YMCA Your Mesh Comparison Application

Transcription

1 YMCA Your Mesh Comprison Appliction Johnn Schmidt, Reinhold Preiner, Thoms Auzinger, Michel Wimmer, M. Edurd Gröller, Memer, IEEE CS, nd Stefn Bruckner Memer, IEEE CS Alg. 01 Alg. 02 Alg. 03 Alg. 01 Alg. 02 Alg. 03 c d e Fig. 1: Visul nlysis for mesh comprison. We propose YMCA, system tht comines explicit encoding, juxtposition nd quntittive mesures to llow the user to compre multiple meshes. YMCA conveys n overview of the ville dt (, ), points to interesting fetures in the dt (c) nd llows for the inspection of locl res of interest (d,e). Astrct Polygonl meshes cn e creted in severl different wys. In this pper we focus on the reconstruction of meshes from point clouds, which re sets of points in 3D. Severl lgorithms tht tckle this tsk lredy exist, ut they hve different enefits nd drwcks, which leds to lrge numer of possile reconstruction results (i.e., meshes). The evlution of those techniques requires extensive comprisons etween different meshes which is up to now done y either plcing imges of rendered meshes side-y-side, or y encoding differences y het mps. A mjor drwck of oth pproches is tht they do not scle well with the numer of meshes. This pper introduces new comprtive visul nlysis technique for 3D meshes which enles the simultneous comprison of severl meshes nd llows for the interctive explortion of their differences. Our pproch gives n overview of the differences of the input meshes in 2D view. By selecting certin res of interest, the user cn switch to 3D representtion nd explore the sptil differences in detil. To inspect locl vritions, we provide mgic lens tool in 3D. The loction nd size of the lens provide further informtion on the vritions of the reconstructions in the selected re. With our comprtive visuliztion pproch, differences etween severl mesh reconstruction lgorithms cn e esily loclized nd inspected. Index Terms Visul nlysis, comprtive visuliztion, 3D dt explortion, focus+context, mesh comprison 1 INTRODUCTION Polygonl meshes re one of the most commonly used surfce representtions in 3D computer grphics. Their explicit description of the surfce loction in 3D together with locl connectivity informtion enles memory-efficient storge nd provides convenient dt structure for wide rnge of pplictions (e.g., in geometric processing). For mny tsks relted to mesh cretion nd/or editing, multitude of proposed methods exist. Polygonl meshes my serve oth s input nd output for mjority of such techniques. As consequence, the chrcteristics nd cpilities of different pproches for common tsk hve to e evluted on the sis of their results, which inevitly leds to the need to compre n often lrge numer of similr meshes. While forml geometric properties (e.g., polygon res) cn e evluted y purely mthemticl methods, esthetic considertions lmost lwys require humn in Johnn Schmidt, Vienn University of Technology, Austri Reinhold Preiner, Vienn University of Technology, Austri Thoms Auzinger, Vienn University of Technology, Austri Michel Wimmer, Vienn University of Technology, Austri M. Edurd Gröller, Vienn University of Technology, Vienn, Austri Stefn Bruckner, University of Bergen, Norwy Accepted for puliction y IEEE. (c) 2014 IEEE. Personl use of this mteril is permitted. Permission from IEEE must e otined for ll other uses, in ny current or future medi, including reprinting/repulishing this mteril for dvertising or promotionl purposes, creting new collective works, for resle or redistriution to servers or lists, or reuse of ny copyrighted component of this work in other works. the loop. The plesntness of the finl form is of mjor importnce for severl geometric processing tsks such s mesh resmpling, mesh denoising, nd mesh reconstruction from point clouds. Especilly the lst exmple is currently hot topic in reserch [6], s the dvent of ffordle scnners hs mde the cretion of virtul representtions of rel-world ojects commodity. Beyond computer grphics, other fields tht del with 3D ojects, like CAD or iomoleculr modeling, would lso enefit from new trends for multi-mesh comprison. As n exemplry use cse, we further concentrte on mesh reconstruction, which refers to extrcting meshes