A pipeline for neuron reconstruction based on spatial sliding volume filter seeding

Research ArticleA Pipeline for Neuron Reconstruction Based on Spatial SlidingVolume Filter Seeding

Dong Sui1 Kuanquan Wang1 Jinseok Chae2 Yue Zhang1 and Henggui Zhang13

1 Biocomputing Research Center School of Computer Science and Technology Harbin Institute of TechnologyHarbin 150001 China

2Department of Computer Science and Engineering Incheon National University Incheon 402-751 Republic of Korea3 School of Physics amp Astronomy University of Manchester Manchester M13 9PL UK

Correspondence should be addressed to Kuanquan Wang wangkqhiteducn

Received 8 February 2014 Accepted 16 June 2014 Published 2 July 2014

Academic Editor Huiru Zheng

Copyright copy 2014 Dong Sui et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Neuronrsquos shape and dendritic architecture are important for biosignal transduction in neuron networks And the anatomyarchitecture reconstruction of neuron cell is one of the foremost challenges and important issues in neuroscience Accurate recon-struction results can facilitate the subsequent neuron system simulationWith the development of confocal microscopy technologyresearchers can scan neurons at submicron resolution for experiments These make the reconstruction of complex dendritic treesbecomemore feasible however it is still a tedious time consuming and labor intensity task For decades computer aided methodshave been playing an important role in this task but none of the prevalent algorithms can reconstruct full anatomy structureautomatically All of these make it essential for developing new method for reconstruction This paper proposes a pipeline with anovel seeding method for reconstructing neuron structures from 3Dmicroscopy images stacksThe pipeline is initialized with a setof seeds detected by sliding volume filter (SVF) and then the open curve snake is applied to the detected seeds for reconstructingthe full structure of neuron cells The experimental results demonstrate that the proposed pipeline exhibits excellent performancein terms of accuracy compared with traditional method which is clearly a benefit for 3D neuron detection and reconstruction

1 Introduction

Higher-order cognitive functions in anthropic brain areintricately linked with the processes of nervous system atdifferent biological levels (such as molecular level cellularlevel and system level) The morphological properties ofaxonal and dendritic arborizations are important aspects ofneuronal phenotypeThese properties assure the connectivityin the neuron network thereby facilitate the biological signalstransduction in nervous system [1] Therefore depicting thefunction and anatomy structure of neuron cell and networksis of great importance for understanding the way brainworks in modern neuron science [2] Furthermore greatunderstanding of the mechanism of nervous system can alsopromote drugs and therapies researching for neurologicaland psychiatric disease treating

Extracting neuron morphology from microscopic imagedata sets is a key point in neurology research Accurate and

efficient reconstruction protocol can facilitate the researcheson the function and anatomy structure of neuronal cells andnetworks Unfortunately manually reconstructing neuronstructure from microscopy image data sets is labor intensityand time consuming since the axonal arbors and dendriticare so complex in scale and structure Therefore developingnew computational methods for neuronal anatomy studyingis of particular importance in this context During the pastdecades lots of algorithms and software have been proposedfor this task but most of them achieved limited success

Since Cohenrsquos team proposed the first fully automated 3Dneuron tracing algorithm [3] a large number of approacheshave been published for handling the same task in theliterature Generally speaking these methods can be mainlycategorized as minimal path based tracing methods [4 5]minimum spanning tree methods [6 7] sequential tracingmethods [8 9] skeletonization methods [3 10] neuromus-cular projection fibers tracing methods [11ndash16] and active

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2014 Article ID 386974 8 pageshttpdxdoiorg1011552014386974

2 Computational and Mathematical Methods in Medicine

contour based tracing methods [17 18] In the minimal pathbased tracing methods algorithms were performed in imagesubregions instead of the entire image but these methodscannot extract the exact centerline of tubular structures suchas vessels and neuron fibers In the minimum spanning treemethods serious of critical seed points were detected firstlyand then the detected seeds were linked into tree representa-tion such as MDL-MST method and k-MST method [6 7]The sequential tracing methods were starting from a set ofseed points but the results of these methods were affected byforeground discontinuity such as gaps and holes and thesedefects required additional post- or preprocessing proceduresto overcome [8 9] The skeletonization methods mainlyrelayed on a point-spread function based protocol to tracethe neuron anatomy structure but they were also prone toproduce loops and spurs which needed extra postprocessingto smooth the noise [10] Active contour based methods wereparticularly attractive for neuron tracing and reconstructionwas themost employedprotocol for this task [17 18] Schmittrsquosgroup proposed the first active contour tracing method [17]in which the neuron skeleton was parameterized into a4D snaxels sets that was characterized by its location andradius [17] But this method needed to manually set somebranching ending and other critical points Vasilkoski andStepanyants [18] proposed a new method for optimizingthe tracing based on the active contours Following thatRoysamrsquos team proposed an open curve snake based tracingmethod which was broadly applied in this area [19] andit can allow fully automated processing and user controltracing but thismethod can only handle distinct edge neuronimages data sets and cannot get accurate neuron radiusin vague boundary [19] Beyond that there still are someautomated tracing tools such as Neuromantic [20] SimpleNeurite Tracer [21] NeuronJ [22] and a complete list of thetracing tools that can be founded in the survey paper ofMeijering [23]Howevermost of these tools still needmanualassistance to reconstruct the dendritic and axonal arborsTherefore automated 3D neurons anatomy tracing tools needa continuous improvement in the future time

