronic orbitals in the focal vol-me, as determined by the nonlinear dependence on thexcitation intensities and concentration of molecularonds or orbitals. Thus, it is not a straightforward sum ofmplitudes but involves interference phenomena; inARS microscopy it also involves interference with theonresonant background at the borders of the objects.

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he consequence of these characteristic properties of theignal generation in CARS microscopy is that the imageormation cannot be treated as a conventional convolutionf the true object with a PSF, since each object point is notn independent point scatterer. Instead, it requires a fullvaluation of the wave equation over the spatial extent ofach object present in the sample. The true contours ofhe object can then not simply be deduced by a deconvo-ution operation but is influenced by the size and the op-ical properties of the object. This complex image forma-ion raises the questions of to what extent conventionalize measures such as the FWHM can be used andhether available image analysis routines can be em-loyed for automatic identification, quantification, andharacterization of objects in coherent, nonlinear micros-opy. As the collection of proof-of-principle images foundn the scientific literature has so far not required any ad-anced processing—the visual two-dimensional informa-ion has been of value in itself—the nonlinear microscopymage is unexplored ground within image analysis. Still,ts potential for a wide range of biological applications isnder investigation, such as for membrane imaging [5,6];isualization of lipid storage [7–9], imaging of tumor tis-ue [10–12], muscle tissue [13–15], cardiovascular tissue,nd blood cells [16–18]; imaging within the neurosciences19–21]; and developmental biology [9,22–24]. Nonlinear

icroscopy has also found many important applicationsithin the material sciences, e.g., in the disciplines of bio-

echnology [25–27], semiconductor technology [28–30]nd nanotechnology [31,32]. This long list of recent stud-es has attracted great attention and signifies that non-inear microscopy will become a truly useful instrumentor full-scale studies, which makes the present studyimely and important. The spreading of coherent, nonlin-

008 Optical Society of America

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2196 J. Opt. Soc. Am. A/Vol. 25, No. 9 /September 2008 Hagmar et al.

ar microscopy beyond the physics departments is to aarge extent driven by its unique capabilities: label-freemaging of the structures or specific macromoleculesrobed as well as dynamic imaging with high three-imensional resolution of processes in complex samplesuch as living cells/organisms. As this category of tech-iques also enables the visualization of the many smallerolecules (lipids, carbohydrates, and other metabolites)

nd structures not possible to label without affectingheir natural properties, it is recognized as an importantuture complement to fluorescence microscopy. In addi-ion, the fact that coherent, nonlinear microscopy pro-ides a true image of the distribution of the targetolecule/structure, rather than generating an indirect

epresentation of a reporter molecule biased by the influ-nce of the local environment and a varying labeling effi-acy, must be emphasized.

In order to support the dissemination and use of non-inear microscopy within the applied sciences, we here ex-lore how quantitative parameters can be extracted frommages generated by a coherent, nonlinear opticalrocess—the CARS process. We show that the widelysed parameter FWHM provides erroneous measures ofbject size. Instead, we systematically investigate the ap-licability of the main categories of image analysis rou-ines employing (i) the intensity histogram of the image,ii) a kernel operator evaluating local intensity variations,iii) the gradient intensity map, and (iv) the minimizationf an energy function guiding the evolution of object con-our curves. They were represented by global and localhresholding and watershed and level set segmentation,espectively. Their ability to automatically segment, i.e.,dentify, and quantify representations of target objects ofifferent degrees of complexity were evaluated in bothheoretically and experimentally generated CARS micros-opy images. A series of theoretical images of polystyrenepheres of different and well-defined diameters were con-tructed in order to elucidate the influence of object size.xperimentally collected images of polystyrene beads im-ersed in agar added the complexity of objects sur-

ounded by a natural background and a destructive inter-erence border. CARS microscopy images of well-eparated lipid stores in living yeast cells challenged withheir structured background formed by the contours ofhe cells. Finally, images of adjacent objects in terms ofssemblies of lipid droplets in the nematode Caenorhab-itis elegans were evaluated.

. MATERIAL AND METHODS. CARS Microscope

n CARS microscopy, the characteristic vibrational prop-rties of molecules in the sample are mapped to an image.his is achieved by tuning the frequency difference of twoxcitation laser beams, the pump (frequency �p) andtokes ��S� beams, to form a beating field with a fre-uency that matches a vibrational resonance frequency ofhe target molecule. Ensembles of molecules in the high-ntensity region of the focal volume are set into a coherentibration by the beating excitation field. They are thenrobed by another beam, a so-called probe beam (fre-uency ��), which is inelastically scattered with a positive
p
requency shift (anti-Stokes) corresponding to the molecu-ar vibration. A schematic illustration of this multiphotonnteraction process is shown as an energy level diagramn Fig. 1(a). The CARS photons all oscillate coherently inhase and are emitted in a specific direction. Thus, the re-ulting CARS signal, ICARS, is emitted as a laserlike beamt a shorter wavelength (higher frequency �aS=�p−�S�p�) than the excitation beams and with an intensity thatssentially scales as the cube of the input intensities (Ip,S, and Ip�, respectively)

ICARS � ��3��2IpISIp� , �1�

here ��3� is the third-order susceptibility, which can beeparated into two terms,