from point clouds s ccurtely s possile. A wide vriety of techniques hs lredy een developed, nd these lgorithms differ (more or less) sutly in their reconstruction ehvior especilly in the presence of noise, outliers or other errors in the input dt [7]. Furthermore, with lmost every technique the output depends on severl, prtly very sensitive, prmeters with vrying suitility for different kinds of dt. All these fcts crete lrge spce of possile results when reconstructing mesh from point cloud. Especilly the evlution of new technique currently requires extensive lorious comprisons, not only etween smples of the pproch in its own prmeter spce, ut lso to existing stte-ofthe-rt methods. Such comprison tsks re dditionlly complicted y the fct tht the desired outcomes cn e highly tsk-dependent nd difficult to quntify, which mkes visul inspection unvoidle. Comprtive visuliztion refers to the process of visully depicting differences nd similrities in two or more dtsets [23]. Within the lst yers vrious comprtive visuliztion systems hve een developed, which demonstrte tht there is strong demnd for the support of comprison tsks in vrious domins. According to Gleicher et l. [16] there re three min pproches to compre dt: juxtposition (i.e., side-y-side comprison), superposition (i.e., lending), nd ex-

2 Fig. 2: Common mesh comprison pproches. Current tools employ either sttisticl evlution (), juxtposition () or explicit encoding y color (c) to show differences etween meshes (Section 2). plicit encoding (i.e., difference encoding y some strct prmeter). Up to now, the tool-set for visul comprisons of mesh reconstructions is limited to sttisticl evlution (e.g., glol error), simple juxtposition, or explicit encoding y color (Figure 2). The existing pproches do not scle well with the numer of instnces, nd siclly support only pirwise comprisons. Color-coding of differences only prtilly chrcterizes the ehvior of the underlying lgorithm (e.g., whether the dt is smoothed). We elieve tht comintion of explicit encoding, juxtposition nd quntittive mesures cn support mesh comprison tsks nd provide more insight into the underlying dt. We propose YMCA, new comprtive visul nlysis pproch which llows users to compre severl meshes ginst ech other. Our ppliction, on the one hnd, helps to identify res in the dt where reconstruction lgorithms produce different results, nd lso llows for detiled explortion of locl vritions. On the other hnd, our system supports users in gining insight into the chrcteristics of different mesh reconstruction lgorithms. The min fetures of our pproch re: Comprison of multiple entities: Our visul nlysis methods re designed to overcome the prolems of previous pproches tht do not scle well with lrger numer of meshes. With our pproch users re le to get n overview of ll studied lgorithm results. It is lso possile to evlute the performnce of individul lgorithms ginst others. Focus+context: As strting point of the nlysis process, we provide n overview of the comprison results. Users cn then further concentrte on locl vritions nd explore them in more detil without losing the context informtion. Flexiility: The proposed visul nlysis tools cn e pplied to different mesh comprison tsks, e.g., compring meshes fter mesh simplifiction, s well s compring different reconstructed meshes. The pproch is neither tied to certin type of mesh (e.g., wtertight mesh), nor to certin mesh comprison metric. The pper is orgnized s follows: Section 2 contins survey of previous work relted to the topics of comprtive visuliztion, mesh reconstruction, nd focus+context interction techniques. Section 3 provides n overview of the tsks nd chllenges we ddress. In Section 4, the process of identifying mesh differences is descried, nd our interctive visuliztion tools re introduced. Implementtion detils re discussed in Section 5 nd results re presented in Section 6. We lso collected feedck which is descried in Section 7 to evlute our pproch. In Section 8 we discuss the dvntges nd limittions of our pproch nd n outlook on future work is given. The pper is concluded in Section 9. c 2 RELATED WORK The work presented in this pper is locted in the field of comprtive visuliztion. In