IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 7 ...qji/Papers/TIP_microtubule.pdf · Kinetochore Microtubules and Plus-Ends From Electron Tomography Volume Ming Jiang, Qiang

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 7, JULY 2006 2035

Automated Extraction of Fine Features ofKinetochore Microtubules and Plus-Ends

From Electron Tomography VolumeMing Jiang, Qiang Ji, Senior Member, IEEE, and Bruce F. McEwen

Abstract—Kinetochore microtubules (KMTs) and the associatedplus-ends have been areas of intense investigation in both cell bi-ology and molecular medicine. Though electron tomography opensup new possibilities in understanding their function by imagingtheir high-resolution structures, the interpretation of the acquireddata remains an obstacle because of the complex and clutteredcellular environment. As a result, practical segmentation of theelectron tomography data has been dominated by manual oper-ation, which is time consuming and subjective. In this paper, wepropose a model-based automated approach to extracting KMTsand the associated plus-ends with a coarse-to-fine scale schemeconsisting of volume preprocessing, microtubule segmentationand plus-end tracing. In volume preprocessing, we first apply ananisotropic invariant wavelet transform and a tube-enhancingfilter to enhance the microtubules at coarse level for localization.This is followed with a surface-enhancing filter to accentuate thefine microtubule boundary features. The microtubule body is thensegmented using a modified active shape model method. Startingfrom the segmented microtubule body, the plus-ends are extractedwith a probabilistic tracing method improved with rectangularwindow based feature detection and the integration of multiplecues. Experimental results demonstrate that our automatedmethod produces results comparable to manual segmentation butusing only a fraction of the manual segmentation time.

Index Terms—Electron tomography, image enhancement, mi-crotubule, model-based segmentation, plus-end.

I. INTRODUCTION

M ICROTUBULES are long, tube-shaped (25 nm in diam-eter) protein polymers that are essential in all eukary-

otic cells. They form the skeleton of cells and serve as the in-tracellular network for protein transportation. More importantly,the microtubules attach to chromosomes via kinetochore and in-teract with kinetochore to drive the movement of chromosomesduring mitosis. The behavior of microtubules, thus, has been anarea of intense investigation in both cell biology and molecularmedicine. For example, a direction in anti-cancer drug devel-opment is to disrupt microtubule dynamics to stop cells fromproliferating [23]. Though it has been known that the dynamics

Manuscript received December 13, 2004; revised September 30, 2005. Thiswork was supported in part by the National Institutes of Health under GrantGM066270 and Grant RR01219 and in part by the Wadsworth Core Facilityfor Electron Microscopy. The associate editor coordinating the review of thismanuscript and approving it for publication was Dr. Gaudenz Danuser.

M. Jiang and Q. Ji are with the Department of Electrical, Computer andSystem Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 USA(e-mail: [email protected]).

B. F. McEwen is with the Wadsworth Center, New York State Department ofHealth, Albany, NY 12201 USA.

Digital Object Identifier 10.1109/TIP.2006.877054

Fig. 1. Left: Microtubules, indicated by arrows, are embedded in noise andsurrounding cellular materials. Right: Close view of a microtubule with plus-endindicated by arrow.

of the microtubules is related to the structure of their filamen-tous ends embedded in kinetochore (called the plus-ends) [17],a precise understanding of the functions of microtubules andthe plus-ends has not been obtained yet due to the limitationof previous experimental methods. One research strategy is tocreate a database of high-resolution structural maps of KMTs(microtubules embedded in kinetochore) during different stagesof mitosis. Statistical analysis can then be performed on suchdatabase to correlate the microtubule conformations with theirfunctions.

Recently, the application of electron tomography by struc-tural biologists has opened up new possibilities of imaging high-resolution structures of cellular components [25], [28], [34],including KMTs and their plus-ends [30], [38]. Unfortunately,in the low-contrast tomography volume, the interpretation ofthe data remains challenging since the KMTs and plus-end fea-tures are in close contact to the cellular context and are denselysurrounded by proteins of similar appearance, as shown inFig. 1. Consequently, practical segmentation of the tomographyvolume is dominated by manual operation, which is subjectiveand time consuming, even with the help of softwares suchas IMOD [19] and Sterecon [29]. Therefore, improving theaccuracy and efficiency of volume segmentation and reducingthe subjectivity will have enormous impact on the study ofmicrotubules.

Though the automatic segmentation of microtubules is a newapplication, the segmentation of biological structures from elec-tron tomography has already received some attention. Shen et al.[42] reported an algorithm for the segmentation of filamentousstructures by propagating manually segmented features acrosssuccessive slices. The segmentation is not robust since in eachslice it uses two-dimensional (2-D) features only. As a result,periodic manual segmentation is often needed. Bartesaghi et

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2036 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 7, JULY 2006

al. [5] developed a geodesic active contour for the semi-auto-matic segmentation of features in cellular electron tomography.A point inside cell features is required to initialize the algo-rithm. Bajaj et al. [4] proposed two procedures for cell tomo-graphic images: 1) gradient vector diffusion followed by fastmarching for boundary segmentation and 2) gradient vector dif-fusion followed by tracing for skeletonization. While their workpresents reasonable results, the tracing does not aim at providingaccurate geometry parameters of the individual filaments and,hence, is working at a different resolution level than our appli-cation. Normalized cut [12] and watershed [48] have recentlyalso been applied to the segmentation of electron tomographydata. While normalized cut is advantageous as a global opti-mization process, it has difficulty in incorporating high-level do-main specific constraints other than spatial proximity and graylevel similarity. Though the results of [48] are visually pleasing,the watershed method produces clusters of structures withoutfurther extracting the smaller objects. Such segmentation is suit-able for visualization, but is less useful for quantitative analysisthat requires concise representation of the individual objects inthe image. Another important object identification technique inelectron tomography is template matching [6], [16]. However,template matching usually requires higher resolution, and, thus,it is not applicable to our problem because at this time cellulartomography does not have sufficient resolution to identify sub-units of the microtubules or any other filaments.