��3� = �r�3� + �nr

�3�, �2�

epresenting contributions from the resonant vibrationalxcitations (first term) and nonresonant excitations (lasterm), respectively. Whereas the resonant part is highlyrequency dependent, the nonresonant contribution is es-entially frequency independent, making it unspecific.his nonresonant background is a problem in manyARS microscopy applications, since its presence reduces

mage contrast and renders the automatic analysis ofARS microscopy images more difficult.CARS microscopy in practice requires tight focusing of

wo synchronized laser beams onto the sample. Their spa-ial as well as temporal overlap is crucial in order to si-ultaneously interact with the molecules in the focal vol-me and hereby induce the CARS signal. For theeneration of the excitation beams, a high-power, picosec-nd Nd:VAN laser (HighQ Laser Production GmbH, wave-ength 1064 nm, output power 10 W, pulse duration 7 ps,epetition rate 76 MHz) was here used, seeding anntracavity-doubled optical parametric oscillator (LevantePO, APE GmbH). A fraction of the output power of thed:VAN laser acting as the Stokes beam was directly

oupled into an inverted microscope (Nikon, EclipseE2000-E), while the pump beam in the CARS processas generated by tuning the OPO to 817.0 nm. This

ig. 1. (Color online) Optical process involving the interactionf the pump, Stokes, and probe breams for the generation of aARS signal is schematically illustrated in the energy level dia-ram in (a), where � represents the molecular vibration. Below,he experimental setup used for the generation of CARS micros-opy images of polystyrene spheres, living yeast cells, and nema-odes is shown. The probe geometry assumed in the theoreticalodel is depicted in (b), showing the focused excitation beams

canning the object (a polystyrene sphere), as well as the coordi-ate system of a detection point in the far-field regime.

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avelength combination probes the carbon–hydrogen vi-ration at 2845 cm−1. The temporal overlap of the beamsas achieved using an optical delay line for the OPO out-ut. They were then guided into the microscope via a mir-or scanning unit (Nikon, C1) and focused onto theample by high-numerical-aperture objectives (Nikon,PO, 60� N.A. 1.2 water immersion or 100� N.A. 1.3 oil

mmersion). Each probe site containing high densities of–H bonds generates a CARS signal collected by an as-herical lens (N.A. 0.8) in transmission mode. Two-imensional CARS images of the distribution of moleculesith high contents of C–H bonds, such as lipids, were

ormed by scanning the excitation beams over the sample256�256 pixels, 20 s integration time). The forward-mitted, blueshifted CARS signal was separated from thexcitation beams by bandpass filters before the signal fi-ally was recorded by a single-photon-counting photomul-iplier tube (Hamamatsu, PMC-100-20 PMT). By collect-ng a series of two-dimensional images while moving the

icroscope objective in the vertical direction, a z stack isbtained and provides a three-dimensional reconstructionf the sample. A schematic of the setup is presented inig. 1(a).

. Theoretical CARS Microscopy Imagescollection of synthetic CARS microscopy images of poly-

tyrene spheres was generated by the superposition of in-ividual CARS fields emitted from point scatterers in thebject following the formalism outlined by Cheng et al.33] implemented in MATLAB. The expressions for theARS fields were obtained by solving the wave equationtilizing Green’s function for two Gaussian input beams,olarized in the x direction and propagating in the z di-ection [see Fig. 1(b)], representing the pump and Stokeseams:

Ep�r,t� = Ep�r�exp�− i�pt� + c.c.,

ES�r,t� = ES�r�exp�− i�St� + c.c. �3�

fter the tightly focusing microscope objective, the spatialistributions of the incident fields are instead describedy

Ejinc�� = Ej0 exp�− f2 sin2 �/�0

2�, �4�

here j=p, s stands for pump and Stokes beams, � is thencident angle, f is the focal length of the focusing objec-ive, and �0 is the width of the beam waist. As the focalelds of the two beams consist primarily of polarizationomponents in the original x direction [33], they could bexpressed as

Ej��,�,z� =ikjf exp�− ikjf�

2I00 �5�

n cylindrical coordinates, where kj=2nj� /j is the waveector amplitude (nj is the refractive index, and j is theavelength). Here I is given by
00
I00 =�0

�max

Ejinc��sin ��cos �

��1 + cos ��J0�kj� sin ��exp�ikjx cos ��, �6�

here �max is the maximum of the cone angle of the inci-ent light and J0 is the zero-order Bessel function. An ad-itional assumption made is that there is no differenceetween the refractive indices of the scatterer and thosef the surrounding medium. With these expressions of thenput fields, the wave equation was solved for a pointcatterer using Green’s function, followed by linear super-osition, resulting in a far-field CARS signal for a fullhree-dimensional object:

EaS�R� = −�aS

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�R� �V

dV exp�− ikaSR · r

�R� ��

0 0 0

cos cos � cos sin � − sin

− sin � cos � 0

� Px

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iR

i

i�

, �7�

here the detection position R �R ,� ,�� is given inpherical coordinates; �aS corresponds to the frequency ofhe anti-Stokes field; c is the speed of light; and iR, i�, and

� are unit vectors in the R, �, and � directions, respec-ively. Since the y and z polarization components were ne-lected, Py