the lst yers gret vriety of systems nd pproches for comprtive visuliztion hve lredy een developed, which re discussed in this section. Since we compre severl meshes in 3D, we included comprison of our pproch to existing techniques in the re of mesh comprison. The meshes we use hve een reconstructed from point clouds, nd here we revert to well-studied findings from the field of surfce reconstruction. Our work mkes use of severl well-known interction concepts (i.e., focus+context nd linking nd rushing), which re lso discussed in this section. Comprtive visuliztion. Some pproches from the field of comprtive visuliztion del with compring 2D dt (e.g., imges [33]), ut there is lso representtive group of systems used to compre 3D dt. Some of these pproches nlyze multiple 3D dt structures (e.g., shpes or volumes) y compring 2D representtions of the dt [14, 24]. Mlik et l. [21] proposed method to compre different volume dtsets y nlyzing 2D slices. Other methods concentrte on the comprison of dt in 3D, similr to our pproch. Msud et l. [22] visully nlyzed 3D shpes of ncient Chinese ronze mirrors y color-coding their differences. Wtshi et l. [31] used criticl point grphs to depict similrities in volume dtsets. Ali et l. [1] presented method for side-y-side comprison of surfces in 3D. All together, these systems show the demnd for tools tht explicitly support comprison tsks in 2D s well s in 3D. Mesh comprison. Due to the need to evlute mesh editing tools (e.g., for mesh simplifiction), mny pproches hve een developed tht support mesh comprison. Vrious techniques focused on the mthemticl ckground nd estlished metrics which cn e used to compre meshes. Aspert et l. [4] proposed n pproch to mesure differences etween two meshes y using the Husdorff distnce. Roy et l. [26] introduced new mesh comprison method using n ttriute devition metric. MeshL, y Cignoni et l. [9], ws implemented to comine mesh comprison s well s mesh editing tools. In our work we focus on visul support for mesh comprison, nd some interesting pproches hve lredy een developed in this re. Cignoni et l. [11] presented Metro, system tht llows for pirwise comprison of surfces. A similr pproch ws lter proposed y Silv et l. [28]. Their system, which is clled PolyMeCo, llowed users to compre meshes ginst reference mesh. Existing pproches for mesh comprison use color to encode the differences nd present the results y juxtposition. Therefore, they re limited to smll numer of meshes. Aprt from zooming, the systems lso do not provide mens to inspect locl res. In our pproch we extend these ides to provide mens to compre multiple meshes, nd to inspect locl regions in more detil. Surfce reconstruction. The cquisition of virtul representtions of scnned rel-world ojects from point clouds is referred to s surfce reconstruction. In contrst to point-set surfcerepresenttions [2, 3], this pper focuses on mesh reconstruction from point clouds. Meshes re reconstructed ccording to different formultions of implicit surfces defined on the input points, rnging from loclly fitted tngent plnes [18], rdil sis functions [8], to Poisson reconstruction [20]. All these techniques exhiit their own chrcteristic reconstruction ehvior in terms of roustness nd ccurcy, nd require vrious prmeters which influence the result. Berger et l. [6] present enchmrk tool for surfce reconstruction lgorithms, where the user cn test different lgorithms on different point cloud dtsets. When presenting the results, they use juxtposition where rendered models re plced side y side. This wy the complex tsk of finding relevnt differences in the dt is shifted to the user. Linking-nd-rushing. The concept of linking-nd-rushing is well-known in visuliztion. It refers to the connection of two or more views in wy tht chnge to the representtion in one view ffects the representtion in the other one s well [30]. Linking-nd-rushing is very flexile concept tht cn e pplied to mny different dt representtions, like 2D dt (e.g., sctter plots [5]) s well s 3D