Outside the field of electron tomography, many techniqueshave been developed in medical imaging for the segmentationof similar tubular structures such as blood vessels. Frangi et al.[14] developed a three-dimensional (3-D) parametric de-formable model consisting of a central vessel axis coupled toa vessel wall surface. The curve and surface models are repre-sented with B-spline. Yim et al. [49] used a tubular deformablemodel that is able to avoid self-intersection of the vessel sur-face. Both Frangi’s and Yim’s methods define energy functionsbased on vessel boundary features. This can be problematicwhen there are severely missing boundaries or clutters nearby,which happens frequently in our electron tomography data sets.

Several geometric deformable models [9], [27], [46], [47]have also been proposed for the segmentation of thin tubularfeatures. As these pure data-driven deformable models are un-able to converge correctly when image quality is poor, statisticalshape constraints have been incorporated to make the segmen-tation robust [26], [41], [45]. While the advantages of geometricdeformable contours are more obvious for high dimensions andcomplex topologies, the construction of statistical shape modelbecomes very difficult in this situation.

Tracing approaches start from a known point and recursivelyperform local analysis along the longitudinal direction to tracethe whole structure. In [1] and [7], the image is not preprocessedand the tracing is guided by a template based on the cross-sectional profile of the target structure. This makes the tracingefficient but sensitive to significant morphology and intensitychanges along the structures. In [35], an interactive tracingmethod was developed. The elongated features in the image arefirst detected using a second order operator. A graph-searchingalgorithm is then used to obtain globally optimal tracing be-tween user-defined control points. A common problem with

Fig. 2. Flowchart of the automated extraction scheme.

most tracing methods is that their automatic initialization is dif-ficult when applied to the noisy electron tomography volume.

Hough transforms are widely used in detecting line skeletons[24] and curves [43]. However, because of the overlapping ir-relevant structures with similar gray level appearance in the to-mography volume, the Hough detection will be less reliable dueto insufficient accumulation of feature evidence. Besides, theHough transform also has high computation cost for line detec-tion in 3-D.

It is apparent that no single existing method alone can handlethe segmentation of the tubular KMTs and the filamentous plus-ends. The successful segmentation requires the systematic com-bination of multiple methods and the incorporation of domain-specific prior knowledge into the segmentation procedures. Inthis paper, we propose a model-based automated approach toextracting the KMTs and the plus-ends with a coarse-to-finescale scheme consisting of volume preprocessing, microtubulesegmentation and plus-end tracing. The procedures of this auto-mated extraction scheme are shown in Fig. 2. In volume prepro-cessing, we first apply an anisotropic invariant wavelet trans-form and a tube-enhancing filter to enhance the microtubulesat coarse level for centerline extraction. We then use a surface-enhancing filter in the localized volume to accentuate the finemicrotubule boundary features. The tubular body of the micro-tubule is obtained with a modified active shape model (ASM)method [8] that incorporates the prior knowledge about micro-tubule shape. Starting from the end of the microtubule body,the plus-ends are extracted with a probabilistic tracing method.In designing the automated segmentation procedure, we havemade contributions by fully taking advantage of the prior knowl-edge about the unique geometric and photometric propertiesof KMTs and the plus-ends. First, we make the wavelet ad-vantageous for the enhancement of anisotropic features in low-contrast image by using anisotropic basis and realizing invarianttransform. Second, we use the eigenvalues of the Weingartenmatrix to construct the 3-D enhancing filters to provide better lo-calization of tubular and surface features in the low-contrast to-mography volume. Third, in plus-end tracing, we use a movingrectangular window for feature detection to improve the robust-ness against clutters and gaps. We also incorporate both geo-metric cue and intensity cue to improve the likelihood estima-tion in the particle filter based tracing procedure.

The automated approach has been applied to kinetochoretomography volumes acquired with the electron microscopyfacilities at Wadsworth Center, New York State Department ofHealth, Albany. Quantitative study shows that the microtubules

JIANG et al.: AUTOMATED EXTRACTION OF FINE FEATURES 2037

segmented with automated approach are in close agreementwith those produced by manual segmentation and using onlya fraction of the time of the latter. The automated tracing alsoreliably characterizes the shape variabilities of the plus-ends.

The remainder of this paper is organized as follows. In Sec-tion II, we describe the image acquisition procedure and ourautomated approach to extracting microtubules and plus-endsfrom the tomography volume. In Section III, we present the ex-perimental results and evaluations. We then conclude with sum-mary and conclusions in Section IV.

II. MATERIALS AND METHODS

A. Sample Preparation and Electron Microscopy

PtK1 cells were grown on sapphire disks and prepared byhigh-pressure freezing and freeze substitution as described in[31]. Briefly, after high-pressure freezing the cells were placedin acetone with 0.5% glutaraldehyde and 0.1% tannic acid andmaintained at 90 C for 24 h. The specimens were then rinsedwith acetone and transferred to acetone with 1% OsO4 and0.1% uranyl acetate, all at 90 C. After 24 h, the specimenswere slowly brought to room temperature, rinsed with acetoneand embedded in Epon. Serial sections were cut at a thicknessof 140–250 nm and post stained with lead citrate and uranylacetate.