�3��r�=Pz�3��r�=0 and

Px�3��r� = 3�1111

�3� ��aS,r�Ep2�r�ES

* �r�, �8�

here �1111�3� ��aS ,r� is a component of the third-order sus-

eptibility tensor, which can be recognized from Eq. (2).he collected radiative power pCARS of the generatedARS signal was finally computed by integrating over theollection cone from �1 and �2:

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8��

1

2

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2�

d��EaS�R��2R2 sin . �9�

ll input parameters were chosen to match the experi-ental conditions (see below). The wavelengths of the

ump and Stokes beams were therefore chosen to be p817 nm and S=1064 nm, respectively. The focal lengthnd numerical aperture of the focusing objective were seto f=0.37 mm and N.A.=1.3, respectively, matching theroperties of the oil immersion objective used in the ex-eriments. The refractive index was set to n=1.5 through-ut the model, which is close to the experimentally mea-ured refractive index of polystyrene [34]. Assuming thathe incident beams filled the back aperture of the objec-ive, their widths in the focal point were given by w0f sin �max. The CARS intensity at each pixel (256�256

n total) in the image was then formed by superimposinghe CARS fields generated by all point scatterers in theocal volume as illustrated in Fig. 1(b). By shifting the po-ition of the probe volume with 0.078 m relative to the

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bject and repeating the superposition computations, theeighboring pixel intensity was then formed for a totalrea of 20�20 m2. The computations were first con-ucted for polystyrene spheres with diameters of 1.072nd 2.836 m for validation with experimental images ofolystyrene spheres with these well-defined diameters. Inrder to investigate the possible influence of object size,he computations were repeated for 16 polystyrenepheres with diameters in the range of 0.5–2 m corre-ponding to those typical for organelles. The advantageith a theoretical approach is that many data points canasily be generated in the relevant size range and the un-ertainty associated with the individual size variability ofhe calibration spheres is avoided (typical coefficient ofariance, 5%). However, as the theory does not considerhe phase shifts associated with the CARS process [35] orhe generation of nonresonant background, interferencehenomena are not included in the model. To investigatehe impact of these effects, a second set of images wasormed by adding a border of destructive interference,ypically observed for objects with a refractive index sig-ificantly different from that of the surrounding medium.xperimentally we found a destructive interference bor-er for the polystyrene spheres corresponding to2% ±1% of the peak intensity at a distance of.20±0.05 m from the true object border, which wasdded to the theoretical representations.

. Model Systemstacks of experimentally generated CARS microscopy im-ges of three different model systems were collected andnalyzed in this work: polystyrene spheres, Saccharomy-es cerevisiae (yeast), and Caenorhabditis elegans (aematode). They are all highly relevant, as they belong tohe most frequently studied objects within microscopy.olystyrene spheres, commercially offered in a wide rangef well-defined sizes, provide versatile calibration stan-ards. Yeast is an attractive model organism within cellnd molecular biology, sharing a large number of genesnd cellular processes with humans, though convenientlyccessible through easy cultivation and short generationime. This is also the case for the nematode C. elegans,ith the additional advantage that it exhibits cell-ifferentiated and organism-wide regulation processes,llowing for full systemic studies. With these model sys-ems a set of images with different degrees of complexityas formed, ranging from a single spherical object with aell-defined diameter, to well-separated lipid particles in

iving single-cell organisms (yeast), to geometrically com-lex clusters of lipid stores of varying sizes in theultiple-cell organism C. elegans.Polystyrene spheres. Sphere sizes used in the study

ere 1.072 and 2.836 m in diameter (Polysciences Inc.),orresponding to sizes of subcellular organelles in generalnd lipid stores in particular. Due to their high density ofarbon–hydrogen bonds, they generate a strong CARSignal when probing the C–H vibration at 2845 cm−1 andlearly appear in the CARS microscopy images. In ordero assure that the spheres did not move during the acqui-ition time of the entire z stack, the spheres were immo-ilized in agar. The z stacks consisted of 30 two-imensional images, each covering an area of 20

20 m2, spanning the full depth of the particle. Fivetacks of each sphere size were collected with excitationowers of 56+39 mW (pump/probe+Stokes beams at theample position). The image in the z stack having theighest measured maximum signal was chosen for evalu-tion using the FWHM parameter and the segmentationlgorithms.Saccharomyces cerevisiae (yeast). Subsamples of bak-

r’s yeast cultured overnight at 30 °C were collected andransferred to a microwell, mounted on a microscopeover slide coated with polylysine. By probing the C–H vi-ration at 2845 cm−1 with excitation powers of 2720 mW (pump/probe+Stokes beams at the sample posi-

ion), the lipid droplets in the yeast cells clearly appear inhe CARS images as a result of the high density of C–Honds. Twenty-one images were analyzed, covering anrea of 20�20 m2.C. elegans. Nematodes of the N2 strain (wild type) of

. elegans were cultured on agar plates at 20 °C. For aetailed description of the culturing protocol, the readers referred to Sulston and Hodgkin [36]. Larvae were putn a microscope cover glass with a thin agar film depos-ted on the surface. In order to keep the larvae immobi-ized, they were anaesthetized with minimal amounts ofevamisol added to the sample. The sample was sealed byently placing a second cover glass on top of the agar filmith the immersed nematodes. It was placed in the micro-

cope, and the distribution of lipid droplets (by probinghe C–H vibration at 2845 cm−1) of a central region of thearva was mapped. Depending on the size of the larva, therea scanned by the laser beams varied between 20.520.5 m2 and 100�100 m2. The z stacks consisting of

9–100 CARS images, covering a depth of 9.9–40 m,ere collected. Excitation powers were typically 15 mW

pump/probe beam) and 7.5 mW (Stokes beam).