Traditionally speaking the pipeline of tracing was initial-ized by a serious of preprocessing methods followed by acritical point detection procedure which was called seedingThen these points were linked by center line extractionmethod and finally radius estimation was applied to recon-struct the full structure [17] As depicted in Figure 1 the fullpipeline was organized in the work flow In this pipeline as akey step excellent seeding method can assure the accuracy ofthe following skeletonization There are two approaches forseeding (i) segmentation and (ii) filtering The first one isbased on a segmentation process inwhich the image volumescovered by the neuron were separated from tissue such asthree-dimensional thinning algorithm but this method issensitive to noise The second approach is using a filter toenhance the line elements Satorsquos [24] group proposed a 3Dmultiscale liner image filter to extract the critical propertyin medical images This method employed a combination ofeigenvalues in hessian matrix of image intensities Followingthis approach Pizerrsquos group proposed another method basedon the concept of cores that detected medial points of the

Images

Preprocessing

SeedingUser interaction

Correction Centerline extraction

Radius estimation

Manual fitting

Manual fitting

DataProcessing

Manually interactionWork flow

Figure 1 Work flow of neuron tracing pipeline

object by correlating opposite boundary points [25] Butmostof the seed points detected by thesemethods were distributedunevenly and located at noncritical position [19]

Radius estimation is another important part in thispipeline for it is essential for neuron system simulation [23]Pockrsquosmethodwas greatly accepted inmany tracing tasks andwas also used in this paper for the tube-like radius estimation

In this paper we proposed a new 3D image filter calledsliding volume filter (SVF) to enhance the 3D neuron imagedata sets and then the most listed voxels were chosen as thefinal seed pointsThen an open curve snake was employed toreconstruct the neuron anatomy structure Compared withtraditional seed detection method the SVF method couldimprove the accuracy of neuron anatomy structure in 3Dtracing Finally radius estimation was applied to the trace theresult for the future functional simulation And the rest ofthis paper was organized as follows data sets collection andmethod designwere illustrated in Section 2 the experimentalresults and discussions were presented in Section 3 andfinally the conclusions were drawn in Section 4

2 Methodology

Our works were greatly related to Roysamrsquos pipeline forneuron reconstruction which was based on open curvesnake tracing [19] In this paper a SVF was designed forseeding by enhancing the spatial tube-like regions and itcould provide seed points for the automatic initialization ofopen-snake models At last Pockrsquos method was applied forradius estimation [23]

SVFwas expanded from 2D sliding band filter (SBF) As itwas depicted in Quelhasrsquo work [26] the 2D SBF could detectrounded convex region in images It was firstly introduced fordetecting cell center in 2Dmicroscopic images [26] Recentlyour research group employed the SBF to detect cells in sectionimages of cat retinal [27] and another transformed SBF todetect insect cells in light field microscopic images [28] In3D volume data sets a rounded convex region was the sameas they were in 2D images in gradient vector distribution andwe called it spatial convex region

Computational and Mathematical Methods in Medicine 3

Figure 2 Test data Helix tube

Figure 3 Drosophila olfactory axonal data

21 Data Sets Used in This Paper In this paper we choosetwo kinds of data sets to validate our proposed seedingmethod Figure 2 shows a helix image volume data whichis a classical test data in neuron tracing [19] Figure 3 isdrosophila olfactory axonal image volume data and thisimage data set is firstly designed for single cell label andimage registration Both of these data sets were visualizedusing Ray casting algorithm in our work and all of the tracingalgorithms were performed on these volume data sets

22 2D Sliding Band Filter (SBF) To introduce SVF a conceptof 2D SBF is important for understanding The 2D SBFis a member of Convergence Index (CI) family and firstlyintroduced for detecting cell center in 2Dmicroscopic images[26] Unlike most of the liner filtersrsquo small support regions(119898 times 119898 pixels where 119898 isin 2 3 5 ) the SBF filter has alarger support region It has a band with fixed width supportregion whose position changes in each radius direction andthat allows the maximization of the average ConvergenceIndex in the bandwidth Figure 4 indicates the support regionin SBF and is defined as

