Page - 178 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

Thiswork ismotivatedby the task toextractcuneiformcharactersandother imprintedfeaturesoutof 3D-modelsof tablets. Themodelsareacquiredusingoptical scannersbasedon theprincipleofstruc- tured light [12].HavingarobustfilterusingMulti-Scale Integral Invariants (MSIIs) [7]weextended, thefilteringusing theprincipleof thenon-maximumsuppressionasknownfromtheCannyedgede- tector [2]. Thereforewehad toextend thealgorithmfor anarbitrarynumberofneighboringvertices as there is nofixednumber of neighboringpixels/vertices. AsMSIIfilteringdoesnot provide agra- dient directionwehad to add an estimator using the normals of the triangles (faces) connecting the vertices. To improve robustnessweapplya localmeshsimplification forflat areas. Theseprocessing stepsaredescribedwithinthenextsectionsandareembeddedwithinourmodularGigaMeshsoftware framework[8,9],whichprovides theMSII–andotherfilter results–asprecomputedfunctionvalues f(·) for irregularmeshes. Thiswork is used for further processing to gain high-level knowledge of cuneiformtablets asknownfromthedomainofHandwritingTextRecognition (HTR) [1]. 2. RidgeTracingonIrregularGrids Theacquired3D-models consist ofmeshes describedby lists of verticespi=(xi,yi,zi)T and faces (triangles) ti := {pAi,pBi,pCi} having an orientation. The mesh is a discrete two-dimensional manifoldM2 inR3havingorientatededges{eai,ebi,eci},whichare implicitlygivenby theoriented faces[7]. Theorientatedfacesallowtodetermine thespaceenclosedbythemesh. Theindex i isused to address all the elements of themeshprocessed consecutively,while j addresses all elements next to the elementwith index i. Note that computational expensive calculations – especially theMSII filter – areparallelizedwithinGigaMesh. Thevertices of the1-ringneighborhoodaredenotedaspj around the central vertexpi. The 1-ring contains all faces sharingpi. Additionally each face t has a normal vector denoted as denoted byn, which are normalized nˆ= n/|n| before e.g. computing the dot product �nˆi,nˆj�. Furthermorewe compute a normal vectorni for each vertexpi using the normalsnj of theadjacent facestj. Experimentshaveshown that this approximation is sufficient for ouralgorithmandmorecomplexmethods likenormalvectorvoting [11]arenotnecessary. 2.1. Retrievalandsimplificationofordered1-rings For the following stepsof thenon-maximumsuppression theverticesnext to eachother are required to be in the sequence given by the orientation of the edges. Our algorithm then uses the implicitly given adjacencies of themesh to fetch all faces ot the 1-ring ofpi following the orientation of the edges, adding theverticespj to a sorted listwithout duplicates excludingpi.GigaMesh ensures that non-manifold vertices and edges are removed [7, p. 121] before computing the sorted list. Ifpi is a vertex on the border∂M2 of themesh, a second iteration using the opposite orientation of faces’ edges isnecessary–otherwiseanarbitrarynumberofverticesof the1-ringwill bemissing. As subsets of consecutive verticespj can be on a plane the 1-ring has to be simplified to provide a robust tracing of ridge points. For this reason each subset of consecutive vertices are reduced to one representative vertex denoted asp� in the following example, which is shown in Figure 1. It showsconsecutivevertices{p5, ..,p9},whichare located togetherwithpi inoneplane, i.e. the faces defined by those vertices have the same direction of their normals. Theoreticallywe can detectflat partswithin the 1-ring by pairwise computing the dot product of adjacent triangles’ normals. Such sets of triangles could be replaced by one bigger triangle. As triangle normals can only provide gradient directions within its 1-ring, we have chosen to use the vertex normals, which can store arbitrary normals computed from a range ofmethods, e.g. aweighted average or computed using 178