. Image Analysisour different methods to segment objects from the back-round were evaluated based on the global intensity his-ogram, on a kernel convolution operation, on the inten-ity gradient map, and on the minimization of an energyunction, all representing main categories of image analy-is techniques.

Global thresholding. Global thresholding identifies theixels as either background or object based on a thresholdntensity value, determined as the intersection point be-ween two fitted intensity distributions in the intensityistogram of the entire image employing various optimi-ation criteria [37]. The separating threshold was auto-atically found by minimizing the intraclass variances

nd maximizing the between-class variance using thetsu algorithm [38] as implemented in MATLAB. This im-ge analysis method does not require any input data orpriori information.Local thresholding. A routine for local thresholding was

eveloped and implemented in MATLAB. An adaptive in-ensity threshold is here formed as a function of pixel po-ition in order to define it as either background or object,aking only the intensity variations in the local neighbor-ood into account. This has the advantage that a reliablevaluation of images being collected with a strong illumi-ation gradient also can be achieved. For each pixel a

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hreshold was computed as three standard deviationsrom the mean intensity in the local neighborhood. It wasccomplished by convoluting the image with a kernel, de-ning the area of the local neighborhood. The size of theernel had to be given as an input parameter so that auitable size was used for each category of object: largenough to simultaneously cover sufficient foreground andackground pixels and small enough to not pick up slowntensity variations caused by nonuniform illuminationnd inhomogeneous background. Hence, the kernel size isetter optimized for each set of images. For images of theell-separated polystyrene spheres and lipid droplets ineast collected with a smaller field of view �20�20 m2�llowing for homogenous illumination, a kernel area sig-ificantly larger than the object size could be used. Threeernel sizes (1.24�1.24, 2.3�2.3, and 7.8�7.8 m2)ere tested on the different model systems, and the mid-

ized kernel �2.3�2.3 m2� was found to be the widestpplicable and useful for all object sizes. For images of thedjacent lipid stores in C. elegans collected with a largereld of view, where the edges were less efficiently illumi-ated, the smallest kernel size of 1.24�1.24 m2 washosen.

Watershed segmentation. By regarding the image as anntensity landscape consisting of local minima and

axima, object borders are found in the high gradient re-ions. Thus, object and background areas can conve-iently be identified by forming an intensity gradientap of the CARS microscopy image. This can be achievedith a mathematical operation analogous to immersing

he landscape in water, leaving the objects as islands. Aast watershed algorithm simulating such a flooding pro-ess, originally presented by Vincent and Soille [39], wasere implemented in MATLAB. As there usually are farore islands formed than objects present due to, e.g.,

oise and an inhomogeneous background, starting pointsor the segmentation had to be created based either on theost prominent intensity maxima (for the polystyrene

pheres and yeast cells) or on the collection of localaxima obtained from a blob-filtered version of the origi-

al image (for C. elegans). The consequence of this is thatn individual seeding map must be generated for each im-ge as input information to the watershed algorithm inrder to reduce the risk of oversegmentation. However,nce a suitable criterion has been identified for this, theeeds can automatically be generated as a part of the seg-entation algorithm.Level set segmentation. In level set methods, the idea is

o evolve an object border curve, C, starting at a given dis-ance, R, from the center of the object while minimizingn energy function F given by

F�c1,c2,C� = · Length�C� + � · Area�inside�C��

+ 1�inside�C�

�u0�x,y� − c1�2dxdy

+ 2�outside�C�

�u0�x,y� − c2�2dxdy, �10�

here u0�x ,y� is the intensity matrix of the image; c1 andare the mean intensities of the regions inside and out-
2
ide the curve C, respectively; and ,� ,1 ,2�0 are fixedarameters, determining to what extent the differenterms should contribute to the energy function. In thisork standard values of 1=1, 2=1, and �=0.01�2552

ere used. For the polystyrene spheres the contour pa-ameter was defined as 0.0001�2552 and somewhatarger for the yeast cells and the nematode: 0.01�2552.he minimization procedure started with a curve defineds a circle with a radius of 2 m from the center of thebject. As for the watershed segmentation, level sets re-uire a priori information on the center positions of thebjects for each image, given as an individual seedingap based on the intensity maxima (polystyrene spheres,

east cells) or on the collection of local maxima obtainedrom the blob-filtered image (C. elegans). Still, level setegmentation has the advantage that the contour of anbject can be identified without the need for gradient com-utations.

. RESULTS. Validation of Model and Segmentation of TheoreticalARS Imagesn order to validate the theoretical framework, CARS mi-roscopy images of spheres with sizes matching the poly-tyrene beads used in the experimental investigation1.072 m and 2.836 m) were constructed and fittedleast-squares fit) to the normalized CARS intensity pro-les. The simulated and measured CARS intensity pro-les along the diameter of the spheres are shown in Fig.. Except for the borders of destructive interference, thexperimentally generated images and corresponding pro-les are well described by the theoretical model, with anverage difference at the peak value of −0.9±6% for the.072 m spheres and −2% ±10% for the 2.836 mpheres.

