Giannakopoulos, Stilianos

Ouzounis, Georgios K.

Simopoulos, Constantinos E.

Wilkinson, Michael H.F.

English

In medical imaging, anatomical and other structures such as urinary stones, are often extracted with the aid of active contour/surface models. Active surface-based methods have robustness limitations and are computationally expensive. In this paper we present a morphological method based on attribute filters and the newly presented sphericity attribute. The operators involved, extract the targeted objects in their entirety without shape/size distortions and proceed rapidly. Experiments on three real 3D data-sets demonstrate their efficiency and their performance is discussed

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   University of GroningenRobust extraction of urinary stones from CT data using attribute filtersOuzounis, Georgios K.; Giannakopoulos, Stilianos; Simopoulos, Constantinos E.; Wilkinson,Michael H.F.Published in:EPRINTS-BOOK-TITLEIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2009Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Ouzounis, G. K., Giannakopoulos, S., Simopoulos, C. E., & Wilkinson, M. H. F. (2009). Robust extraction ofurinary stones from CT data using attribute filters. In EPRINTS-BOOK-TITLE University of Groningen,Johann Bernoulli Institute for Mathematics and Computer Science.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 08-06-2022ROBUST EXTRACTION OF URINARY STONES FROM CT DATA USING ATTRIBUTEFILTERSGeorgios K. Ouzounis,Stilianos Giannakopoulos,Constantinos E. Simopoulos ∗School of Medicine,Democritus University of Thrace, UniversityGeneral Hospital of Alexandroupoli,68100 Alexandroupoli, GreeceMichael, H.F. WilkinsonInstitute of Mathematics and ComputingScience, University of Groningen,P.O. Box 407, 9700 AK Groningen,The NetherlandsABSTRACTIn medical imaging, anatomical and other structures such asurinary stones, are often extracted with the aid of active con-tour/surface models. Active surface-based methods have ro-bustness limitations and are computationally expensive. Inthis paper we present a morphological method based on at-tribute filters and the newly presented sphericity attribute. Theoperators involved, extract the targeted objects in their en-tirety without shape/size distortions and proceed rapidly. Ex-periments on three real 3D data-sets demonstrate their effi-ciency and their performance is discussed.Index Terms— Urinary stones, attribute filters, spheric-ity.1. INTRODUCTIONUrinary stones are hard mineral masses usually formed insidethe kidneys, in the process of filtering blood to remove liquidwaste. Aided by urine, the stones can travel along the urinarytract which apart from the kidneys consists of the ureter, thebladder and the urethra. If small in size, they often are ex-pelled from the body without any noticeable symptoms. Incertain cases though, either due to size or shape, they may getstuck inside the kidneys or in other parts of the urinary tractcausing severe pain. This condition is known as urolithiasisand is diagnosed with the aid of ultrasound (US), helical com-puterized tomography (CT) or intravenous pyelograms (IVP).All three methods provide visual data assisting the diagno-sis, the localization of the stones and possibly pre-operativeplanning.Stacks of progressive CT scans can be used to construct3D models which offer a number of advantages in the visual-ization of the targeted structures [1]. Extracting urinary stones∗The data-sets were kindly made available by dr.V. Souftas and Prof. P.Prassopoulos from the Dep. of Radiology and Medical Imaging of the sameinstitution.from 3D data-sets, like many other segmentation problems inmedical imaging, commonly relies on active surfaces [2] oractive contours stacked after processing. Active surfaces havethree distinctive drawbacks; the require careful, and sometimes manual initialization, they might converge inaccuratelyif mislead by noise or other nearby objects and they are com-putationally expensive due to their iterative nature. Instead, inthis paper we propose an alternative, morphological methodbased on attribute filters. It relies on two filtering steps, onebased on the newly presented sphericity attribute and the sec-ond on size. We validate it on three different cases dealingwith a stone in a kidney, three smaller stones in the ureter anda major stone inside the bladder. The