Electron microscopy was performed on a LEO 910 EM and/oran FEI Tecnai F20. Specimens were preselected from low-mag-nification 2-D images for distinct kinetochores with a robustnumber of microtubules oriented roughly parallel to the planeof the section. Dual axis tomographic tilt series were collectedusing the cosine tilt scheme with a zero-degree angular intervalof 1.5 or 2.0 , and a total angular range of 120 –140 [33].The microscope magnification (16 kX) was chosen to providea 1.6-nm pixel size in the projection images (1.6-nm voxel sizein the reconstructed volumes). Tilt-series images were collectedusing automated collection schemes that minimize exposure tononimaging electrons. However, since stained plastic sectionsare relatively stable to the electron beam (compared to frozen-hydrated specimens), tilt series images were recorded with suffi-cient electron dose so that signal-to-noise is not a limiting factor[33], [51]. Rather, interpretability is limited by specimen com-plexity, and the high background staining that occurs because ofthe minimal amount of cytoplasmic extraction in well-preservedspecimens.

Tomographic reconstructions were computed using a combi-nation of the SPIDER [15] and IMOD-ETOMO software pack-ages [19]. Alignment of the tilt images was accomplished usingcolloidal gold particles as fiducial markers, and the three-dimen-sional (3-D) reconstruction was computed using the modifiedback projection algorithm [32], [40]. The resulting 3-D volumeswere viewed as ortho slices from all three axes.

B. Volume Preprocessing

The volume preprocessing is performed in two phases to ac-centuate the microtubules, while attenuating noise and irrele-vant structures. In the first phase, we combine an anisotropicinvariant wavelet transform with a tube-enhancing filter to en-hance the microtubules at coarse level. Based on this coarse en-

hancement, the microtubules are localized by extracting theircenterlines. In the second phase, we apply a surface-enhancingfilter to the localized volume to accentuate microtubule bound-aries and plus-ends features at fine scale to enable subsequentsegmentation.

1) Anisotropic Invariant Wavelet Filtering: In the tomog-raphy volume, the microtubule features are so weak locally thatany general averaging denoising technique will easily smoothout the microtubules completely. While wavelet transformshave been well recognized in electron microscope domain[2], [44], [50] for their strong ability of reducing noise andpreserving useful image features, traditional wavelet transformsuse an isotropic basis that is not particularly designed to en-hance highly anisotropic image features. Nonlinear anisotropicdiffusions [2], [11], the other family of well known filteringtechniques, seem to be good alternatives with their adaptive-ness to image structures. However, they are not suitable forour application either, because as semi-local methods, they aresensitive to clutters and cannot utilize the global anisotropyof the microtubules in the reconstructed crowded cellularenvironment.

This motivates us to apply wavelet transform with anisotropicbasis to enhance the microtubules globally, since the waveletwith anisotropic basis is more advantageous than the waveletwith isotropic basis in preserving the elongated microtubule fea-tures while removing noise and isotropic features.

To explain this mathematically, we start with a one-dimen-sional (1-D) orthogonal wavelet basis

(1)

where is the integer set. The anisotropic basis functions forhigher dimension then can be constructed by the tensor productof such 1-D wavelet basis functions. For example, the basisfunctions for 2-D wavelet transform can be obtained as the fol-lowing equation:

(2)

where , .The anisotropic basis, thus, has more combinations of dif-

ferent scales/frequencies along horizontal and vertical direc-tions. This makes anisotropic basis suitable for capturing objectwith different scales along different directions [37].

Even with anisotropic basis, we still need to deal with the lackof shift invariance of conventional wavelet, which will result inartifacts on inverse transform. In our application, to overcomethis problem, the wavelet transform is made shift invariant byaveraging over shifts, which can be expressed mathematicallyas

(3)

where is the shift invariant denoising process, is the noisyimage, is a set of shifts, is the average operation, is theshift operation, is the shift sensitive denoising operation.

To handle the microtubules located along arbitrary orienta-tions in the image, we use max over rotation instead of averageover rotation [50] since our goal is to enhance the tubular fea-


Fig. 3. Enhancement of synthetic volume data set with various wavelet transforms: (a) 3-D visualization of the volume including tubes of various lengths andorientations, with one slightly out-of-plane tube; (b) a sectional view of the volume, the bottom feature is the intersection of the out-of-plane tube with the planethat passes the other four tubes on (c) the top image corrupted with Gaussian noise; (d) enhanced with anisotropic invariant wavelet; (e) from another sectionalview, the top is the out-of-plane tube embedded in noise, the bottom is the corresponding enhanced image; (f) result with isotropic invariant wavelet; (g) resultwith noninvariant anisotropic wavelet.

tures to the best, without preserving other image features. Themax operation is expressed as

(4)

where is the rotation invariant denoising operator, is a setof angles, is a rotation operator. The image is rotated by aset of angles and denoised with shift invariant operator at eachangle. The denoised images are then rotated back to the orig-inal orientation and the resultant image is obtained by keepingthe maximum values of the pixels across the corresponding po-sitions in the images.

In practice, we process the 3-D tomography volume in aslice-by-slice manner using 2-D wavelet transform, which ismuch more computation efficient than the true 3-D invarianttransform. With the sample preparation and imaging proceduredescribed in Section II-A, the microtubules in the tomographyvolume are roughly parallel to the 2-D - plane. This makesthe slice-by-slice wavelet filtering sufficient to capture themicrotubule features.

Fig. 3(a)–(e) demonstrates that the anisotropic invariantwavelet transform can enhance elongated features with var-ious orientations and lengths, including slightly out-of-planefeatures. The comparison among Fig. 3(d)–(g) indicates thatboth invariance and anisotropy of the wavelet are importantfor the enhancement. Fig. 5(b) shows the enhancement ofthe tomography image with the anisotropic invariant wavelettransform. Symmlet 8 basis was used to produce the result inFig. 5 and the results in Section III. The wavelet threshold valuewas chosen as two percent of the maximum magnitude of thetransform coefficients.