The theoretical model was thereafter used to generateseries of images of polystyrene spheres with well-

efined sizes, three of which (diameters of 0.5, 1, and m) are exemplified in Fig. 3. Cross marks indicate the

rue border of the spheres in the accompanying intensityrofiles, and the FWHM, frequently used for size determi-ation in conventional microscopy, is highlighted asashed lines. Comparing Figs. 3(b)–3(d), it is clear thathe CARS intensity at the true border of the objects variesith the size of the sphere. The border intensities varyetween 10%–20% relative to the peak intensity, whicheans that the fixed 50% definition of the parameterWHM provides significantly smaller size parameters

han the true values with size-dependent estimation er-ors. Averaged over all object sizes, the FWHM provides aiameter 27% ±7% smaller than the true size (see Table). This prompts the use of other segmentation proce-ures in coherent, nonlinear microscopy.Figure 4 presents the capabilities of four different rou-

ines for segmentation of the theoretical CARS micros-opy images as representatives of the main categoriessed within image analysis. A significant impact of objectize was found for all methods; the relative estimation er-or decreases in general with increasing sphere diameter.e distinguish two groupings: one comprising theWHM, global thresholding, and watershed segmenta-

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ion protocols, consistently estimating a smaller object di-meter than the true size; and one group represented byocal thresholding (kernel size 2.3�2.3 m2) and levelets �R=2 m�, where good estimations are achieved in aroad size range by accommodating the input parameters.

ig. 3. (Color online) Series of theoretically generated images ofolystyrene spheres with diameters of 0.5, 1, and 2 m arehown in (a). The dashed circles highlight the measure ofWHM. The corresponding normalized profiles are shown in theiagrams below with the FWHM marked with dashed verticalines. Compared to the true size, indicated by cross marks, theWHM provides a significantly smaller diameter.

ig. 2. (Color online) Experimentally generated CARS microscohown in (a) and (b). In (c) and (d) the profiles along the lines inetically generated images of corresponding spheres. Except for tively) is obtained, which validates the use of the theoretical moicroscopy.

able 1 provides a summary of the accuracy of the esti-ated diameters, averaged over object sizes typical for

ell organelles �0.5–2 m�. It confirms that large devia-ions in the size estimates are obtained for global thresh-lding, watersheds, and FWHM, all underestimating thebject size with on average as much as 65, 76, and9 pixels per object, respectively. Significantly better re-ults are obtained for local thresholding and level sets,ith average deviations corresponding to 18 and 7 pixelsver the object area, respectively.

When adding a destructive interference border, typi-ally observed in CARS microscopy images of high-efractive-index objects, to the theoretically generated im-ges, no significant changes in the performance of theifferent image analysis routines can be reported with thexception of level sets (see Table 1). For the smallest ob-ects �D�0.7 m� the evolution of the border line curveoes in the outward direction rather than toward the cen-er of the object. Thus, it seeks to identify the surroundingackground and completely fails to segment the small-ized objects.

. Segmentation of Experimental Images of Polystyrenepheresn order to investigate the impact of a more realistic sig-al and background generation characterized by larger

ages of polystyrene spheres of sizes 1.072 m and 2.836 m ared in the images are compared with profiles sampled from theo-ers of interference, an excellent match (−0.9% and −2%, respec-systematic evaluation of image analysis routines within CARS

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ixel-to-pixel variance, experimentally collected CARSicroscopy images of polystyrene spheres of two different

iameters (1.072 m and 2.836 m) were evaluated. Ex-mples of images with corresponding normalized inten-ity profiles are shown in Fig. 5. Here the natural varia-ions in the registered intensities as well as theestructive interference border can be noted. The objectize as defined by the FWHM parameter is marked andgain provides smaller estimates compared to the truealue. In addition, the contours identified by means ofevel sets are shown, matching the true border well. Theerformance of all different routines for the analysis ofxperimentally collected CARS microscopy images isuantified in Table 2. As for the theoretically generatedmages, the FWHM underestimates and the level sets

atches the true object size, respectively. The perfor-ance of global thresholding also corresponds to that

chieved for noiseless images for the larger spheres (annderestimation of �20%), while for the smaller sphereshe overlap between foreground and background in the in-ensity histogram instead results in an overestimation. Aignificant impact of the experimental intensity variabil-ty is also observed for local thresholding, now underesti-

ating the object size by �20%. The watershed segmen-ation manages to identify the true object border better

Table 1. Segmentation of Theoretical CARS Microsthe Border of Des

MethodMean Diff

without Int

FWHM −2Global thresholding, Otsu −1

Watersheds −24Local thresholdingb −5Level sets, R=2 m 4

aThe difference between estimated and true diameters for spherical objects in the rnterference border �for D�0.7 m no segmentation was possible; see text for deta

bKernel size: 2.3�2.3 m2.

ig. 4. Relative error in the size estimates of polystyrenepheres in the size range of 0.5–2 m obtained from the theoret-cal images using different image analysis algorithms are plottedersus the true diameters. Whereas local thresholding and levelets identify object sizes with a high accuracy in the range of D0.7–2 m, global thresholding and watersheds perform almosts poorly as the FWHM parameter.

copy Images of Polystyrene Spheres With and Withouttructive Interferencea

erence: Sphereserference Border

Mean Difference: Sphereswith Interference Border

7% ±7% −24% ±7%8% ±4% −18% ±4%% ±10% −17% ±9%% ±10% −6% ±7%% ±2% D�0.7 m −2% ±4%

ange of 0.5–2 m is presented, with the exception for level set segmentation of spheres withils�.