results show that themethod extracts all stones present robustly and in their en-tirety, while the timings suggest a clear speed advantage overother methods. Note that this is not a comparison paper be-tween this method and others; it simply aims to demonstratethe performance of connected morphology in medical imag-ing. A full comparative study is in progress.2. ATTRIBUTE FILTERS2.1. Connectivity Openings and FiltersAttribute filters [3] are a class of edge preserving operatorsacting on connected image regions instead of individual pix-els. They are based on connectivity openings [4,5] Γx and caneither remove or preserve objects in their entirety but cannotintroduce new edges. An object in a binary image X , is aset Cx ⊆ X of path-wise connected points, of maximal ex-tent. This means that there cannot be any other set C ′x ⊃ Cxsuch that C ′x ⊆ X using the same connectivity rules. Cxin this case is also referred to as a connected component. Aconnectivity opening Γx(X) given a point x ∈ X , returnsthe connected component containing x or ∅ otherwise. It ischaracterized by the following three properties; for any twosets X, Y it is anti-extensive i.e. Γx(X) ⊆ X , it is increas-2629978-1-4244-5654-3/09/$26.00 ©2009 IEEE ICIP 2009ing i.e. if X ⊆ Y ⇒ Γx(X) ⊆ Γx(Y ), and idempotent i.e.Γx(Γx(X)) = Γx(X). Furthermore, for all X ⊆ E, with Ebeing some arbitrary superset, x, y ∈ E, Γx(X) and Γy(X)are either equal or disjoint.Attribute filters work by imposing attribute-based con-straints on Γx in the form of binary criteriaΛ. These are put inplace by means of a trivial opening ΓΛ. The latter yields Cxif Λ(Cx) is true, and ∅ otherwise. Furthermore, ΓΛ(∅) = ∅.They are typically expressed as:Λ(Cx) = Attr(Cx) ≥ λ, (1)with Attr(Cx) being some real-value attribute of Cx, and λan attribute threshold.Definition 1 The binary attribute filter ΓΛ of a setX with anincreasing criterion Λ is given by:ΓΛ =⋃x∈XΓΛ(Γx(X)). (2)An example of increasing attributes and thus increasing cri-teria is the volume measure. Non-increasing criteria usuallyrely on shape descriptors such as moment-invariants, elonga-tion, flatness, sparseness, e.t.c. [6]. Connected operators em-ploying such attribute criteria are referred to shape filters. Tocompensate for their non-increasingness they are required tobe rotation, translation and scale-invariant [7]. Following wediscuss a new shape attribute employed in our method.2.2. The Sphericity AttributeSphericity SPH [8] is a unit-free measure of how sphericalan object is. It is quantified by using a unique mathematicalproperty of the sphere; the sphere has the lowest surface-to-volume ratio of any solid geometric objects. Sphericity is de-fined as the surface area Se of a sphere of the same volumeas the connected component Cx, divided by the actual surfacearea Sa of Cx, i.e.:SPH = Se/Sa, (3)Wadell [8] expanded this further by giving the surface area ofa sphere Se, in terms of its volume V .S3e = (4πr2) = 43π3r3 = 4π(42π2r6)= 4π32(42π232r6)= 36π(4π3r3)2 = 36πV 2,(4)therefore,Se = (36πV 2)13 = π13 (6V )23 . (5)Substituting into (3) yields:SPH =π13 (6V )23Sa(6)The sphericity measure has a maximum of 1 for a solid sphereand decreases as the object gets more sparse or hollowed.The actual surface area of a 3D object can be measuredin a number of different ways. A problem with most pixel-based methods though, is that they are not rotation invari-ant. To counter this, estimates of surface area are computedwhich though they can ensure rotation invariance, cause arounding effect in corners thus missing the contribution ofcertain pixels. In our method we used an extension of the city-block perimeter metric to 3D. For every pixel p visited, weretrieve its neighbors and initialize a variable peri to the dif-ference between the maximum number of neighbors (6-wayadjacency) and the actual ones. For each neighbor with inten-sity higher than that of p, peri is incremented and the oppo-site. After all neighbors are processed, the attribute measureof the connected component visited is updated. Though notrotation invariant, the specific metric was seen to perform sat-isfactory and was further employed to compute sphericity.3. EXPERIMENTAL METHOD AND TESTSBoth the volume and surface area attributes are computed us-ing the Max-Tree algorithm [9]. Max-Trees are versatile datastructures introduced in the context of anti-extensive attributefiltering. They