2) Three-Dimensional Tube-Enhancing Filter: Afterwavelet filtering, the microtubules are still embedded in thelow-contrast volume. In this situation, it is difficult to useintensity-based methods to further enhance the desired fea-tures. Therefore, we enhance the microtubules with a 3-D tubeenhancing filter by exploiting the local tubular properties of mi-crotubules with the eigenvalues of the Weingarten matrix [36].

Consider the hyper-surface associated with the3-D volume intensity described by

, the Weingarten matrix is expressed as

(5)

with first fundamental form

(6)

and second fundamental form

(7)

where subscript denotes image derivative, which we computerobustly using a cubic fitting model [21] rather than convolvingthe image with derivative Gaussian kernel [13].

Let , , be the eigenvalues of the matrix with, and be the corr,esponding eigen-

vectors. The eigenvalues are the curvatures of the hyper-surface.For bright tubular structures against dark background in 3-Dimage, it can be assumed that is small, while bothand have large magnitude and negative signs. Based onthis knowledge, we design the following filter to producemaximum response to voxels on the centerline of a tubularobject [see (8), show at the bottom of the page] where localshape measure indicates cross-sectional

circularity, and indicates elongation.

is used to suppress weak backgroundfeatures. , , and are thresholds selected experimentally:both and are set to 0.5, is set to half of the maximum

in the image. By calculating the output value of this filter ateach voxel, we can selectively enhance tubular structures andattenuate other structures.

if or

else (8)


Fig. 4. Enhancement with tube-enhancing filter and surface-enhancing filter on synthetic data. (a)–(d) Enhancement of tubular feature with the tube-enhancingfilters. (a) The original image contains a tubular object and an isotropic object, (b) noise added, (c) enhanced with our method, and (d) enhanced with the Hessianbased method. Our filter not only accentuates the object centerline significantly but also attenuates other morphology more effectively. (e)–(g) Surface enhancement.(e) The cross-sectional view of a cylinder with contrast variations along the boundary, (f) the image contaminated with Gaussian noise, and (g) boundary obtainedwith surface enhancement.

Fig. 5. Sample enhancement result. (a) The original image. (b) Enhanced with the wavelet filtering: Most of the background image structures are removed, withthe white tubular features corresponding to microtubules. (c) Enhanced by applying the tube-enhancing filter to (b). (d) Microtubule centerlines extracted basedon image in (c).

Fig. 6. Top row: Cross-sectional images of the localized microtubule volume.Middle row: Enhanced with our surface-enhancing filter. Bottom row: Enhancedwith the surface-enhancing filter based on the Hessian matrix.

Fig. 4(a)–(d) compares the enhancement of synthetic imagewith our filter and the Hessian based filter [13], with our filtershowing superior performance for enhancing elongated featuresand attenuating irrelevant objects. Fig. 5(c) illustrates the en-hancement of the microtubules with our tube-enhancing filter.Compared with Hessian matrix based filter, our filters based onWeingarten matrix are less sensitive to contrast variations andprovide better localization. This is better illustrated in Fig. 6.

3) Microtubule Localization: We localize the microtubuleby extracting their centerlines in the enhanced volume, exploitingthe property of tubular structures. Our method is similar to[3], but it requires neither seeding points nor given tracingdirections. Specifically, the centerline extraction consists of:

• finding local maxima at each foreground voxel againstits eight neighbors in the local normal plane defined in3-D by the eigenvectors and , perpendicular to theprincipal direction defined by ;

• forming centerlines by connecting the neighboring localmaxima voxles;

• in the end, only long centerlines are kept as reliable refer-ences for localization of the microtubules, while center-lines too short are discarded; in practice, we choose thediscarding threshold as half of the length of the longestcenterline in the volume.

Fig. 5(d) illustrates the extracted centerlines that are finallyused to localize the volume containing each individual micro-tubule. Fine feature enhancement are then performed on theselocalized volumes, as described in Section II-B4.

4) Three-Dimensional Surface-Enhancing Filter: In pre-vious steps, most of the fine features are smoothed out as theprice of enhancement for localization at a large scale. In thisstep, we enhance the localized volume at a finer scale witha surface-enhancing filter, since the microtubule boundariesand the plus-ends can be characterized as surface patches orfilamentous sheets.

With the Weingarten matrix and its eigenvalues calculated inthe same way as in Section II-B2, for voxel on the microtubulewall, ideally, it can be assumed that is small, is slightlylarger than while is significantly larger than and

. However, in practice, since the wall surface can be locallyflat and, thus, and are approximately the same, assuming

will produce bias towards surface of high curvature.Therefore, we design the following filter using only the largestand the smallest eigenvalues to estimate a voxel’s likeliness tobe on a bright surface morphology [see (9), shown at the bottomof the next page] where . , and have thesame meaning as in (8). and are also selected to have thesame values as in (8).

Figs. 4(e)–(g) and 6 demonstrate the efficacy of the surface-enhancing filter on synthetic data and real data respectively.


Fig. 7. Effect of individually varying the first three modes of the microtubulecontour model.

C. Segmentation of Microtubule Body With Active ShapeModel

The segmentation in this step is to obtain the surface mor-phology of the microtubule main body and also provide thestarting points for subsequent plus-ends extraction. We adaptASM [8] method for the segmentation to overcome the con-fusing image features and missing boundaries along the micro-tubules. The details about this modified ASM method can befound in our previous publication [22].

The shape statistics of the microtubule cross-sectional con-tour is obtained by applying principal component analysis to aset of manually annotated contours. First, all the training con-tours are interpolated to have the same number of boundarypoints and aligned using Procrustes method [18]. Second, themean shape , the covariance matrix and the eigensystem of

are calculated. Any shape in the training set can then beapproximated using the mean shape and a weighted sum of theprincipal components

(10)

where is a matrix whose columns are the unit eigenvectorsof corresponding to the large eigenvalues, and is a vectorof weights for the eigenvectors. By varying the parameters in

within suitable limits, only new shape similar to those in thetraining set will be allowed to be segmented.