Table 2. Segmentation of ExperimentallyGenerated CARS Microscopy Images ofPolystyrene Spheres with Two Different

Diametersa

Method

Mean DifferenceSphere Size:

1.072 m

Mean DifferenceSphere Size:

2.836 m

WHM −28% ±2% −19% ±6%lobal thresholding,

Otsu14% ±3% −17% ±2%

atersheds 0.7% ±0.7% −12% ±5%ocal thresholdingb −22.8% ±0.9% −20% ±5%evel sets, R=2 m 3% ±1% −12% ±5%

aThe difference between estimated and true diameters is presented.bKernel size: 2.3�2.3 m2.

ig. 5. (Color online) CARS microscopy images of polystyrenepheres with sizes 1.072 m and 2.836 m are shown in (a) andb) respectively. The white circles mark the area identified as ob-ect by the level sets algorithm. The corresponding intensity pro-les are displayed in (c) and (d), also showing the borders as de-ned by level sets (circles) and the FWHM (vertical lines). Foromparison, the true sizes of the spheres are indicated by crossarks.

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han for the theoretical images, particularly for themaller spheres.

. Segmentation of Images of S. cerevisiaen CARS microscopy images of biological samples, the ob-ects of interest often consist of subcellular organelles,enerating a strong CARS signal, surrounded by low-ntensity regions of the intracellular matrix. This is exem-lified by a subsection of a CARS microscopy image of aingle yeast cell in Fig. 6, obtained by probing the densityf carbon-hydrogen bonds �2845 cm−1�. It shows a high-ensity region corresponding to a distinct lipid dropleturrounded by a low-density region of the organic mol-cules present inside the cell. The cells are in turn sur-ounded by a medium, consisting primarily of water, con-ributing to a weak nonresonant signal as illustrated inhe overview image in Fig. 6(a). Thus, analysis routinesor CARS microscopy images must have the capability ofdentifing objects in a highly structured environment. Inrder to evaluate this capability, lipid droplets were seg-ented in 21 CARS microscopy images of S. cerevisiae

yeast) by means of the different protocols. The true sizef the lipid droplets were determined by fitting their in-ensity profiles with CARS microscopy theory computa-ions of spherical objects with diameters in the relevantange of 0.5–2 m. Figures 6(c)–6(f) exemplify the perfor-ance of the different image analysis routines. Their

bilities to segment biological CARS microscopy imagesre further quantified in terms of the mean difference be-ween estimated and true diameters in Table 3. It demon-trates that global thresholding fails to identify the indi-idual lipid droplets and instead segments the entire cellFig. 6(c)]. This is also the case for level sets, irrespectivef the size of the radius of the initial contour curve [Fig.(f)]. The watershed segmentation is able to identify theipid droplets but underestimates their sizes significantly52%). The only method that successfully identifies androvides reasonable size estimates of objects in a highlytructured surrounding is local thresholding, clearlyhowing the best results �−18% �.

ig. 6. (Color online) CARS microscopy image of lipid dropletsn living yeast cells is shown in (a). A close-up of the rectangularrea highlighted in (a) is displayed in (b). The borders of the lipidroplet as identified by global thresholding, watersheds, localhresholding, and level sets are shown in (c), (d), (e), and (f), re-pectively. Whereas watersheds and local thresholding are suc-essful in identifying the lipid droplet, global thresholding andevel sets rather identify the surrounding structure correspond-ng to the outline of the entire cell.

. Segmentation of Images of C. elegansARS microscopy images of lipid stores in the nematode. elegans present a complex problem to the segmentationlgorithms, which even further highlight their individualtrengths and weaknesses. The lipid stores are here lessircular; thus, it is difficult to define a true size by meansf CARS microscopy theory. Instead of quantitative evalu-tion, the performance of the different image analysisoutines was determined from their ability to identify theipid stores. This is a challenge in itself for several rea-ons. The lipid droplets are in close vicinity to one an-ther, forming clusters as exemplified in Fig. 7(b), whichrovides a true challenge for the algorithms to identifyhe single units. In addition, the lipid droplets are distrib-ted over a larger depth range, as the nematode is aultiple-cell organism, resulting in the appearance of

ome droplets as diffuse, low-intensity, out-of-focus ob-ects and others as high-intensity, focused objects [see Fig.(b)]. They also contain varying densities of lipids, gener-ting corresponding CARS intensities. Thus, some low-ensity, out-of-focus lipid stores appear at intensitiesqual to those generated by high-density, focused tissueatrix areas. Finally, due to the larger field of view re-

uired, the objects located at the outskirts of the imageend to be less efficiently excited, resulting in a risk of be-ng neglected by the segmentation procedures. This all

akes it a difficult task to classify regions as object orackground. Global thresholding fails to identify lipidroplets in larvae with highly varying tissue matrix sig-als and in images of larger field of view due to the sub-ptimal overlap of the excitation laser beams at the edges.hen the lipid stores indeed could be segmented from the