3 + Error Vrinces High Vrince Locliztion Visul Anlysis meshes m 1... mn reference mesh mref vrince mp high-vrince regions Fig. 3: Overview of our visul nlysis pproch. The input dt consists of set of n meshes nd one reference mesh. The surfce devitions of the meshes re clculted to get the corresponding vrince mp (Section 4.1). Afterwrds high-vrince regions re locted in the dt (Section 4.2). The results re finlly presented in n interctive visuliztion s descried in Section 4.3 nd Section 4.4. dt [15]. We use linking-nd-rushing to keep trck of user selections. Elements in our summry representtions cn e selected, which will mrk them s selected lso in the detiled view (nd vice vers). Focus+context. The strength of focus+context nd in-plce interction techniques is tht they give n overview of the ville dt, ut lso llow us to further inspect detils on demnd. Severl focus+context pproches cn e found in the literture [12]. Similr to linking-nd-rushing, focus+context is very flexile concept which hs lredy een pplied in mny different visuliztion pproches (e.g., sctter plots [25] or sets of imges [27]). To loclly explore dt in 3D, Zho et l. [32] employed focus+context with locl shpe preservtion y using conforml mpping. Cignoni et l. [10] estlished 3D mgic lens tool with user-specific content (e.g., different rendering techniques or the result of filtering opertions). In our system we use mgic lens tool, which is similr to the two ltter pproches. The user cn employ this tool to mke selections, which will provide more detiled insights into certin dt prts. The selection is mde on the 3D representtion of the dt, wherey the context of the selection is lwys preserved. 3 CHALLENGES OF MULTI-MESH COMPARISON The need to compre different meshes cn e the result of vrious geometric opertions. As n exemplry use cse, we focus on the reconstruction of meshes from point clouds. Severl meshes cn e constructed from the sme point cloud with different lgorithms. The lgorithms differ in their reconstruction ehvior [7], which mens tht the resulting meshes exhiit sutle differences. The nlysis of such dtsets poses interesting chllenges. We therefore introduce Your Mesh Comprison Appliction (YMCA) of choice, which ddresses the chllenges of multi-mesh comprison, s discussed elow: Notion of qulity. When reconstructing point cloud, the user is interested in surfces tht mtch the shpe of the originl specimen s ccurtely s possile. In prctice, users often fce trde-off etween the preservtion of geometric detil nd the roust removl of scnning rtifcts like noise or holes. From sttisticl point of view, the qulity of reconstruction is defined y the residul distnces of ech surfce point from the reference shpe. However, sttisticl evlution lone hrdly communictes full understnding of technique s strengths nd weknesses on different types of dt. For exmple, it might hppen tht lgorithms with low overll error rte smooth certin fetures in the dt, which might not e desired y the user. YMCA presents generl error mesurement to the user, nd lso llows to judge the visul qulity of the resulting shpes. Giving the user insights into the results nd providing him/her the possiility to compre them ginst ech other, lso supports understnding the ehvior of the different reconstruction lgorithms. For exmple, users will identify undesired chrcteristics like over-smoothing or sensitivity to noise. YMCA provides mens to quickly eliminte lgorithms from further comprisons if they do not show desired ehvior, which cn help to nrrow down the serch spce quite fst. Complexity nd sclility. Current mesh comprison methods provide mens to inspect the shpe nd error of mesh smple individully [6], or llow for mostly pirwise comprisons mong the smple set [9, 28]. These methods quickly ecome unsuitle for lrger smple sets, e.g., when using multiple smples in the prmeter spces of different reconstruction lgorithms. YMCA provides compct visul overview tht presents individul qulity informtion (e.g., reconstruction error) in the pproprite context nd tht shows the most relevnt differences t glnce. It is no longer necessry to scn/rotte/zoom into severl 3D meshes one fter nother, since the mesh elements cn now e explored t once. Evlution. For newly developed reconstruction techniques, common tsk is their evlution nd clssifiction with respect to existing methods. So fr these required tedious