In our application, we build the microtubule contour shapemodel with 300 manually annotated training contours, each withabout 40 boundary points resampled up to the same number.Ninety percent shape variation is selected to be captured bythe statistical model. Fig. 7 demonstrates the valid shapes byvarying the first three modes of the shape model.

The microtubule boundary in the image is then searched alongthe normals of the model in the cross-sectional slices for thepoints with maximum value given by (9), with constraints im-posed by (10). In [22], we have improved the shape searchingwith a weighted fitting in the cross-sectional slices and a Kalmanfiltering to utilize the longitudinal smoothness along the micro-tubules. The ASM modified in this way is robust against missingdata and outliers frequently present in the kinetochore tomog-raphy volume.

To initialize the ASM model, the rough microtubule contoursas shown in Fig. 6 are located using Hough transform basedcircular shape detection, the computation cost of which is af-fordable in the subvolume. The positions of the detected circlesare correlated across the slices to eliminate false detections. TheHough transform also provides the stopping locations for ASMby detecting the ends of the microtubule, which is difficult to de-termine precisely using centerline extraction alone as discussedin [3]. Between the two ends of the microtubule, circles are de-tected consistently. Outside the end points, the circles are de-tected randomly. Fig. 13 shows the segmented microtubule bodywith the ASM method. The segmented microtubule body pro-vides the starting point to trace the plus-ends with the methoddescribed in Section II-D.

D. Probabilistic Plus-Ends Tracing

The heavily cluttered cellular environment makes it difficultto use data-driven deformable models for plus-end segmenta-tion. It is also not straightforward to model plus-ends using sta-tistical methods since they have various lengths and large shapevariabilities. On the other hand, the fact that the plus-ends arefilamentous features connected with microtubule body suggeststhe usage of tracing for the segmentation task. To this end, wedesign a probabilistic plus-end tracing method in the frame-work of particle filtering, which has been proven to be adept attracking in the presence of complicated likelihood functions andnonlinear dynamics. It has also been recently applied success-fully to interactive contour extraction and road detection [39].We improve the robustness of the particle filter based tracingby integrating geometric cue and intensity cue within a movingrectangular probing windows, instead of the point-wise gradient[39]. The rectangular window also makes the tracing robustagainst gaps.

In the sections to follow, the radial slicing of the localizedvolume and the initialization of the tracing are first described.The probabilistic framework for the tracing is then formulatedwith particle filtering. Details are then given on the integrationof multiple cues for likelihood estimation.

1) Radial Slicing of Localized Volume and Initialization ofTracing: When the lateral molecular force bounding the fila-ments of the microtubule is too weak, one end of the tubularstructure becomes plus-end, breaking into protofilaments radi-ally extending away, as illustrated in the left image in Fig. 8.As the result of the force balance among the molecular mate-rials, the ideal plus-end protofilaments are shown to be planarfilamentous with curvatures varying with their widths [20].

In kinetochore volume, the plus-end protofilaments havemore irregular conformations due to the interference fromthe kinetochore attachment, which makes accurate segmen-tation very difficult. However, instead of obtaining a perfectsegmentation of the protofilaments, our goal is to obtain their

if or

else (9)


Fig. 8. Left: Ideal plus-end filaments. Middle: Cross-sectional view of theradial slicing. The circle represents the microtubule. The cutting planes areperpendicular to the paper. Right: A sample radial slice (enhanced feature), thestarting points for subsequent tracing are indicated by the bright spots on themicrotubule wall.

approximation for the classification of the plus-ends, which de-pends mostly on the in-plane morphology of the protofilaments[30], [38]. It is, therefore, sufficient to trace the part of theprotofilaments intersected with the radial slices passing throughthe axis of the microtubules. This is further justified by anotherobservation: The protofilaments in the tomography volume arediffused and wider laterally that makes it less likely to miss afilament in radial slicing. Compared with tracing in 3-D, tracingin such 2-D plane leads to robust performance since the adverseinfluence from other structures is significantly decreased.

The radial slicing is performed around the microtubule as il-lustrated in the middle of Fig. 8. The regions beyond angularrange [ 60 :60 ] have lower signal-noise-ratio due to the lim-ited projection angles of the tomography process. To be conser-vative, we limit the radial slicing within [ 40 :40 ]. With 13or 15 protofilaments for each microtubule, there are about sixor seven protofilaments within [ 40 , 40 ]. Therefore, the an-gles of are enough for sam-pling the protofilaments. We have also tested with finer angularslicing, but it does not influence the final plus-end classification.

Given a segmented microtubule, the center of the radialslicing is chosen as the centroid of the microtubule contoursnear to the tube end. In each radial slice, the starting point anddirection of the tracing is selected on the end of the microtubulebody, illustrated in the right of Fig. 8. The tracing is selectedtowards the direction of large microtubule contour deformation.

2) Plus-End Segmentation as Probabilistic Tracing: Werepresent the plus-ends under tracing with an ordered sequence

, where are random points in theimage plane. The tracing is then to grow this sequence basedon prior dynamics and a data model , where is theobserved image data.