ackground, entire clusters were rather identified as ob-ects; see Fig. 7(c). Local thresholding successfully sepa-ates adjacent lipid droplets, as observed in Fig. 7(e). Inddition, it has inherently no difficulties in identifyinghe lipid stores despite exhibiting a wide intensity range,lso overlapping that of the tissue matrix. Instead, it hastendency to include some nondroplet elements as false

ositives. This is in contrast to level sets, which merelyegments the most prominent lipid droplets, leaving aarge population of false negatives [see Fig. 7(f)]. The bestesult is obtained for watersheds, identifying more low-ntensity lipid droplets (fewer false negatives) and reject-ng most of the nondroplet elements (fewer false posi-ives). In addition, it separates the individual lipid storesell, as illustrated in Fig. 7(d). However, it requires andvanced seeding scheme consisting of blob filtering toefine the positions of the lipid stores.

Table 3. Segmentation of CARS MicroscopyImages of Lipid Droplets in Living Yeast Cells

Showing the Impact of a Structured Surroundinga

ethod Mean Difference

WHM −36% ±2%atersheds −52% ±10%lobal thresholding, Otsu 434% ±176%ocal thresholdingb −18% ±15%evel Sets, R=2 m 270% ±150%

aThe difference between estimated and true diameters is presented.bKernel size: 2.3�2.3 m2.

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. DISCUSSIONoherent, nonlinear microscopy is a novel and promisingategory of techniques, offering the appealing possibilityf noninvasive and label-free imaging of macromoleculesnd characteristic structures in cells in vivo with thenique combination of submicrometer resolution in threeimensions down to millimeter depths. Still, in order toecome a truly useful tool, going beyond phenomenologi-al studies, the visual information needs to be translatednto relevant quantitative data. In order to fully exploithe wealth of information stored, sophisticated analysislgorithms are needed. There exists a wide range of ad-anced tools for image analysis [37], though, to the best ofur knowledge, all assume that the representations of thebjects are formed by linear and incoherent light emissionrocesses. With the emerging category of microscopy tech-iques relying on nonlinear optical processes [40–42], ahorough evaluation of to what extent present analysisethods can be used is motivated.In the present study we investigate the impact of the

onlinearity and coherency of signal generation on themage formation by studying both theoretical and experi-

ental CARS microcopy images. We show that the men-ioned properties have significant implications for par-icularly the appearance of border regions andonsequently on size estimates. At the border, the de-reasing number of contributing molecules present in therobe volume results in a nonlinear decline in intensitycompare Eq. (1)]. Theoretically generated images of poly-

ig. 7. (Color online) CARS microscopy images of lipid stores inllustration of a nematode in (a). An example of such an image ibjects. The borders of the lipid stores as identified by global thresd), (e), and (f), respectively. It can be noted that global thresholdo separate the single droplets. Whereas level sets (f) fails to idenalse positives at the right edge of the image. Combined with andentify most of the important lipid stores as single objects witho

tyrene spheres of diameters in the range of 0.5–2 m

onsequently reveal that the intensity at the border mea-ures 10%–20% of the peak intensity at the center of thebject. This signifies that the parameter FWHM (bordert 50% of peak intensity), frequently used in conventionalinear microscopy, is not useful within nonlinear micros-opy. For all the CARS microscopy images investigated,overing different degrees of image complexity, theWHM parameter provides too-small size estimates.hus, image analysis routines estimating object sizeased on more advanced criteria are needed. Four differ-nt categories are explored in this work: two based on theistogram of the intensity values in the entire image (glo-al thresholding) alternatively in a subimage through aernel operation (local thresholding), one based on theradient map of the image (watersheds), and finally onen iterative computations of contours guided by the mini-ization of an energy function (level sets). Global thresh-

lding and watersheds perform almost as poorly as theWHM measure for theoretical images, representing theimplest degree of complexity (a single object surroundedy a noiseless, zero-level background). Neither of theseethods provides a simple means to adjust the segmen-

ation procedure via input parameters or to compensateor the estimation error afterward with e.g., a general cor-ection factor, as the deviation varies with the unknownrue object size. Local thresholding and level sets offer theossibility to accommodate their segmentation algorithmso the size range of the objects with input parameterskernel size and /�, respectively), here resulting in sizestimates with an average deviation of merely a few per-

C. elegans were collected in the region indicated in the schematicn in (b), clearly visualizing the lipid stores as adjacent circularg, watersheds, local thresholding, and level sets are shown in (c),tends to identify the lipid stores as larger clusters, being unableany of the lipid stores, local thresholding (e) provides a series ofblob filtering of the image, watersheds (d) is able to successfully

accompanying false positives.

livings showholdining (c)tify m

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ent over a, from a biological perspective, fairly large sizeange �0.5–2 m�. In images with a more homogeneousbject size distribution, the size-dependent input param-ters of these two algorithms can be optimized so thatven better results may be obtained.

