Mathematical and Computational Issues for Live Cell Segmentation in Fluorescence Microscopy

1. Metodi Matematici nel Trattamento delle Immagini SapienzaUniversitàdi Roma 15-16 Gennaio 2013 Mathematical and Computational Issues for Live Cell Segmentation in Fluorescence Microscopy Laura Antonelli laura.antonelli@cnr.it Institutefor High Performance Computing and Networking (ICAR)

2. ResearchContext • FIRB 2010 project – “Future in Research” Programme RoleofPolycomb mediatedepigeneticsignature in laminopathies: analysisby innovative genome wide technology and high-performancenumericalalgorithms for Live CellImaging • CNR Insititutesinvolved INMM • Instituteof • Neurobiologyand • Molecular Medicine • Institutefor • High Performance Computing • and Networking (Lanzuolo, Casalbore, Ciotti) (Oliva, Antonelli, Gregoretti)

3. Laminopathies • Gene regulationis the processofturninggenes on and off. • Itisaccomplishedby a varietyofmechanisms • includingregulatoryproteinslikePolycombgroupproteins. cell DNA lamin chromosome nucleus mutation Laminopathies are a group of rare  genetic disorders caused by mutations in genes encoding proteins of the nuclear lamin.

4. RoleofPolycombproteins in laminopathies • Whatis the involvementoflaminin the coordinationof gene expressionregulatingsub-set ofgenesthroughdirector indirectinteractionswithPolycombcomplexes? merge lamin Polycombs Fluorescenceimages highlightdramatically aberrant morphology in cell nucleus of progeria patients. Normal progeriasyndrome • Identification of new candidate genes involved in laminopathies • Design of algorithms to identify and analyze lamin and polycombs • interaction in fluorescence images microscopy

5. FluorescencemicroscopyIssues • Huge amount of data • many image sequences • # frames per sequence: from 60 to 120 • single frame size: 1024 x 1280 • Manualanalysistoextract information bymeansoflarge volume of light microscopyimagesisslow,timeconsuming • andsubjecttoobservervariance • FeaturesofFluorescenceimages • The varietyoffluorescentproteins and labelingtechniquesleadstoconsiderabledifferences in the appearanceofcells • Sincecells are sensibletophotodamage, fluorescencemicroscopies produce imageswithvery low contrast • Fluorescenceimagesmaycontainautofluorescence • Existing imaging tools are limited in their scope and capacity to analyze live cell images

6. Goals Work in progress 2013 - 2015 Development of an open source library for live cell imaging in high performance computingenvironment • Visualizing and Analysis • Visualizing, quantifying and modelling cellular and sub-cellular morphological features with high spatial and temporal resolution • Preprocessing/Postprocessing • denoising, deblurring, scaling, contrastenhancement, featuresextraction • Processing • segmentation “easy” descriptionofcellimages •  featuresextraction • tracking temporalanalysisofdynamiccellularprocesses

7. CellSegmentationModels and Methods • The kindoffeaturestobehighlightedisdirectlyrelatedto the biologicalexperiment, therefore the choiceof the modelisfundamental in orderto produce a correctsegmentation. • microscopyimagesfeatures: • smoothboundaries • twophaseimages: regionsof interest and background • presenceofnoise • ActiveContoursModels • model image contours as curves that match the highest gradient • edge detector based on imagegradient • edge detector NOT based on imagegradient • RegionBasedModels • provide a simplifiedimageas a combinationofregionsofcostantintensities: • Mumford and Shahapproach • Global tresholding • watershedalgorithm

8. ActiveContourModels • bounded open set withboundary∂Ω • givenimage • parameterized curve Kass, Witkin, Terzopoulus, “Snakes: ActiveContourModels”, Int. J. Comput. Vis. ClassicalModel Chan, Vese, “ ActiveContourWithoutEdges”, IEEE Trans. on Im. Proc. Chan-VeseModel

9. AC Chan-VeseLevel Set Formulation Sethian, “ Level Set Methods and Fast MarchingMethods” The paramaterizedcurve C Ωisrepresentedby the zero level set of a Lipschtzfunction :  Keepingfixed, we can computec1 and c2asfunctionof

10. Regularization Wedetermine bymeansthe gradient-descentmethod and Euler-Lagrangeequations Regularizedfunction Since the functional is non-convex, the use of regularized functions can drive the Euler-Lagrange equation towards the global minimizer Euler-Lagrangeequation

11. NumericalAlgorithm Chan-VeseSegmentation • Inizialize 0 • forn = 1,2, …, Nmax • computec1( n) andc2( n) • compute n+1 solving EL equation • reinitialize n+1 to the signeddistancefunction • Checkwethersolutionisstationary. • If yes, stop iterations The reinitialization process is made by using the following PDE:

12. test 1: fluorescenceimagesegmentation 1/3 • Mouse embryonic • stemcells • Analysisof the laminrole in PcGmediatedmuscleand neuronalcelldifferentiation Polycombs DNA Imagesize 1024 X 1280 • touchingcellsnotseparated!