The point sequence is then modelled with a second order priordynamics

(11)

The a prior density on is

(12)

Assuming measurement on is an independent processthen

(13)

where denotes the measurement locations in the image plane,denotes the likelihood when is on the curve, denotes

the likelihood when is not on the curve.Using Bayesian rules, the posterior density on is de-

rived up to a multiplicative factor independent of

(14)

where denotes the point wise likelihood ratio.The tracing relies on the computation of the posterior density

based on the following recursion derived from (14)

(15)

Although we may have analytical expressions for the priorand the likelihood, the recursion in (15) cannot be computedanalytically since there is no closed-form expression for theposterior distributions. Instead, the posterior distribution canbe propagated using Sequential Monte Carlo methods [10]. Inthis framework, the posteriors are approximated by a finite set

of samples or particles

(16)

where denotes the Dirac delta measure and denotes theimportance weight attached to particle .

At each iteration, the weights are chosen using importancesampling. As it is difficult to draw samples directly from theposterior , we draw the samples using the prior densityas the proposal function. The weights, thus, are given by thelikelihood [10]

(17)

where is the position predicted based on prior dynamicsdescribed in Section II-D3.

In summary, the particle filter based tracing consists of thefollowing steps.

1) Initialization with starting points .2) Importance Sampling Step. For each particle ,

do:a) predict the next position using prior dynamics;b) evaluate the weight based on likelihood at

, as described in (17).


Fig. 9. Illustration of the rectangular probing window for shape cue estimation.Enclosed in the window are both desired features and clutters.

3) Selection Step. Select the most probable next point usingMAP estimate, according to the normalized importanceweights . Go to step 2.

In our application, we choose the prior dynamics to be spec-ified by the direction change at a given point . Given normaldistribution , the next point is predictedas

(18)

where is a rotation matrix

(19)

In implementation, – particles are used andis tuned to be 15 . The remaining task is now to incorporateappropriate cues in the likelihood term.

3) Image Likelihood Combining Shape and IntensityCues: While the probabilistic framework is powerful forrobust tracing, its success depends largely on the appropriatefeatures to use in tracing. In our application, we use both shapeand gray level intensity information in rectangular probingwindows determined by the current point and the predictedpoint. The shape cue is derived from images processed with 3-Dsurface-enhancing filter, as shown in Fig. 11(c). The gray levelintensity cue is the intensity similarity between the plus-endfeature and the microtubule body, with intensity value fromthe denoised image as shown in Fig. 11(b). These two types ofinformation are complementary to each other. For example, atbranches the shape cue is weak but intensity cue is still strong.The estimation with the two type of cues are finally combinedto provide the likelihood ratio . In contrast, [39] uses gradientinformation only that may not be able to distinguish usefulfeatures from clutters with high gradient.

Shape CueThe shape cue indicates how well the orientation of the cur-

rent probing window is supported by the underlying image fea-ture in the window. The probing window is illustrated in Fig. 9.The length of the window equals the step length of the tracingalgorithm (tuned as 6) so that the plus-end curve can be approx-imated as line segment within the window. The width is chosento be half of the length. This rectangular window allows morereliable feature estimation than an isotropic window.

Let a line passing the window along the direction be de-scribed by

(20)

Fig. 10. Typical histogram of voxel intensities on microtubule body.

where and is the distance from the line to theorigin.

Within the window, for each image point ,the distance from this point to the origin is

(21)

Then, a line can be fit along direction by minimizing theweighted fitting error

(22)

where is the weight decided by the magnitude of the point inthe enhanced image.

From this, we obtain

(23)

The contribution of shape information to the likelihood ratiois then modelled using the line fitting residual

(24)

where is a parameter selected experimentally.Gray Level Appearance SimilarityTo calculate this likelihood term, the distribution of the gray

level intensity on the microtubule body is first sampled auto-matically once the microtubule body is segmented in previousstep. A sample histogram is shown in Fig. 10. A normal dis-tribution is then estimated automatically using theintensity values of the points on the microtubule surface. In thisway, we take into account the intensity variations among themicrotubules introduced by specimen preparation and imagingprocess.

In each probing window, the contribution of intensity simi-larity to likelihood ratio is given by

(25)

where denotes the average intensity in the probing window.


Fig. 11. Illustration of the effect of our tracing algorithm. (a) Original radial slice; (b) denoised image corresponding to image in (a); (c) enhanced imagecorresponding to (b); (b) and (c) are sliced from the volume after the denoising and the enhancement; (d) traced with shape cue only; (e) traced with both shapeand intensity cue; (f)–(h) tracing results capture the shape changes of the plus-ends across the other radial slices in the same volume, respectively.

The entire likelihood ratio is then produced by combining thetwo individual likelihood terms as

(26)

Fig. 11(d) and (e) illustrates the efficacy of the multiple cues.In Fig. 11(d), the algorithm fails to trace the left protofilamentfeature since only shape information is used, which is very weakfor the left protofilament. In this case, the intensity similarity cancompensate shape information, as shown in Fig. 11(e).

From Fig. 11(f)–(h), it can be seen that the tracing success-fully captures the plus-end conformation changes in differentradial slices in the same volume. This is quite difficult forhuman operators as it is too tedious to manually perform thistracing process, which requires precise localization of micro-tubule, careful rotation of the volume and examination of toomany slices.

III. RESULTS AND EVALUATION

A. Experimental Results

In this section, we present sample enhancement and segmen-tation results. First, we show the enhancement of tomographyvolumes with multiple micotubules. We applied our method tothree volume data sets with dimension of 300 300 60 asshown in Fig. 12. The volumes are preselected from larger vol-umes by manually choosing the bounding boxes. The micro-tubules are not obvious in the raw volumes since they are buriedin noise and surrounded by numerous cellular materials. Thevolumes are first filtered with wavelet transform in a slice-by-slice manner as described in Section II-B1. To achieve rotationinvariance, each slice is rotated over eight angles only in the

- plane. After the anisotropic invariant wavelet filtering, theprocessed slices are stacked together to form 3-D volumes andare further processed with tube enhancing filter. It can be seenthat the microtubules stand out obviously after the enhancement.The enhancement results also demonstrate that our method canenhance the tomography volumes with various image qualityand contrast variations. Fig. 12 bottom row shows that the ex-tracted microtubule centerlines localize the microtubules in thevolume corresponding to the top row.