explortion of the high dimensionl spce spnned y the input dt (e.g., shpe, or mount of noise) nd the lgorithm prmeters (e.g., kernel functions or ndwidth). With YMCA it is possile to quickly extrct the regions on the mesh where the lgorithm of interest shows etter/worse results thn the other ones it is compred to. YMCA cn extrct the most prolemtic regions of the mesh, which re those where the reconstruction results hve high vrince. None of the existing methods used for mesh comprison ccommodte the ove spects so fr (Section 2). YMCA llows for n intuitive, guided nd flexile visul nlysis of sclle set of similr meshes to explore the differences mong them. 4 YMCA YOUR MESH COMPARISON APPLICATION YMCA comines explicit encoding, juxtposition, prllel coordintes, nd interction techniques (i.e., linking-nd-rushing nd focus+context) to convey n overview of mesh differences, nd to llow the user to inspect locl res of interest. As mentioned in Section 3, we focus on tringulr mesh dt produced y different mesh reconstruction lgorithms. The dt hs een creted y the surfce reconstruction enchmrk tool implemented y Berger et l. [6]. The meshes re lredy registered. No pre-processing (e.g., filtering) hs een pplied to the meshes. In ddition, reference mesh is ssumed to e ville for every point cloud. See the discussion in Section 8 for our strtegy, if such reference is not ville. To provide condensed representtion of ll differences in the dt, we propose to project the vrinces of the mesh devitions onto the reference mesh. The clcultion of the vrinces is descried in Section 4.1. In ddition, we locte prolemtic regions (i.e., regions of high vrince) in the model to provide dditionl guidnce to the user when exploring the dt. The detection of such regions is outlined in Section 4.2. The prolemtic regions re used to uild prllel coordintes plot to visulize the performnce of the reconstruction lgorithms (Section 4.3). The inspection of locl res provides interesting insights into the ehvior of the reconstruction lgorithms. The visul nlysis tools of YMCA re descried in Section 4.4. The whole pipeline of YMCA is outlined in Figure Clcultion of Error Vrinces The visul nlysis of vritions in multiple meshes requires the computtion of mesh differences. For the mesh comprison we use n ttriute devition metric s descried y Roy et l. [26]. This metric compres meshes in pirwise mnner nd clcultes point-wise devitions from reference mesh to nother mesh. The devition is

4 x c x i isotropic kernel N x i x j nisotropic kernel Fig. 4: Surfce-wre Men-Shift. Insted of using n isotropic kernel (), we employ surfce-wre Men-Shift with n nisotropic kernel () round the current men x i. This prevents the mens from moving wy from the model surfce (x c ). Insted, y considering the norml vector N, the mens sty close to the intrinsic surfce (x j ). defined s the distnce etween vertex of the reference mesh nd the nerest point on the surfce of the other mesh. Our pproch is not tied to certin type of metric. In this pper we concentrte primrily on the clcultion of the regions of high vrince (Section 4.2) nd the visul nlysis of the mesh differences (Section 4.3 nd 4.4). The metric to clculte the mesh differences my e exchnged, s it is outlined in Section 8. Given n input meshes M 1,...,M n, the mesh comprison results in set of n surfce devition vlues (in the following simply denoted y errors) for every vertex in the reference mesh M ref. We then clculte the per-vertex error vrinces (sed on the n error vlues) for ll vertices in M ref. In YMCA, we cll this discrete distriution of vrinces the vrince mp. 4.2 Automtic High Vrince Locliztion To guide the user in the comprtive nlysis nd explortion process, we provide n overview of the surfce regions showing the h highest error vrinces. These re ssumed to e the most interesting res for comprison due to the high disgreement etween the reconstruction methods. To this end, we use the vrince mp computed in the previous section to locte locl mxim in the distriution of per-vertex vrinces on the surfce. These mxim re found y employing weighted Men-Shift [13] lgorithm in R 3 on the set of mesh vertices, where the per-vertex vrinces define the weights. This