Fisher, M

Wang, W

Zhang, L

English

University of East Anglia digital repository

PAREDES et al.: COMPARISON OF VESSEL DETECTION ALGORITHMS 1??Performance Comparison of Low-levelVessel Detection Algorithms forSegmentation of X-ray AngiogramsDaniel Paredes Soto1el10dap@sheffield.ac.ukPhilip Chan2p.chan@sheffield.ac.ukPeter Rockett1p.rockett@sheffield.ac.uk1 Department of Electronic and ElectricalEngineeringUniversity of SheffieldSheffieldS1 3JD, UK2 Sheffield Vascular InstituteNorthern General HospitalSheffieldS5 7AU, UKAbstractUsing examples generated with a realistic model of the imaging physics, we haveassessed and compared the performance of three popular multi-scale vessel detectorsdue to: Frangi et al., Sato et al. and Lorenz et al. We find that there is only a smalldifference between the performances of the Frangi and Sato detectors for the conditionsconsidered in this work; for small-diameter vessels the response of these two detectors iscomplex although both suggest some promise for segmenting the vessels in the collateralbed around an occlusion. The Lorenz detector is shown to be the worst performing acrossa range of conditions.1 IntroductionOcclusive vascular disease affecting arterial circulations is the major and fastest growinghealth problem worldwide, and underlies common conditions such as heart attack, strokeand peripheral vascular disease. The World Heath Organisation estimates that these diseaseswere responsible for 17.3 million deaths worldwide in 2008, forecast to rise to 23.6 millionin 2030. Occlusion of major arteries is naturally compensated, to some extent, by the devel-opment of minor channels to carry blood around the occlusion, termed collateral circulation.Traditionally, occlusive disease is treated by surgical methods although recently, phar-macological treatments, especially biological products have been researched. Unlike bypassor angioplasty, pharmacological candidates do not address the occlusion directly but arethought to encourage the formation of additional or better collateral vessels either throughangiogenesis (the development of new blood vessels) and arteriogenesis (the development offlow-carrying arterial circulation from capillary precursors). Currently the success of treat-ments is judged on clinical endpoints like improved exercise ability or fewer amputations;such endpoints are massively confounded by other variables apart from blood flow changes.c© 2012. The copyright of this document resides with its authors.It may be distributed unchanged freely in print or electronic forms.??? PAREDES et al.: COMPARISON OF VESSEL DETECTION ALGORITHMSThus a major roadblock to the clinical evaluation of new drug treatments is the lack of anobjective anatomical measurement of any enhancement in the blood conveying capacity of acollateral circulation—the development of such a methodology is our longer term goal. Sucha direct measure of anatomical change from before to after-treatment would not be subjectto confounding factors, and provide credible evidence of effect.As a precursor to progress in this area, a means of accurately quantifying the propertiesthe collateral network is needed and a fundamental step in this is the extraction of the, oftenfine, vessel segments which comprise the collateral bed. We have consequently studied theperformance of a number of popular, low-level multi-scale vessel extraction algorithms [2,4, 5] for digital-subtraction X-ray angiography, a common diagnostic procedure for patientspresenting with the symptoms of occlusive vascular disease. This preliminary study seeksto compare performance in the ideal case of an isolated, straight vessel of infinite extent—see, however, Section 4 (Future Work). (We envisage that the low-level detector outputswill ultimately be combined to extract the whole vessel network using tracking, or Markovrandom field approaches; such higher-level methods are not the immediate concern of thispaper.)Here, we principally address two research questions: i) Which low-level vessel detectorhas the ‘best’ properties, and