extend binary operators to gray-scale throughthe concept of threshold superposition and allow for their ef-ficient computation. A Max-Tree demo [6] for both attributefiltering and 3D visualization is available at our web-site athttp://www.cs.rug.nl/∼michael/MTdemo.Our method for extracting the urinary stones consists oftwo filtering steps. The first subjects our test data-sets to thesphericity criterion, preserving only compact structures. Avolume opening follows to remove noise and other smaller,compact artifacts. We experiment on three real data-sets, thefirst and third of which are down-sampled to 8-bit sets, cour-tesy of the Department of Radiology and Medical Imaging,University General Hospital of Alexandroupolis, Greece.The first data-set (top row in Fig. 1) is a 512× 512× 77,8-bit volume of the upper abdominal region with a renal cal-culus present at the left kidney. The first image from the leftshows an axial ortho-slice in which the stone is visible as abright disk within the renal pelvis. Setting λSPH = 0.4 andλV = 460, the final result of the two filters is shown in themiddle image which is an iso-surface projection at iso-level1. The spikes visible are of low intensity which can eitherbe thin crystal protrusions lodging the stone to the kidney orconnected noise particles. To remove them, an open-close op-eration with a spherical structuring element of a rather smallradius is sufficient. The segmented stone superimposed withthe spinal cord is shown at the right most image.The second data-set was acquired in the process of evalu-ating a pelvic bone disorder. It is a 512 × 512 × 125, 16-bitvolume in which, incidentally, a cluster of three urinary stonesare visible along the ureter. The first image of the second row2630Fig. 1. Axial ortho-slices (CT) of three cases of urinary stones: in a kidney, along the ureter and in the prostate (first columnfrom the left); the extracted stones (second column); the stones superimposed with other anatomical structures (third column).- Fig. (1) shows the cross-section of one of them, next to thepelvic bone (small bright disk). All three stones are morespherical than the previous case allowing for a higher valuefor λSPH . This, removes further noise at the first step al-ready. The filter settings for this set are λSPH = 0.6 andλV = 5 and the result is shown at iso-level 5, middle image.The final result is superimposed with an enhanced view of thepelvic bones for localization - right most image.The third case is of a patient suffering from a urinary blad-der stone. The data-set shown in third row of Fig. (1), isa 512 × 512 × 31, 8-bit volume. Using λSPH = 0.6 andλV = 40, clears entirely the image leaving the stone alone.It is shown at iso-level 1 in the middle image. The third im-age, like the two previous cases, shows the segmented resultsuperimposed with parts of pelvic bones for localization.4. DISCUSSIONStacks of CT scans used to construct 3D models often containanisotropic data which have an undesirable effect on the qual-ity of the visualization methods chosen. The data-sets usedin the previous section, though not highly anisotropic, havean impact on the filter parameters too, which is particularlynoticeable in the last experiment. The stone, even though itappears to be spherical enough to expect a higher λSPH , it isremoved for any value higher than 0.6. If spacing informationare not taken into consideration, it can be seen that the stoneactually looks more like an oblate spheroid. This is a rotation-2631ally symmetric ellipsoid having a polar axis shorter than thediameter of the equatorial circle whose plane bisects it. Thesphericity measure of such a spheroid is given bySPH =2 3√ab2a+ b2√a2−b2 ln(a+√a2−b2b ), (7)where a, b are the semi-major and semi-minor axes respec-tively. As b gets smaller the volume is reduced at a higherrate than the surface area, thus SPH reduces too. Addition-ally, it can be shown that in the case of isotropic voxels, thearea of a sphere is approximated in the 6-neighbor case as 6π r2(the surface seen face-on times the six faces). This means thatthe sphericity of a digital sphere is 4/6 in this case while foran axis aligned cube it is 0.82, as expected. Both factors arecountered in an anisotropy-invariant volume and surface areametric (also rotation invariant), currently under development.For the second data-set, using any higher λSPH