SBF (119909 119910)

=

1

119873

119873

sum

rad=1max119877minlt119903lt119877max

(

1

Bw + 1

119903+(Bw2)sum

119903minus(Bw2)CI (rad 119899))

(1)

(x y)

rO

Rmin

Rmax

Bw

120572(120593rad n)

Figure 4 2D sliding band filter (SBF)

where

CI (rad 119899) = cos (120593rad minus 120572 (120593rad 119899))

120593rad =2120587 (rad minus 1)

119873

120572 (120593rad 119899) = arctan(Grad119899119862

Grad119899119877

)

(2)

where Grad119899119862

and Grad119899119877

represent the column and rowgradient at image position 119899 119873 represents the number ofsupport region lines irradiate from the center pixel (119909 119910) Bwrepresents the sliding band width 119903 represents the poison ofband center in the support region line ranging from 119877min to119877max and cos(120593rad minus 120572(120593rad 119899)) represents the angle betweenthe gradient vector at (120593rad 119899) and the direction of 120593rad

23 SVF Seed Detecting Before the SVF this part firstlyintroduces a concept of Spatial Convergence Index (SCI) seeFigure 5 Point 119874(119909 119910 119911) is the origin in 3D space and thecenter of support region 119877 Point 119901 is the voxel in supportregion119877 and its coordinate relative to119874 is (119894 119895 119896)The radiusof the support region 119877 is 119903 120601 represents the angle betweenthe gradient vector of 119875 and 119875119874 And the SCI of 119875 relative 119874is defined as follows

SCI119875119874(119894 119895 119896) = cos120593 (119894 119895 119896) (3)

Then the SCI of point 119874 in the support region iscalculated as

SCI119874=

1

119873

sum

119901isin119877

cos120593 (119894119901 119895119901 119896119901) (4)


r

L

M

r

2r

2r

2r

R

120601

O(x y z)P(i j k)

Figure 5 Scheme of spatial convergence index (SCI)

where119873 is the number of voxel in the support region119877 Basedon these concepts the SVF is defined as

SVF (119909 119910 119911)

=

1

119872 lowast 119875119899

times

119872minus1

sum

119904=0

119875119899

sum


(

1

119881119905+ 1

times

119903+(1198811199052)

sum

119903minus(1198811199052)

SCI119904119874119876(119902119909119903 119902119910119903 119902119911119903))

(5)

where

SCI (119909 119910 119911) = 1

119872 lowast 119875119899

119872minus1

sum

119904=0

sum

(119894119898119895119898119896119898)isin119877119904

cos120593 (119894119898 119895119898 119896119898)

(6)

where119872 represents the section in the support region 119877 119875119899

represents the support region line in the 119904th section and 119881119905

represents the thickness of the sliding volumeThe scheme ofSVF is depicted in Figure 6

Seed detection is a critical step before the tracing it canprovide seed points for automatic initialization of the open-snake models In this paper seed points are detected by SVFfilter voxel by voxel from the start position to the end positionin the volume data firstly and then candidate seeds are chosenif they are extreme in the normal plane of the vesselaxonDetected seeds are then sorted by the SVF response valuesfrom the largest to the smallest value and created a seed listfor tracing

z

r

y

xd

RminRmax

O

RadR support region

Rs sliding volume

Q(qxr qyr qzr)

Figure 6 Scheme of sliding volume filter (SVF)

24 Neuron Tracing Model Accurate neuron anatomy struc-ture reconstruction is an import task in neurology In thispart after initial points selection by the SVF filter anopen-curve snake model for neuron 3D tracing is used forreconstructing the full structure The open-curve snake is aparametric open curve model Let 119888(119904) = (119909(119904) 119910(119904) 119911(119904))119904 isin [0 1] and let the snake energy to be minimized as

119864total = int1

0

119864int (119888 (119904)) + 119864ext (119888 (119904)) 119889119904 (7)

where 119864int(119888(119904)) represents the internal energy for smooth-ness constraint

119864int (119888 (119904)) = 120572 (119904)1003816100381610038161003816119888119904(119904)1003816100381610038161003816

2+ 120573 (119904)

1003816100381610038161003816119888119904119904(119904)1003816100381610038161003816

2 (8)

where 120572(119904) and 120573(119904) represent the ldquoelasticityrdquo and ldquostiffnessrdquoin the snake respectively and

119864External = 119864im (119888 (119904)) + 119896 (119904) 119892119864str (119888 (119904)) (9)

where

nabla119864im = minusnabla119868GVF (119909 (119904) 119910 (119904) 119911 (119904))

nabla119864str (119888 (119904))