ii) How do these detectors perform on small-diameter vesselssince these are a major concern for imaging collateral beds. We find that within the limits ofthis work, there is little to choose between the Frangi and Sato detectors. As far as we areaware, we are the first to present a quantitative comparison of these vessel detectors.2 MethodologyWe compare the performance of three much-used multi-scale detectors due to: Frangi etal. [2], Sato et al. [5] and Lorenz et al. [4]. All three algorithms calculate the eigen-decomposition of the Hessian matrix of the image at multiple scales. They then computesome scalar measure of ‘vessel-ness’ at each scale and select as the final vessel-ness mea-sure, the maximum response across all scales. Essentially, the detectors only differ in howthe hand-crafted scalar measures are calculated from the eigenvalues of the Hessian, λ1 andλ2. The Frangi detector [2] computes as a measure of eigenvalue eccentricity RB = λ1/λ2,where |λ1|≤ |λ2|. For some scale σ , the measure of ‘vessel-ness’, LF is given by:LF(σ) ={0 λ2 > 0exp(−RB2/2β 2)[1− exp(−S 2/2c2)] otherwise(1)where S =√λ 21 +λ22 . We have used Frangi’s suggestions of taking β = 0.5 and adjustingc for best results.The vessel-ness measure due to Sato [5] is defined, for |λ1|< |λ2|, by:LS(σ) =−λ2 exp(−λ 212(α1λc)2) (λ2 < 0)∧ (λ1 < 0)−λ2 exp(−λ 212(α2λc)2) (λ2 < 0)∧ (λ1 > 0)where α1 < α2. We have used Sato’s suggested values of α1 = 0.5 and α2 = 2.For the (parameter-less) detector of Lorenz [4] and |λ1|≤ |λ2|, LL(σ) = |λ1|/|λ2|.PAREDES et al.: COMPARISON OF VESSEL DETECTION ALGORITHMS ???We compute the Hessian matrix over the ten linearly-spaced scales of σ = 1 to 10 pixelunits and take the overall vessel-ness measure as the maximum detector response across allscales. We then threshold this measure to decide a label (vessel of non-vessel).Obtaining ground-truth data in medical image processing is an enduring problem due tothe uncertainties of inter- and intra-expert hand labelling. Here we adopt the well-establishedprocedure of using synthetic data based on a physically-realistic model of the image forma-tion process. Starting with out assumption of an isolated, straight vessel of infinite extentand circular cross-section irradiated with a uniform X-ray beam normal to the longitudinalvessel direction. We assume the vessel is uniformly filled with contrast agent. As the rayspass through the vessel, the intensity of the X-ray beam will be reduced according to theBeer-Lambert Law, I = I0 exp(−αℓ) where I0 is the incident beam intensity, α is the ab-sorption coefficient, and ℓ is the path length through the (contrast agent in the) vessel. SeeFigure 1. Cleary ℓ = ℓ(x), where x is the spatial dimension in Figure 1, which also showsthe resulting intensity profile projected onto the camera’s focal plane. We selected α to givemaximum contrast at the largest vessel diameter considered while allowing±3σ ‘headroom’for the largest noise perturbations of the pixel values in the output image. The process thusmirrors a radiographer optimising the X-ray imaging conditions.			Figure 1: Formation of the vessel intensitymodel. The lower figure shows the projectedintensity profile.A distinguishing feature of the presentwork is the realistic image formationmodel: previous work, for example Kris-sian et al. [3], has usually assumed theprojected vessel intensity profile is Gaus-sian with a physically-implausible infiniteregion of support. Drechsler and Laura [1]used the data of Krissian et al. in a qualita-tive comparison of vessel detectors.We have no a priori reason to supposethat a vessel will present at any particularorientation to, or displacement from the im-age lattice so we select a uniformly-randomorientation θ ∈ [0 . . .45o] and a displace-ment ∆x ∈ [−0.5 pixel . . .