Page - 180 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

pi t p� p1 p2p3 p4 (a) t p� p1 pi p2p3 p4 b plm pjk (b) Figure2: (a)Thevector tdescribes theprincipal directionoutbound frompi. (b)Thevertices on the orthogonal secondarydirectionbarepjk=p12 andplm=p34. 2.3. Non-maximumsuppressionwithborder treatment Finallywedistinguishverticesbeingmaximafromthosebeingnon-maxima: • If eitherf(pjk)orf(plm) is larger thanf(pi), thenpi is suppressedbydiscarding thisvertex. • Otherwisepi is amaximumandadded to the listLmax. In casepi is on the border∂M2, we treat the vertex by checking the existance of the edgesejk and elm intersecting theplaneτnb. Forexistingedgesweproceedasdescribedabove.Otherwisewehave to choose a functionvalueofpj close toτnb: If there is an edgeeijwith �eˆij,b�> 0wechoose the functionvaluef(pj)of theedgehaving thedotproduct closest to1. Havingnopositivevalue for the dot product leads to suppression of the vertex. This procedure is repeated using−b for the second secondarydirection. 3. Results The execution times for various realworld and synthetic test cases behave linear, depending on the number of vertices of themesh. This heuristically determined computational complexity ofO(n) withn being the number of vertices is shown in Table 1. The resulting ridge points on a detail of a three-dimensionally acquired cuneiform tablet is shown inFigure 3. These selected points can be exportedusingthecurrentviewanditsunderlyingOpenGLprojectionmatrixwithinGigaMesheither asperspectiveorasorthogonalprojection. The latter is true toscaleassumingacalibrated3D-model. While the surfaces are rendered as raster images, the ridge points are exported as overlays using the Scalable VectorGraphics (SVG) [4]file format, which describes their exact location using the eXtensibleMarkupLanguage (XML), commonlyusedwithin theDigitalHumanities. Results onahigh resolutiondata set are shown inFigure4a. Due to thehighdensityof vertices, the algorithm responds to small disturbances i.e. noise of the surface, leading to false positives. These can be eliminated by smoothing the surface prior to the application of our algorithm. In Figure 4b a combination of Taubin andTwoStep smoothingwas applied usingMeshLab [3]. This increase in robustness behaves – as expected – like theCanny edge detector, which has a smoothing step as a prerequisite. 180