= minus

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 0

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 1

0 119904 isin (0 1)

(10)

In (8) 120572(119904) and 120573(119904) are ldquoelasticity coefficientrdquo and ldquostiffnesscoefficientrdquo respectively in internal energy and they embed-ded the regularity of the curve 120572(119904) was selected to be 0 for119904 isin [0 1] and set 120573(119904) was selected to be 0 at 119904 = 0 and 119904 = 1In (10) the external energy term is employed for making thesnake deform along the center line of the neuron fiber where


Figure 7 Thresholding seeds detection method

nabla119864im is the negative normalized gradient vector flow 119896(119904) isa weighted parameter 119890V

1(119888(119904)) is the first principal direction

of the Jacobian matrix and the nabla119864str(119888(119904)) is nonzero itemwhen it is located at the tail and the end pointing to the rightdirection of the snake

25 Radius Estimation In the following work to providemore detailed information for functional simulation theradius estimation is applied to each point on the snake aftertracing As shown in Figure 9 Pockrsquos method is applied forboundaries measurement to detect the tube edge [23] Theedge of the tube-like volume is119861 and it is defined as a circularcentered at 119874 which is a seed point shown in Figure 9Equation (11) describes the boundary as follows

119861 (119900 119903)

=

1

119873

119873

sum

119894=1

grad (119900 + 119903Vai) gmax (minusnabla119868GVF (119900 + 119903Vai) gVai 0)

(11)

where Vai = cos(ai)V1+ sin(ai)V

2is the radial vector in the

V1-V2plane of point 119874 on the snake and grad(119900 + 119903Vai) is the

gradient magnitude of the point on the circle The radius 119903 issampled in the circle by a certain angle distance and in thispaper the119873 is set as 8 in the radius circle

3 Results and Discussion

For all the image data sets the following parameters werechosen as the default setting by visual estimation of diameterin average radius of the neuron cross-section For seedsdetection parameter 119872 = 32 119875

119899= 32 was chosen

respectively the remaining parameters of SVF were chosenas 119881119905= 8 119877min = 10 and 119877max = 30 and the unit of all

parameters was ldquopixelsrdquo Comparison of test data sets seedingresults between threshold method and SVF method resultshas shown an excellent detection results of SVF method inseed detection Figure 7 shows a traditional threshold seeding

Figure 8 SVF seeds detection method

1

2

ai

O(x y z)

3 =cs(x y z)

cs(x y z)

nablaIGVF(O+ rai)

Figure 9 Illustration of the circular cross-section V3is the tangent

vector in point 119874 and V1and V

2are the two orthogonal vectors

defining the normal plane

method and there are some seed points that fall out of theedge of real Helix body which are headlight with red arrowsAnd Figure 8 is of the same perspective as Figure 7 and showsthat the SVF seeding method can detect most of the criticalpoints as candidate seeds After tracing from the detectingseeds points by SVF the whole structure of test data sets isgenerated accurately which are shown in Figure 10

When it is applied to real data sets the SVF seedingmethod can detect most of the critical seed points in the bodyof olfactory axonal shown in Figure 11 Threshold seedingmethod is not shown here for its poor results After specifyingthe branching points the tracing result of the open curvesnake is shown in Figure 12 and it clearly indicates that nearlyall of the anatomy structure is reconstructed after tracing

After tracing the full structure the radius of the olfactoryaxonal is estimated as a following-upprocedure for functionalsimulation As shown in Figure 13 the gray and black arearepresents the body of the olfactory axonal the green linerepresents the central line of the olfactory axonal and the


Figure 10 Tracing results by SVF seeds

Figure 11 SVF seed detection results for olfactory axonal

Figure 12 Open curve snake tracing results of olfactory axonal

blue ring represents the radius of each part from the centralline and it depicts that most of the radius is estimated bythe method Figure 14 exhibits a magnification of the redrectangle area in Figure 13 And another magnification of redrectangle area in Figure 14 is shown in Figure 15

In Figure 15 the width of olfactory axonal estimatedradius and center line are marked separately This task isfor the future functional neuronal simulation which is notdiscussed in this paper

4 Conclusion

In this paper a novel seeding method based on spatial SVF isproposed for neuron reconstruction frommicroscopic image

Figure 13 Radius estimation of olfactory axonal

Figure 14 Magnification part of olfactory axonal radius estimationin Figure 11

Width of neuron

Radius

Centerline

Figure 15 Magnification part of olfactory axonal radius estimationin Figure 12 and detail of radius estimation


data sets which were collected by confocal microscopy Theseeding results comparison shows that the SVF method candetect seed points accurately in test data sets and detectmost of the critical points in olfactory axonal data sets Afteropen curve snake tracing both of the data setrsquos structures arereconstructed from SVF seeds In the last part of our work aradius estimation method is applied to the tracing result forfuture functional simulation