+ 0.5 pixel] fromthe notional origin in Figure 1. (In prac-tice, these are applied by an affine trans-formation of the projected intensity imageabove.) To account for the limitations ofthe imaging optics, we convolve the affine-transformed image with a Gaussian ofσPSF = 1 and then add Gaussian-distributednoise of some σN which assumes that thedominant noise process is due to thermalnoise in the camera/electronics. Finally, wequantise the pixel intensities into the range[0 . . .255] to mimic analogue-to-digital con-version in the camera. This final image con-taining a single vessel is passed to one ofthe above detectors. In assessing a detector, we consider only the label of the central pixel??? PAREDES et al.: COMPARISON OF VESSEL DETECTION ALGORITHMSof the image through which the centreline of the vessel passes. Our rationale here is thatthe signal-to-noise ratio is maximised at the centre of the vessel—if the vessel cannot bedetected at its centre, it cannot probably be detected anywhere else across its diameter. Wethus implicitly investigate the upper bound of the detectors’ performance. Additionally, eachimage represents an independent Monte Carlo trial.To form counter-example images (i.e. genuine absence of a vessel) we form an image ofuniform background intensity but with each pixel corrupted by noise of the same variance asthe positive vessel examples. The method of generating positive and negative examples thusclosely mirrors the process of digital-subtraction X-ray angiography.We have repeated the above steps of generating positive and negative vessel examplesin a Monte Carlo experiment (1000 trials) and and labelled with each of the detectors usingvarious thresholds to construct receiver operating characteristic (ROC) plots. We also usethe area-under-the-curve (AUC) as a summary statistic for the ROC plot.3 ResultsWe have considered a range of vessel diameters (D ∈ [1,3,5,7 . . . ,15] pixel units) and noisepowers (σN ∈ [5,10,15,20,25]). For brevity we only show results for the four permutationsof small/large vessels, and lowest/highest noise powers since these represent the extremesof detector performance between which there is a more-or-less smooth variation. For the(physically unrealistic) absence of noise (σN = 0) all three detectors perform ‘perfectly’(AUC = 1.0) apart from the case of unit vessel width (D = 1) where the Frangi and Lorenzdetectors are tied (AUC = 0.95) and perform slightly worse than Sato (AUC = 0.97).Fig. 2(a) and 2(b) show the ROC plots for D = 1 and the extremes of (a) low-noise(σN = 5) and (b) high-noise (σN = 25). Interestingly, in the low-noise regime all threedetectors perform to some degree although the Sato and Frangi detectors are clearly betterthan Lorenz. (The straight line segments of the ROC plots are due to the discontinuitiesintroduced by the case of λ2 = 0 in Eqn. 1, and so on.) The detectors’ behaviour is quitecomplex with the ROC plots crossing although there is generally little to choose betweenFrangi and Sato. Note that for the case of high noise, the performance of all three methodsreduces to little better than random guessing—the 45o line—as might be expected since thesignal-to-noise (SNR) ratio becomes very low for this case. Since we have use a fixed valueof attenuation coefficient (α), the SNR reduces as a function of reducing vessel diameter,hence small vessels are intrinsically harder to label.For D = 1 and 3, and σN = 25 (high noise), there is little to choose between the perfor-mances of all three detectors. There is , however, an interesting transition between D = 3and D = 5 (see Fig. 2(c) and (d)) where the Frangi and Sato algorithms begin to out-performLorenz, with Frangi slightly ahead of Sato, a trend which continues up to large diameters.Fig. 2(e) and (f) show the corresponding plots for D = 15. At this stage, the Sato andFrangi algorithms both perform ‘perfectly’ (AUC = 1) regardless of noise power. The Lorenzdetector, however, is clearly inferior, even for low noise powers.As a summary, Fig. 3 shows the AUC statistic vs. vessel diameter D. The region betweenthese two pairs of curves (low noise and high noise) delineates the useful operating envelopeof the two detectors.PAREDES et al.: COMPARISON OF VESSEL DETECTION ALGORITHMS ???(a) (b) (c)(d) (e) (f)Figure 2: ROC plots for: D = 1 and (a) low-noise (σN = 5) and (b) high-noise (σN = 25).