13. test 1: fluorescenceimagesegmentation 2/3 ModelParameters Architecture CPU Intel I5 750 @2.67GHz (quad-core) MEMORY 4GB gcc version 4.7.1 OS debian wheezy Imagelibrarylibtiff Polycombs DNA Polycombs DNA Imagesize 1024 X 1280

14. test 1: fluorescenceimagesegmentation 3/3 ModelParameters Architecture CPU Intel I5 750 @2.67GHz (quad-core) MEMORY 4GB gcc version 4.7.1 OS debian wheezy Imagelibrarylibtiff Polycombs DNA Polycombs Featuresextraction

15. test 2: time-lapsesegmentation ModelParameters • Mouse embryonicstemcells, • Noisedimages 512 X 256 frame 1 segmentation frame 31 • Verysmoothboundaries! frame 61

16. test 3: imagesequencetracking Chan-VeseTrackingalgorithm • Inizialize 0 • fork = 1,2, …, Nframes • forn = 1,2, …, Nmax • computec1( n) andc2( n) • compute n+1 solving EL equation • reinitialize n+1 to the signeddistancefunction • Checkwethersolutionisstationary. If yes, stop iterationsofn counter • Initialize k+1 = k Architecture • Mouse embryonicstemcells • Timelapseimagesequence CPU Intel I5 750 @2.67GHz (quad-core) MEMORY 4GB gcc version 4.7.1 OS debian wheezy Imagelibrarylibtiff 512 X 256 X 61 frame

17. Model and AlgorithmEvaluation • Advantages • goodsegmentationcellimageswithverysmoothboundaries • robustnesswithrespectnoise • scale adaptivity • semplicityofimplementation • low computational cost of a single iteration • Drawbacks • lackofconvexity (presenceoflocal minima) • dependence on initialcontourposition • high computationalcostforstepreinizializationoflevel set • bad segmentationforimageswithintensityinhomogeneity • tounchingcellsnotseparated • slow convergence rate (toomanyiterationsfortracking!) • possibletrapping inlocalminimum

18. Improving the model Work in progress Extendingmulti-phasesegmentation L. Vese, T. Chan “A MultiphaseLevel Set FrameworkforImageSegmentationUsing the MumfordanShahModel” Work in progress Introducinglocalstatisticalinformation X.FWang, D. Huang, H. Xu “An EfficientlocalChan-Vesemodelforimagesegmentation”

19. Improving the solutionmethod Approach the problem from the optimization point of view Work in progress In collaborationwith D. di Serafino and V. De Simone, SecondUniversityofNaples. • Fastergradient-descentapproaches (non-monotonemethods, exploitation of geometricproperties of the variationalmodel, …) • Newton-typemethods, usingapproximations of the secondvariation • - efficient iterative linear algebra techniques • globalizationtechniques (linesearch or trust region) • Optimizationmethodsfor L1-regularized Chan-Vesemodel (splitBregman, alternate direction of multipliers)

20. Speeding-up the implementation Work in progress Introducing Data Parallelism in trackingalgorithm • Inizialize 0 • fork = 1,2, …, Nframes • forn = 1,2, …, Nmax • computec1( n) andc2( n) • compute n+1 solving EL equation • Reinitialize n+1 to the signeddistancefunction • Checkwethersolutionisstationary. If yes, stop iterationsofn counter • Initialize k+1 = k Framesdistributionbetweenprocesses

21. Acknowledgments • Dr C. Lanzuolo at INMM-CNR forfruitfuldiscussion on biologicalexperiments and forprovidingfluorescenceimagesof mouse embryonicstemcells • Dr. G. Cavalli at InstituteofHumanGenetic–CNRS (France) forprovidingtime-lapsesequencesofMouse embryonicstemcells Thanksforyourattention • any comments and suggestions • are welcome ! laura.antonelli@cnr.it

22. Goalsof FIRB Project A large scale approach • INMM APPROACH  High-Throughput Screening (HTS): • The generation of 4C libraries of lamin dependent gene interactions • Identification of new candidate genes involved in laminopathies that could be useful for prognosis • Investigation of the molecular basis of the disease to eventually design new therapeutical strategies • ICAR APPROACH  High-Throughput Bioimaging (HBS): • Identification of epigenetic dynamics associated with lamin pathology • Design algorithms to identify and analyze biological processes • Development of an open source numerical library for live cell imaging

23. ActiveContourChan-VeseModel Chan, Vese, “ ActiveContourWithoutEdges”, IEEE Trans. on Im. Proc. • Letbe: • Ωa bounded open set of , with∂Ωitsboundary • a givenimage • a parameterized curve Chan-Vesemodelfinds a contourCthatpartitions the imageu0intotworegions: Ωin(objects)andΩout(background) thatdescribeanoptimalpiecewiseconstant approximationof the image. Internalforce Externalforces

24. Euler-LagrangeRegularizedEquations Keeping fixed, we can compute Regularizedfunction

25. Discretization Euler-Lagrangeequationisdiscretized bymeans a finite differencessemi-implicitscheme. Discrete divergenceoperator Rudin, Osher, Fatemi, “ Non Linear Total VariationBasedNoiseRemovalAlgorithm”