Finally it is worth noting that this method can clearly bea benefit for seeding task in the protocol of neuron tracingHowever uneven illumination produced by a microscopeis also a critical factor influenced the seeding accuracyTherefore some illumination correction methods will bestudied to improve our method in the future works

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partly supported by National Nature ScienceFoundation of China (NSFC) Grant no 61173086 and theUniversity of Incheon International Cooperative ResearchGrant in 2012

References

[1] G A Ascoli ldquoNeuroinformatics grand challengesrdquo Neuroinfor-matics vol 6 no 1 pp 1ndash3 2008

[2] M F Bear B W Connors and M A Paradiso NeuroscienceExploring the Brain Lippincott Williams ampWilkins BaltimoreMd USA 3rd edition 2007

[3] A R Cohen B Roysam and J N Turner ldquoAutomated tracingand volume measurements of neurons from 3-D confocalfluorescence microscopy datardquo Journal of Microscopy vol 173part 2 pp 103ndash114 1994

[4] E Meijering M Jacob J-C F Sarria P Steiner H Hirling andM Unser ldquoDesign and validation of a tool for neurite tracingand analysis in fluorescence microscopy imagesrdquo Cytometry Avol 58 no 2 pp 167ndash176 2004

[5] H Peng Z Ruan D Atasoy and S Sternson ldquoAutomatic recon-struction of 3D neuron structures using a graph-augmenteddeformable modelrdquo Bioinformatics vol 26 no 12 pp i38ndashi462010

[6] X Yuan J T Trachtenberg S M Potter and B RoysamldquoMDL constrained 3-d grayscale skeletonization algorithm forautomated extraction of dendrites and spines from fluorescenceconfocal imagesrdquo Neuroinformatics vol 7 no 4 pp 213ndash2322009

[7] G Gonzalez E Turetken F Fleuret and P Fua ldquoDelineatingtrees in noisy 2D images and 3D image-stacksrdquo in Proceedingsof the IEEEConference on Computer Vision and Pattern Recogni-tion (CVPR 10) pp 2799ndash2806 San Francisco Calif USA June2010

[8] K A Al-Kofahi S Lasek D H Szarowski et al ldquoRapidautomated three-dimensional tracing of neurons from confocalimage stacksrdquo IEEE Transactions on Information Technology inBiomedicine vol 6 no 2 pp 171ndash187 2002

[9] S R Aylward and E Bullitt ldquoInitialization noise singularitiesand scale in height ridge traversal for tubular object centerlineextractionrdquo IEEE Transactions on Medical Imaging vol 21 no2 pp 61ndash75 2002

[10] W He T A Hamilton A R Cohen et al ldquoAutomated three-dimensional tracing of neurons in confocal and brightfieldimagesrdquo Microscopy and Microanalysis vol 9 no 4 pp 296ndash310 2003

[11] H Cai X Xu J Lu JW Lichtman S P Yung and S T CWongldquoRepulsive force based snake model to segment and trackneuronal axons in 3D microscopy image stacksrdquo NeuroImagevol 32 no 4 pp 1608ndash1620 2006

[12] H Cai X Xu J Lu J Lichtman S P Yung and S T CWong ldquoUsing nonlinear diffusion and mean shift to detectand connect cross-sections of axons in 3D optical microscopyimagesrdquo Medical Image Analysis vol 12 no 6 pp 666ndash6752008

[13] J Lu J C Fiala and J W Lichtman ldquoSemi-automated recon-struction of neural processes from large numbers of fluores-cence imagesrdquo PLoS ONE vol 4 no 5 Article ID e5655 2009

[14] R Srinivasan X Zhou E L Miller J Lu J W Lichtman andS T C Wong ldquoAutomated axon tracking of 3D confocal laserscanning microscopy images using guided probabilistic regionmergingrdquo Neuroinformatics vol 7 no 1 p 83 2009

[15] R Srinivasan Q Li X Zhou J Lu J Lichtman and ST C Wong ldquoReconstruction of the neuromuscular junctionconnectomerdquo Bioinformatics vol 26 no 12 Article ID btq179pp i64ndashi70 2010

[16] J Wang X Zhou J Lu J Lichtman S Chang and S T CWong ldquoDynamic local tracing for 3D axon curvilinear structuredetection from microscopic image stackrdquo in Proceedings of the4th IEEE International Symposium on Biomedical Imaging FromNano to Macro (ISBI rsquo07) pp 81ndash84 Arlington Va USA April2007

[17] S Schmitt J F Evers C Duch M Scholz and K ObermayerldquoNewmethods for the computer-assisted 3-D reconstruction ofneurons from confocal image stacksrdquo NeuroImage vol 23 no4 pp 1283ndash1298 2004