Segmentation is then performed around each localized mi-crotubule using the improved ASM method. The automaticsegmentation results and the manual results are compared inFig. 13. For illustration purposes, the images were magnified.

Fig. 12. Top three rows: Volumes with multiple microtubules. Left: Imagesrepresenting the original volumes, the first image is a projection of aoriginal volume and the last two images are slices of the other two volumes.Right: Enhanced volumes. Bottom row: Extracted microtubule centerlines seenfrom different views, corresponding to the volume in top row.

Apparently, the automatic results have much more smoothmorphologies, due to the consistency and robustness of theautomated method. The automatic method not only removes


Fig. 13. 3-D segmentation results. Left column: Original tomography volume.Middle: Manual segmentation. Right: Automated segmentation. Images aremagnified for better illustration.

the irrelevant structures in close contact with the microtubule,but also preserves the meaningful surface morphology details.In contrast, the manual method produces very rough surfacemorphology, which is less plausible biologically. Fig. 14presents more 3-D segmentation results of microtubules withvarious surface morphologies. It demonstrates that the auto-matic method can capture the morphological characteristics ofthe microtubules in spite of the cluttered image.

The plus-ends are then traced with the starting points pro-vided by the segmented microtubule body. Figs. 15 and 16 show

Fig. 14. Three-dimensional automatic segmentation reflects the morpho-logical characteristics of the microtubule. Each original slice is followed by thecorresponding volume segmentation.

Fig. 15. Extracted curled shape plus-ends connected with microtubulebody. Leftmost column: Plus-ends traced connected with microtubules. Rightcolumns: Selected original radial slices at angles of �20 , 0 , and 20 .

two sets of extracted plus-end features, which extend in 3-D ina highly ordered manner.

In the above experiments, we have used the same set of pa-rameters as specified in the previous sections and these experi-mentally selected parameters have been demonstrated to be suit-


Fig. 16. Extracted plus-ends of other morphologies.

able for different data sets. This robustness is due to the fol-lowing facts.

• Our method is designed to capture geometrical shapeinformation and is, thus, less sensitive to intensityvariations.

• The scale of the microtubule does not vary among dif-ferent volumes and the tubular shape remains stable eventhere are intensity changes.

For images with sizes varying significantly from those ofthe data sets used in this manuscript, it is always possible touse the same selected wavelet threshold value by scaling theimage sizes to those used in the manuscript. The tube-enhancingfilter and the surface-enhancing filter are robust and changes oftheir parameters do not impact performance significantly. Thetracing algorithm works best with the selected parameter values.Using other values tends to produce poor results. For example,a larger tracing step length cannot adapt to filaments’ shapechange flexibly, while smaller tracing step tends to fail at gaps.Since the scale of the microtubule structures does not vary andthe plus-end protofilaments usually do not change orientationabruptly, these selected tracing parameters can adapt to differentdata sets.

B. Evaluation

To quantitatively evaluate the performance of our automatedapproach, we use contour overlap ratio to compare the manualresults and the automatic results, which is defined as

(27)

with and as the areas enclosed by two contours. Largecontour overlap ratio means that the manual segmentation andautomatic segmentation are in good agreement with each other.

Fig. 17 is the quantitative evaluation of the typical segmen-tation of microtubules. For the poor quality subvolumes, theaverage overlap ratio is 0.75, indicating that the automatic re-sult and manual result roughly agree with each other. In addi-tion, the centroid of the contours segmented also indicates thequality of the segmentation. The automatic segmentation resultshave smooth centroid position change across the slices, whichindicates small shape variations among neighboring slices. Incontrast, the manual results have rough centroid change acrossthe slices, mainly due to the subjectivity and inconsistency ofhuman operator, which also causes most of the mismatches be-tween the two methods. For the subvolumes with better imagequality, the average overlap ratio increases to 0.85. The center-lines of the automatic result and the manual result also closelyfollow each other, without the systematic error shown in the re-sult for poor quality data. It can be seen that the automatic seg-mentation is consistent and reliable for both low-quality dataand good-quality data, while performance of manual segmenta-tion becomes significantly worse against low-quality data.

In our experiments with the limited number of data sets, weeliminated all false positives by using large threshold value atcenterline detection stage, considering that the microtubulesare much longer than the other features in the image. The truepositive rate is determined to be 80% by comparing the numberof the automatically detected microtubules with the number ofall the manually identified microtubules in the volume. Thoughit is tedious to manually delineate the fine morphologies of themicrotubules, it is much easier and reliable to inspect how manymicrotubules are present in the volume. Since the ultimate goalof this research is to make statistical analysis of a large numberof the segmented microtubules instead of one-by-one study,missing 20% of them is tolerable. The centerline thresholdingdoes not introduce bias into the subsequent statistical analysisbecause it does not systematically omitting shorter micro-tubules. Some microtubules appear shorter mainly because oftheir orientation and location in the windowed image. Duringthe corresponding biological stage, the complete microtubulesare actually much longer in the cell, as they extend from theequator of a cell to the two poles of a cell. Therefore, if thecenterline thresholding happens to remove some microtubules,these microtubules are not necessarily the physically shorterones.

The evaluation of the plus-ends results has been performedby visual inspection. The inspection has been conducted intwo ways. The first way is to compare the extracted plus-endfeatures with the patterns in the original slices. In Figs. 15 and16, a careful inspection indicates that the extracted featureshave corresponding patterns in the slices. It should be notedthat no tracing was performed in the regions corresponding tothe missing wedges of the electron tomography.