This also highlights the usefulness of the theoreticalodel for signal generation in nonlinear microscopy for

ystematic evaluations of the performance of different im-ge analysis routines, here supported by the excellentatch with experimental data. More advanced images

an be generated than are exemplified here, for example,onsisting of several objects and including noise. The limi-ation of the theoretical model is that local phase differ-nces in the generated CARS signal, due to, e.g., differ-nces in refractive index, are not considered. Inxperimentally generated CARS microscopy images,hese effects can be observed as contours of destructive in-erference [35], here investigated by extracting their char-cteristics from the experimental images and implement-ng them in the theoretical images. From Table 1 weonclude that this phenomenon does not cause any diffi-ulties for the image analysis routines investigated; localhresholding and level sets still perform best with the ex-eption that level sets fails to identify objects with diam-ters smaller than 0.7 m. Instead, it here defines theurrounding background as the object. A simple effort toorrect for this by means of the size-dependent input pa-ameters was found unsuccessful. However, as small ob-ects of biological nature rarely exhibit these interferenceontours (see the CARS microscopy images of lipid storesn yeast cells and C. elegans), this malfunction is withinhe biosciences of minor practical importance.

For a more complete evaluation of the different rou-ines for the analysis of nonlinear microscopy images, thempact of a more realistic background must be considered.his was studied in the experimentally collected CARSicroscopy images of polystyrene spheres immersed in

gar. Global thresholding still generates estimates withn average deviation of �20%, and the level set segmen-ation continues to perform well, indicating that the natu-al intensity variations in the experimentally generatedmages do not influence their performance significantly.owever, for local thresholding, a background with natu-

al intensity variations interfere, resulting in an underes-imation of object size. In contrast, watersheds manageso identify the true object border better than for the the-retical images (see Table 2). For the segmentation ofingle-object images, it provides size estimates with theighest accuracy.Images of real samples rarely consist of a single object.

he images of yeast cells, showing several lipid dropletsurrounded by an inhomogeneous and structured back-round (cells and medium), provide a more realistic casen this sense. They signified the strength of the dynamicmage analysis, with input parameters adjustable tovailable information on typical size and approximate lo-ation of the target objects. Excellent object segmentationan then be achieved, also in images with a realistic andence a high degree of complexity. As an example, in localhresholding this can be accomplished by an intelligenthoice of kernel size. Small kernels introduced a risk ofefining the center of large-sized objects as background,

nd larger kernels showed a tendency of segmentingarger surrounding structures as, e.g., the entire yeastell rather than the lipid droplets inside. Thus, a priorinformation on the approximate object size, the distancesn between, and the illumination profile can guide theser to a suitable choice of kernel area. As a result, localhresholding performs significantly better for the segmen-ation of objects in a biologically relevant environmenthan the other algorithms. Level sets instead identifieshe structures in the background as objects, i.e., the en-ire cells. In the CARS microscopy images of the nema-ode C. elegans with adjacent lipid stores, the level ofomplexity was even higher. The background consists ofistinct nondroplet structures generating nonresonant asell as weak resonant signals, resulting in a broad inten-

ity histogram partly overlapping that of the objects. Thisverchallenges the level sets segmentation. Its input pa-ameters can only be set such that it merely segments theost prominent lipid droplets, as it otherwise tends to

dentify background regions as objects. Instead, these im-ges exemplify the strength of local thresholding. With aomparably simple algorithm, it is able not only to iden-ify most clusters of lipid droplets from the tissue matrix,espite its structured character and regions of relativelyigh intensities, but also to successfully separate adjacent

ipid droplets. This has to be taken with the price of a fewondroplet elements included as false positives. The wa-ershed segmentation performs in this sense slightly bet-er but requires on the other hand an elaborate prepro-essing of the images in order to generate a useful seedingap.

. CONCLUSIONSe conclude that the segmentation criteria of the FWHM

arameter and global thresholding are insufficient foronlinear, coherent microscopy techniques such as CARSicroscopy, either underestimating object sizes or misin-

erpreting weaker structures in the immediate surround-ng as objects. Watersheds and level sets are able to esti-

ate object size with a deviation corresponding to a fewixels for images of a single, well-defined object (the poly-tyrene sphere). Local thresholding instead shows itstrength for the segmentation of images with, for biologi-al samples (lipid droplets in yeast cells and C. elegans),ealistic complexity level, particularly if the size-ependent input parameter (kernel size) is chosen withespect to the object size and structures in the back-round. Watershed segmentation performs here poorlylone, but when it is preceded by a filtering in order toenerate a reliable seeding map, successful segmentations achieved. In general, local thresholding performs best,s most robust, and requires no a priori information oralibration sets of data for successful quantitative analy-is of microscopy images generated by nonlinear, coherentechniques. Its strength is particularly proved by the suc-essful identification of lipid stores in the complex imagesf the nematode C. elegans, despite challenges such as in-omogeneous illumination and adjacent objects in aighly varying background.

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CKNOWLEDGMENTSoakim Norbeck and Claes Axäng, the Department ofhemical and Biological Engineering, Chalmers Univer-ity of Technology, kindly provided the S. cerevisiae and C.legans samples, respectively. Valuable discussions withohan Degerman, the Department of Signals and Sys-ems, Chalmers University of Technology, and with Matsvarnström, the Fraunhofer–Chalmers Centre for Indus-

rial Mathematics, on the implementation of image analy-is algorithms are gratefully acknowledged. C. Brack-ann, T. Gustavsson, and A. Enejder are supported by

he Swedish Research Council.

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Image analysis in nonlinear microscopy