Wepresentamethodformodellingandestimatingbranchingstructures,such asbloodvesselbifurcations,frommedicalimages.Wemodelbranchesasa superpositionofNGaussianfunctionsinalocalregionwhichdescribethe amplitude,positionandorientationsoflinearfeaturesandalsobranches.The centroidsofcomponentfeaturesareseparatedbyapplyingk-meanstothelocalFourierphaseandthecovariancesandamplitudessubsequentlyestimated byalikelihoodmaximisation.Weapplyapenalisedlikelihoodtest(AIC)to selectthebestfitmodelinaregion.Resultsarepresentedonsyntheticand representative2Dretinalimageswhichshowtheestimationtoberobustand accurateinthepresenceofnoise.Wecompareourresultsascale-spaceoperatormethod.