is done once in pre-processing step, directly fter the vrince mp computtion. A set of initilly rndom smples x i, i = 1...N of mesh vertices re itertively shifted towrd modes in the vrince distriution using smooth kernel θ(r) = e 4(r/s)2 of finite support s. One itertion step is given s x i = j θ(δ i j )σ 2 j p j j θ(δ i j )σ 2 j where σ 2 j gives the vrince t vertex j, while p j is its loction in R 3 nd δ i j denotes its distnce to the smple x i. However, n isotropic kernel might let smples move wy from the intrinsic surfce descried y the locl neighorhood of vertices (Figure 4). Thus, we need to constrin the smple movements close to the locl surfce round x i (Figure 4). We employ surfce-wre distnce metric δ i j, which incorportes the surfce norml n i into the weighting kernel s given y (1) δ i j = p j x i + ni, p j x i. (2) After the smples converged to different high-vrince modes on the surfce, similr points re discrded, nd the remining ones sorted y their mplitude. This gives list of hot-spots tht we use in the consecutive visul nlysis procedure (Section 4.4). Besides the positions p i of the hot-spots, we re lso interested in their extent, which is given y the weighted smple stndrd devition σ of vrince vlues t every hot-spot. 4.3 Prllel Coordintes Plot The list of hot-spots creted in the previous section cn e used to spn multi-dimensionl feture spce. The spce is defined y the numer of hot-spots h nd the error vlues e n for every input mesh t the hot-spot positions. We propose to use the high-dimensionl visuliztion technique of prllel coordintes [19] to nlyze this multidimensionl feture spce. Every hot-spot defines one xis in the prllel coordintes plot, nd the dimensions of the xes re given y the glol minimum nd mximum error vlues. The input meshes re represented s lines in the plot (Figure 5). The xes in the plot re initilly sorted ccording to the hot-spots weighted smple stndrd devition σ of vrince vlues. The sorting of the xes cn e interctively chnged y the user. The prllel coordintes plot gives n overview of the error rte of the reconstruction lgorithms in regions of high vrince. 4.4 Visul Anlysis YMCA provides interctive tools to explore the results of the mesh comprison nlysis. The min elements of the user interfce re illustrted in Figure 1. Overview imge. To provide n overview of the differences in the dt, we propose rendering of the reference mesh (Figure 1). A het mp is projected onto the mesh ccording to the current vrince mp. The defult het-mp colors rnge from lue (low vrince) to red (high vrince). If necessry, the color scle cn e chnged y the user y selecting different colors for the minimum nd mximum vrince vlues. The reference mesh rendering llows the user to inspect differences in the dt without hving to inspect ll individul meshes, ecuse the relevnt informtion is ggregted in one view. An exmple for n overview imge cn e seen in Figure 6. Hot-spots nd prllel coordintes. In the user interfce, the hot-spots re rrnged in prllel coordintes plot s descried in Section 4.3. The prllel coordintes plot, where the hot-spots re emedded in, represents the input meshes s lines, indicting their locl error vlue t the hot-spot positions (Figure 1). To interct with the dt, the users cn chnge the ordering of the xes nd lso eliminte individul hot-spots y mouse interction. It is lso possile to crete new hot-spots during the nlysis (see elow). To give the user n ide out the position nd size of the hot-spots, they re represented y thumnil imges of the mesh displyed t the corresponding prllel coordintes xes (Figure 1c). The thumnil imges re creted when hot-spot is creted in the system. The reference mesh is used to generte the imges, nd the viewports re given y the corresponding hot-spots loctions. The imges cn e ctivted y mouse interction in the interfce. When clicking on one of them, the t 1 t h e min m 1... m n e mx Fig. 5: Prllel coordintes plot. We cn use the hot-spots (Section 4.2) to crete multi-dimensionl feture spce, defined y the numer of hot-spots t 1...t h nd the error vlues e t those positions for ll input meshes. The hot-spots re represented s thumnil imges, nd the input meshes m 1...m n re defined y lines.