[18] Z Vasilkoski and A Stepanyants ldquoDetection of the optimalneuron traces in confocal microscopy imagesrdquo Journal ofNeuroscience Methods vol 178 no 1 pp 197ndash204 2009

[19] Y Wang A Narayanaswamy C-L Tsai and B Roysam ldquoAbroadly applicable 3-D neuron tracing method based on open-curve snakerdquoNeuroinformatics vol 9 no 2-3 pp 193ndash217 2011

[20] Neuromantic the Freeware Neuronal Reconstruction Toolhttpwwwreadingacukneuromantic

[21] Simple Neurite Tracer httppacificmpi-cbgdewikiindexphpSimple Neurite Tracer

[22] NeuronJ httpwwwimagescienceorgmeijeringsoftwareneuronjmanualhtml

[23] E Meijering ldquoNeuron tracing in perspectiverdquoCytometry A vol77 no 7 pp 693ndash704 2010

[24] Y Sato S Nakajima N Shiraga et al ldquoThree-dimensionalmulti-scale line filter for segmentation and visualization ofcurvilinear structures in medical imagesrdquoMedical Image Anal-ysis vol 2 no 2 pp 143ndash168 1998

[25] S M Pizer D Eberly D S Fritsch and B S Morse ldquoZoom-invariant figural shape the mathematics of coresrdquo ComputerVision and Image Understanding vol 69 no 1 pp 55ndash71 1998

[26] P Quelhas M Marcuzzo A M Mendonca and A CampilholdquoCell nuclei and cytoplasm joint segmentation using the slidingband filterrdquo IEEE Transactions on Medical Imaging vol 29 no8 pp 1463ndash1473 2010


[27] D Sui and K Wang ldquoA counting method for density packedcells based on sliding band filter image enhancementrdquo Journalof Microscopy vol 250 no 1 pp 42ndash49 2013

[28] KWang D SuiWWang Y Yuan andW Zuo ldquoA cell countingmethod for BEVS based on nonlinear transformed sliding bandfilterrdquo in Proceedings of the Annual International Conference ofthe IEEE Engineering in Medicine and Biology Society (EMBC12) vol 2012 pp 118ndash121 San Diego Calif USA September2012


contour based tracing methods [17 18] In the minimal pathbased tracing methods algorithms were performed in imagesubregions instead of the entire image but these methodscannot extract the exact centerline of tubular structures suchas vessels and neuron fibers In the minimum spanning treemethods serious of critical seed points were detected firstlyand then the detected seeds were linked into tree representa-tion such as MDL-MST method and k-MST method [6 7]The sequential tracing methods were starting from a set ofseed points but the results of these methods were affected byforeground discontinuity such as gaps and holes and thesedefects required additional post- or preprocessing proceduresto overcome [8 9] The skeletonization methods mainlyrelayed on a point-spread function based protocol to tracethe neuron anatomy structure but they were also prone toproduce loops and spurs which needed extra postprocessingto smooth the noise [10] Active contour based methods wereparticularly attractive for neuron tracing and reconstructionwas themost employedprotocol for this task [17 18] Schmittrsquosgroup proposed the first active contour tracing method [17]in which the neuron skeleton was parameterized into a4D snaxels sets that was characterized by its location andradius [17] But this method needed to manually set somebranching ending and other critical points Vasilkoski andStepanyants [18] proposed a new method for optimizingthe tracing based on the active contours Following thatRoysamrsquos team proposed an open curve snake based tracingmethod which was broadly applied in this area [19] andit can allow fully automated processing and user controltracing but thismethod can only handle distinct edge neuronimages data sets and cannot get accurate neuron radiusin vague boundary [19] Beyond that there still are someautomated tracing tools such as Neuromantic [20] SimpleNeurite Tracer [21] NeuronJ [22] and a complete list of thetracing tools that can be founded in the survey paper ofMeijering [23]Howevermost of these tools still needmanualassistance to reconstruct the dendritic and axonal arborsTherefore automated 3D neurons anatomy tracing tools needa continuous improvement in the future time

Traditionally speaking the pipeline of tracing was initial-ized by a serious of preprocessing methods followed by acritical point detection procedure which was called seedingThen these points were linked by center line extractionmethod and finally radius estimation was applied to recon-struct the full structure [17] As depicted in Figure 1 the fullpipeline was organized in the work flow In this pipeline as akey step excellent seeding method can assure the accuracy ofthe following skeletonization There are two approaches forseeding (i) segmentation and (ii) filtering The first one isbased on a segmentation process inwhich the image volumescovered by the neuron were separated from tissue such asthree-dimensional thinning algorithm but this method issensitive to noise The second approach is using a filter toenhance the line elements Satorsquos [24] group proposed a 3Dmultiscale liner image filter to extract the critical propertyin medical images This method employed a combination ofeigenvalues in hessian matrix of image intensities Followingthis approach Pizerrsquos group proposed another method basedon the concept of cores that detected medial points of the