(c) D = 3 and (d) D = 5; high-noise (σN = 25). D = 15 and low-noise (e) (σN = 5) and (f)high-noise (σN = 25).4 Future WorkFigure 3: AUC vs. vessel diameter D for theFrangi and Sato detectors only.The present preliminary report considersonly the idealised case of a straight, isolatedvessel. In future work, we will consider theeffects on detector response of curved ves-sels and bifurcations. In addition, since thedetectors are all multi-scale approaches, weanticipate that the responses from two ves-sels which approach closer than the scaleof a Gaussian filter will interact with eachother. For extracting vessel networks thisis an important factor. Moreover, the ves-sels in a collateral bed frequently presentas a ‘corkscrew’ and it is possible that theresponse (even) from an isolated corkscrewcollateral could be affected by the proxim-ity of other sections of the same vessel. These and other factors will be the subject of futurestudies.We are assuming all vessels lie in a plane and can be imaged normal to the longitudinal??? PAREDES et al.: COMPARISON OF VESSEL DETECTION ALGORITHMSvessel direction. In reality, it is highly likely that vessels will have some component passinginto a 2D image plane so extracting an entire network will be problematic. In this situation,3D magnetic resonance angiography (MRA) will be highly desirable. We believe, givena suitable MRI simulator, the methodology in this paper can be directly applied to MRAimages—this too is an area of future work.5 ConclusionsFrom constructing a physics-based model of the process by which the image of a vessel isformed in digital-subtraction X-ray angiography, we have compared the performances of thevessel detectors devised by: Frangi et al., Sato et al. and Lorenz et al. On the basis of thepresent results, the Lorenz detector is clearly inferior to the Frangi and Sato detectors be-tween which there is little to choose for anything other than the smallest vessel diameters.Whether Frangi or Sato is better for vessels on the 1 pixel scale would seem to depend on ex-act operating point. Nonetheless, these methods seem to offer some promise for segmentingfine vessels if combined with a contextual approach (e.g. Markov random fields).The present results are limited to straight, isolated vessels. Whether any detector issuperior for real, rather than idealised, vessel networks remains to be established in futurework. For example, qualitative observations suggest the Frangi detector does not performwell at vessel bifurcations [1].References[1] K. Drechsler and C. O. Laura. Comparison of vesselness functions for multiscale anal-ysis of the liver vasculature. In 10th IEEE International Conference on InformationTechnology and Applications in Biomedicine, pages 1–5, Corfu, Greece, 2010.[2] A. F. Frangi, W. J. Niessen, K. L. Vincken, and M. A. Viergever. Multiscale vesselenhancement filtering. In W M Wells, A Colchester, and S L Delp, editors, Medical Im-age Computing and Computer-Assisted Intervention, pages 130–137, Cambridge, MA,1998.[3] K. Krissian, G. Malandain, N. Ayache, R. Vaillant, and Y. Trousset. Model-based detec-tion of tubular structures in 3D images. Computer Vision and Image Understanding, 80(2):130–171, November 2000.[4] C. Lorenz, I.-C. Carlsen, T. M. Buzug, C. Fassnacht, and J. Weese. Multi-scale linesegmentation with automatic estimation of width, contrast and tangential direction in2D and 3D medical images. In 1st Joint Conference on Computer Vision, Virtual Realityand Robotics in Medicine and Medial Robotics and Computer-Assisted Surgery, pages233–242, Grenoble, France, 1997.[5] Y. Sato, S. Nakajima, H. Atsumi, T. Koller, G. Gerig, S. Yoshida, and R. Kikinis. 3Dmulti-scale line filter for segmentation and visualization of curvilinear structures in med-ical images. In 1st Joint Conference on Computer Vision, Virtual Reality and Robotics inMedicine and Medial Robotics and Computer-Assisted Surgery, pages 213–222, Greno-ble, France, 1997.

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