removesthe lower two stones which are not as spherical as the topone. In the first data-set the stone is not very spherical butsufficiently compact to be differentiated from the rest of theanatomical structures. The small, thin protrusions if judgednecessary for volumetric purposes but undesired in visualiza-tion, they can be removed from the scene by increasing theiso-level. Since they do not contain as much calcium as themain body of the stone, they do not reflect much radiation andthus are of low intensity.The timings of all three experiments where taken on a sys-tem with an Intel(R) Core2 CPU T7400 @ 2.16 GHz proces-sor and 2GB RAM, running Windows XP. For each volumethe first set gives the time (sec.) taken for building and fil-tering the Max-Tree with the sphericity attribute and the sec-ond for the volume attribute. Kidney stone: (27.359,0.563),(18.859,0.484); ureter stones: (46.844,1.797), (32.219,1.468);bladder stone: (9.375,0.203), (6.359,0.188). Computing thesphericity attribute takes approximately 1.5 times longer thanthe volume attribute which is explained by the algorithm’s de-mand to revisit each voxel’s 6-neighborhood for computingthe surface measure.5. CONCLUSIONSIn this paper we used two connected attribute filters based onthe sphericity and volume attributes to isolate urinary stonesfrom CT data-sets. Our method, apart from its simplicity hasthree major advantages; the edges of the extracted stones re-main intact after filtering, there is no pre-processing or ini-tialization required and the filters are computed in very shorttimes given the size of the data-sets. The filters operate di-rectly on 3D data and the filter parameters can be changed in-teractively without re-computing the Max-Tree structure [6].In future work, we aim at improving the surface metric.A further study of more complicated cases of kidney stones isalso being carried out. Kidneys may have several stones andof varying size and shape while other artifacts may co-exist,satisfying both criteria. To handle such cases we are lookingat generalized notions of connectivity such as in [10]. More-over, a comparative study between this and active surface-based methods should be carried out to quantify the advan-tages in both speed efficiency and robustness.6. REFERENCES[1] N. P. N. Buchholz, “Three-dimensional ct scan stonereconstruction for the planning of percutaneous surgeryin a morbidly obese patient.,” Journal of Endourology.,vol. 16, no. 4, pp. 215–220, 2000.[2] A. Osorio, O. Traxer, S. Merran, F. Dargent, X. Ripoche,and J. Atif, “Real time fusion of 2d fluoroscopic and 3dsegmented ct images integrated into an augmented real-ity system for percutaneous nephrolithotomies (pcnl),”in RSNA’04, Chicago, USA, November 28-December 32004.[3] E. J. Breen and R. Jones, “Attribute openings, thinningsand granulometries,” Comp. Vis. Image Understand.,vol. 64, no. 3, pp. 377–389, 1996.[4] J. Serra, Ed., Image Analysis and Mathematical Mor-phology. II: Theoretical Advances, Academic Press,London, 1988.[5] C. Ronse, “Set-theoretical algebraic approaches to con-nectivity in continuous or digital spaces,” Journal ofMathematical Imaging and Vision, vol. 8, pp. 41–58,1998.[6] M. A. Westenberg, J. B. T. M. Roerdink, and M. H. F.Wilkinson, “Volumetric attribute filtering and inter-active visualization using the max-tree representation,”IEEE Trans. Image Proc., vol. 16, no. 12, pp. 2943–2952, 2007.[7] E. R. Urbach, J. B. T. M. Roerdink, and M. H. F. Wilkin-son, “Connected shape-size pattern spectra for rotationand scale-invariant classification of gray-scale images,”IEEE Trans. Pattern Anal. Mach. Intell., vol. 29, no. 2,pp. 272–285, 2007.[8] H. Wadell, “Volume, shape and roundness of quartz par-ticles,” Journal of Geology, vol. 43, pp. 250–280, 1935.[9] P. Salembier, A. Oliveras, and L. Garrido, “Anti-extensive connected operators for image and sequenceprocessing,” IEEE Trans. Image Proc., vol. 7, pp. 555–570, 1998.[10] G. K. Ouzounis and M. H. F. Wilkinson, “Mask-based second-generation connectivity and attribute fil-ters,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 29,no. 6, pp. 990–1004, 2007.2632

Robust extraction of urinary stones from CT data using attribute filters

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Robust extraction of urinary stones from CT data using attribute filters

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