Images

Preprocessing

SeedingUser interaction

Correction Centerline extraction

Radius estimation

Manual fitting

Manual fitting

DataProcessing

Manually interactionWork flow

Figure 1 Work flow of neuron tracing pipeline

object by correlating opposite boundary points [25] Butmostof the seed points detected by thesemethods were distributedunevenly and located at noncritical position [19]

Radius estimation is another important part in thispipeline for it is essential for neuron system simulation [23]Pockrsquosmethodwas greatly accepted inmany tracing tasks andwas also used in this paper for the tube-like radius estimation

In this paper we proposed a new 3D image filter calledsliding volume filter (SVF) to enhance the 3D neuron imagedata sets and then the most listed voxels were chosen as thefinal seed pointsThen an open curve snake was employed toreconstruct the neuron anatomy structure Compared withtraditional seed detection method the SVF method couldimprove the accuracy of neuron anatomy structure in 3Dtracing Finally radius estimation was applied to the trace theresult for the future functional simulation And the rest ofthis paper was organized as follows data sets collection andmethod designwere illustrated in Section 2 the experimentalresults and discussions were presented in Section 3 andfinally the conclusions were drawn in Section 4

2 Methodology

Our works were greatly related to Roysamrsquos pipeline forneuron reconstruction which was based on open curvesnake tracing [19] In this paper a SVF was designed forseeding by enhancing the spatial tube-like regions and itcould provide seed points for the automatic initialization ofopen-snake models At last Pockrsquos method was applied forradius estimation [23]

SVFwas expanded from 2D sliding band filter (SBF) As itwas depicted in Quelhasrsquo work [26] the 2D SBF could detectrounded convex region in images It was firstly introduced fordetecting cell center in 2Dmicroscopic images [26] Recentlyour research group employed the SBF to detect cells in sectionimages of cat retinal [27] and another transformed SBF todetect insect cells in light field microscopic images [28] In3D volume data sets a rounded convex region was the sameas they were in 2D images in gradient vector distribution andwe called it spatial convex region






SBF (119909 119910)

=

1

119873

119873

sum


(

1

Bw + 1

119903+(Bw2)sum

119903minus(Bw2)CI (rad 119899))

(1)

(x y)

rO

Rmin

Rmax

Bw

120572(120593rad n)


where


120593rad =2120587 (rad minus 1)

119873

120572 (120593rad 119899) = arctan(Grad119899119862

Grad119899119877

)

(2)


and Grad119899119877



SCI119875119874(119894 119895 119896) = cos120593 (119894 119895 119896) (3)


SCI119874=

1

119873

sum

119901isin119877

cos120593 (119894119901 119895119901 119896119901) (4)


r

L

M

r

2r

2r

2r

R

120601

O(x y z)P(i j k)



SVF (119909 119910 119911)

=

1

119872 lowast 119875119899

times

119872minus1

sum

119904=0

119875119899

sum


(

1

119881119905+ 1

times

119903+(1198811199052)

sum

119903minus(1198811199052)

SCI119904119874119876(119902119909119903 119902119910119903 119902119911119903))

(5)

where

SCI (119909 119910 119911) = 1

119872 lowast 119875119899

119872minus1

sum

119904=0

sum

(119894119898119895119898119896119898)isin119877119904

cos120593 (119894119898 119895119898 119896119898)

(6)





z

r

y

xd

RminRmax

O

RadR support region

Rs sliding volume

Q(qxr qyr qzr)



119864total = int1

0

119864int (119888 (119904)) + 119864ext (119888 (119904)) 119889119904 (7)


119864int (119888 (119904)) = 120572 (119904)1003816100381610038161003816119888119904(119904)1003816100381610038161003816

2+ 120573 (119904)

1003816100381610038161003816119888119904119904(119904)1003816100381610038161003816

2 (8)


119864External = 119864im (119888 (119904)) + 119896 (119904) 119892119864str (119888 (119904)) (9)

where


nabla119864str (119888 (119904))

= minus

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 0

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 1

0 119904 isin (0 1)

(10)








119861 (119900 119903)

=

1

119873

119873

sum

119894=1


(11)











1

2

ai

O(x y z)

3 =cs(x y z)

cs(x y z)

nablaIGVF(O+ rai)














4 Conclusion




Width of neuron

Radius

Centerline







Acknowledgments


References



































SBF (119909 119910)