The other way to evaluate plus-end tracing is to inspectwhether the extracted morphologies agree with manual classi-fication of the overall plus-end features in a volume. In Fig. 15,the plus-ends in all the data sets were manually classifiedas curled plus-ends, a class of plus-ends with a ram’s hornconformation. It can be seen that all the automatically extractedplus-ends do have such overall conformations, with manyplus-end filaments curled downward smoothly.


Fig. 17. Evaluation of the segmentation results. Top row is the typical performance with poor quality subvolume such as the top two rows in Fig. 13; bottom rowis the typical performance with better subvolume such as the bottom two rows in Fig. 13. Left: the contour overlap ratio; middle: the x coordinate of the contourcentroid; right: the y coordinate of the contour centroid.

In Fig. 16, the plus-ends in the first two rows were manuallyclassified as forked plus-ends and the last one as blunt plus-end.However, our automated result indicates that the first row is ofcurled shape. This can be verified by studying the original ra-dial slices in the first row and the corresponding automatic indi-vidual result shown in Fig. 11(f)–(h). Though the plus-end fil-aments are forked in the first two radial slices, they are clearlycurled in the third radial slice, which is captured by the resultin Fig. 11(h). While the human operator may simply fail toexamine the slice containing the curled features, in biologicalstudy even a single curled plus-end filament is enough to decidethe overall classification of the plus-end.

The above analysis indicates that the automated plus-end ex-traction can provide valuable information for plus-end classifi-cation and can detect meaningful features overlooked by humanoperators.

Our automated method is also efficient. For example, on aPC with Pentium 4 processor, 2.0-G Hz, 512-M RAM and Win-dows XP platform, it takes 28 min for the program implementedin Matlab to enhance and localize seven microtubules in onevolume and 5 min to segment each microtubule and its associ-ated plus-ends. This means that it takes min in totalto extract each microtubule and its plus-ends.

IV. SUMMARY AND CONCLUSION

We have presented an automatic approach to extractingKMTs and plus-ends from electron tomography volume. Insolving the domain-specific problem, we have fully incorpo-rated the prior knowledge of microtubules into our model-basedframework. Our three-stage approach consists of microtubulevolume enhancement at coarse level, microtubule body segmen-tation, and extraction of plus-end as fine features. In volume

enhancement, an anisotropic invariant wavelet transform isapplied to globally enhance the microtubule features, followedby a 3-D tube-enhancing filter to capture the local geometricproperties of the tubular structure. A surface-enhancing filteris then used to accentuate the fine microtubule boundaries andplus-ends to enable subsequent segmentation. Our filters areconstructed to provide better localization that is important forfeature extraction in the low-contrast image. We then segmentthe microtubule body with an modified ASM method. Startingfrom the end of the segmented microtubule body, the plus-endsare extracted with a particle filter based tracing method. Toadapt the particle filter to plus-ends tracing, we have integratedmultiple cues in likelihood estimation. We have also performedthe feature detection with a rectangular window so that the algo-rithm is not sensitive to gaps. Experimental results demonstratethat the segmented microtubules are of comparable quality tothat of manual process but uses only a fraction of the time of thelatter. The automated method also robustly extracts plus-endsfeatures that provide valuable information for biological study.

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Ming Jiang received the B.E. and M.E. degrees fromthe Harbin Institute of Technology, Harbin, China, in1993 and 1996, respectively. He is currently pursuingthe Ph.D. degree in electrical engineering at Rensse-laer Polytechnic Institute, Troy, NY.

His current research interests include biomedicalimage analysis, computer vision, pattern recognition,image segmentation, and registration.

Qiang Ji (S’92–M’98–SM’04) received the M.S. andPh.D. degrees in electrical engineering from the Uni-versity of Washington, Seattle, and the University ofArizona, Tucson, respectively.

He is currently an Associate Professor with theDepartment of Electrical, Computer, and SystemsEngineering, Rensselaer Polytechnic Institute, Troy,NY, where he is also the Director of the IntelligentSystems Laboratory. Previously, he held visitingresearch positions with Carnegie Mellon University,Pittsburgh, PA, Western Research Company, and

the Air Force Research Laboratory. He has published more than 90 papers inpeer-reviewed journals and conferences. His research has been funded by localand federal government agencies including the National Science Foundation,the National Institutes of Health, AFOSR, Office of Naval Research, DARPA,and ARO, and by private companies, including Boeing and Honda. His areas ofresearch include computer vision, probabilistic reasoning for decision makingand information fusion, pattern recognition, and robotics.

Bruce F. McEwen received the B.S. and Ph.D.degrees in biochemistry from Cornell University,Ithaca, NY. He did postdoctoral studies with J. Frankat the Wadsworth Center, New York State Depart-ment of Health, Albany.

He subsequently took a position at the WadsworthCenter where he is currently a Research Scientist Vand Associate Professor of biomedical sciences in theGraduate School of Public Health, State Universityof New York, Albany. He has also held a visiting re-search position at the Lawrence Berkeley National

Laboratories, Berkeley, CA, and has studied at the Massachusetts Institute ofTechnology, Cambridge, MA. He has long standing interest in electron mi-croscopy, electron tomography, and the structure of function of microtubulesand the organelles with which they interact. His current research focuses onthe structure of the vertebrate kinetochore and its interaction with microtubules.He has published numbers papers in peer reviews journals, served as the GuestEditor for the Journal of Structural Biology, and organized two internationalconferences on electron tomography. His research is funded by the National In-stitutes of Health and the National Science Foundation.

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IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 15, NO. 7 ...qji/Papers/TIP_microtubule.pdf · Kinetochore Microtubules and Plus-Ends From Electron Tomography Volume Ming Jiang, Qiang