=

1

119873

119873

sum


(

1

Bw + 1

119903+(Bw2)sum

119903minus(Bw2)CI (rad 119899))

(1)

(x y)

rO

Rmin

Rmax

Bw

120572(120593rad n)


where


120593rad =2120587 (rad minus 1)

119873

120572 (120593rad 119899) = arctan(Grad119899119862

Grad119899119877

)

(2)


and Grad119899119877



SCI119875119874(119894 119895 119896) = cos120593 (119894 119895 119896) (3)


SCI119874=

1

119873

sum

119901isin119877

cos120593 (119894119901 119895119901 119896119901) (4)


r

L

M

r

2r

2r

2r

R

120601

O(x y z)P(i j k)



SVF (119909 119910 119911)

=

1

119872 lowast 119875119899

times

119872minus1

sum

119904=0

119875119899

sum


(

1

119881119905+ 1

times

119903+(1198811199052)

sum

119903minus(1198811199052)

SCI119904119874119876(119902119909119903 119902119910119903 119902119911119903))

(5)

where

SCI (119909 119910 119911) = 1

119872 lowast 119875119899

119872minus1

sum

119904=0

sum

(119894119898119895119898119896119898)isin119877119904

cos120593 (119894119898 119895119898 119896119898)

(6)





z

r

y

xd

RminRmax

O

RadR support region

Rs sliding volume

Q(qxr qyr qzr)



119864total = int1

0

119864int (119888 (119904)) + 119864ext (119888 (119904)) 119889119904 (7)


119864int (119888 (119904)) = 120572 (119904)1003816100381610038161003816119888119904(119904)1003816100381610038161003816

2+ 120573 (119904)

1003816100381610038161003816119888119904119904(119904)1003816100381610038161003816

2 (8)


119864External = 119864im (119888 (119904)) + 119896 (119904) 119892119864str (119888 (119904)) (9)

where


nabla119864str (119888 (119904))

= minus

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 0

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 1

0 119904 isin (0 1)

(10)








119861 (119900 119903)

=

1

119873

119873

sum

119894=1


(11)











1

2

ai

O(x y z)

3 =cs(x y z)

cs(x y z)

nablaIGVF(O+ rai)














4 Conclusion




Width of neuron

Radius

Centerline







Acknowledgments


References































r

L

M

r

2r

2r

2r

R

120601

O(x y z)P(i j k)



SVF (119909 119910 119911)

=

1

119872 lowast 119875119899

times

119872minus1

sum

119904=0

119875119899

sum


(

1

119881119905+ 1

times

119903+(1198811199052)

sum

119903minus(1198811199052)

SCI119904119874119876(119902119909119903 119902119910119903 119902119911119903))

(5)

where

SCI (119909 119910 119911) = 1

119872 lowast 119875119899

119872minus1

sum

119904=0

sum

(119894119898119895119898119896119898)isin119877119904

cos120593 (119894119898 119895119898 119896119898)

(6)





z

r

y

xd

RminRmax

O

RadR support region

Rs sliding volume

Q(qxr qyr qzr)



119864total = int1

0

119864int (119888 (119904)) + 119864ext (119888 (119904)) 119889119904 (7)


119864int (119888 (119904)) = 120572 (119904)1003816100381610038161003816119888119904(119904)1003816100381610038161003816

2+ 120573 (119904)

1003816100381610038161003816119888119904119904(119904)1003816100381610038161003816

2 (8)


119864External = 119864im (119888 (119904)) + 119896 (119904) 119892119864str (119888 (119904)) (9)

where


nabla119864str (119888 (119904))

= minus

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 0

sign(minus119888119904 (119904)

1003817100381710038171003817119888119904 (119904)1003817100381710038171003817

sdot 119890V1 (119888 (119904))) sdot 119890V1 (119888 (119904)) 119904 = 1

0 119904 isin (0 1)

(10)








119861 (119900 119903)

=

1

119873

119873

sum

119894=1


(11)











1

2

ai

O(x y z)

3 =cs(x y z)

cs(x y z)

nablaIGVF(O+ rai)














4 Conclusion




Width of neuron

Radius

Centerline







Acknowledgments


References




































119861 (119900 119903)

=

1

119873

119873

sum

119894=1


(11)











1

2

ai

O(x y z)

3 =cs(x y z)

cs(x y z)

nablaIGVF(O+ rai)














4 Conclusion




Width of neuron

Radius

Centerline







Acknowledgments


References




































4 Conclusion




Width of neuron

Radius

Centerline







Acknowledgments


References



































Acknowledgments


References






























A pipeline for neuron reconstruction based on spatial sliding volume filter seeding

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Transcript of A pipeline for neuron reconstruction based on spatial sliding volume filter seeding