5 Fig. 6: Overview imge. In this figure the reference mesh with projected het mp ccording to the vrinces in the dt is shown (), s well s some mesh regions in more detil (). overview is utomticlly rotted to the loction of the hot-spot. The optiml viewing ngle is clculted y ligning the viewing direction with the norml vector of the hot-spot nd centering it in the viewport. To emphsize the hot-spot loctions, we use focus+context pproch in the rendering of the mesh. We employ opque rendering only to the hot-spot re, while the rest of the mesh is depicted with high trnslucency (Section 4.5). The user cn use the prllel coordintes plot nd the hot-spots to quickly depict input meshes contining undesired results nd eliminte them from further nlysis. Mgic lens. Besides providing n overview of the dt, YMCA lso supports mens to further inspect locl vritions. We propose mgic lens tool (Figure 1d) which cn e used to select certin region of the mesh. The mgic lens is circulr, ecuse drwing circle is very intuitive wy of selecting ojects. A colored circle drwn over the mesh indictes the current loction of the lens. The size cn e dynmiclly djusted. Since the circle is trnsprent, the selected prt of the reference mesh is lso shown. Anlyzing locl vritions. The current loction nd size of the mgic lens tool is used to present more detiled informtion out the locl ehvior of the mesh reconstruction lgorithms in detil view (Figure 1e). To provide quntittive informtion, rnking of the mesh lgorithms is provided. The reconstruction lgorithms re sorted ccording to their corresponding ccumulted error t the current lens position. For every lgorithm rectngle is plced t the corresponding position long n error scle. The scle rnges from the glol minimum to the glol mximum error. The user cn ctivte rectngles y mouse interction to revel the nme of the lgorithm t this position. In ddition to the rnking, further visul informtion is needed for the nlysis of the meshes, for which we dded dt summriztion view. Here the meshes re clssified ccording to their ccumulted error t the current lens position (Section 4.6 for further informtion). This summry gives n overview of the vrince nd possile prolems t the current lens position. According to feedck from domin experts, esides hving n overview, it still is necessry to hve ccess to the individul meshes. Therefore, we llow the user to see close-up views of the reconstructed meshes. If more thn one mesh is selected, we plce the close-up views side-y-side ccording to the concept of Smll Multiples [29]. The meshes inside the closeup views re color-coded ccording to the ccumulted error t the current lens position. Here we use different het mp thn the one projected onto the reference mesh to mke cler distinction etween the vrince nd the locl error vlues. All interfce items re updted every time the mgic lens is moved or resized. An exmple of how detil view my look like cn e seen in Figure 7. Additionl user controls. We provide some dditionl controls which cn e used to dpt the system s interfce elements ccording to individul preferences. As mentioned ove, the color scles of the overview imge nd the close-up views of the reconstructed meshes cn e customized y the user. In ddition, the upper nd lower ound of the color het mp in the overview imge cn lso e djusted, which llows the user to concentrte on different vrince rnges. The render mode cn e chnged from hot-spot rendering to het-mp rendering t ny time. In the detil view, the user cn decide whether he/she wnts to see the glol rnking s well, nd whether he/she wnts to concentrte on the dt summriztion, on the individul meshes, or oth. Furthermore, it is possile to replce the reference mesh y some other input mesh. Then ll differences nd vrinces re re-computed nd the dt is re-loded. This option llows the user to compre one mesh ginst ll others in the dtset. 4.5 Hot-Spot Rendering The hot-spots in YMCA cn e dynmiclly ctivted in the user interfce y selecting hot-spot thumnil in the prllel coordintes view (Section 4.3). This utomticlly rottes the overview to n optiml viewing ngle to uncover the region of interest on the reference mesh. However, in mny cses the hot-spots re locted in concvities of the surfce, which re often occluded y other prts of the mesh. Thus, cler view onto the hot-spot my e prevented, nd the user might lose the focus if he/she rottes the model. We therefore use visuliztion technique tht removes ny occlusions of the interesting surfce region y incresing the trnsprency with the distnce to the hot-spot. Given pre-computed hot-spot position p nd its extent σ, we employ smooth trnsprency kernel K(x) = e 4 x p 4 /σ 4 to put the hot-spot into focus (full opcity) while removing occluding surfce prts nd t the sme time providing ckground context (high trnsprency). This is done y ry csting, using two render psses: First, in n ccumultion pss, the whole mesh is drwn into texture using ccumultive lending. Every frgment with corresponding surfce position x is weighted y the kernel K(x). This wy, the resulting texture stores for ech pixel the weighted sum of surfce colors long the respective ry, s well s the sum of ll weights. Then, in the normliztion pss, the ccumulted vlues in the texture re normlized y the sum of their weights nd drwn onto the screen (Figure 8). c d min min Alg. 01 Alg. 02 Alg. 03 Alg. 03 Alg Alg. 02 Alg. 03 Alg. 04 Fig. 7: Detil view. When using the mgic lens tool, the user cn hover over the reference mesh nd inspect prts of it in more detil. The glol error vlue of the input meshes () nd the locl error t the lens position () re displyed t the top. The meshes re clssified ccording to their locl error vlue t the current position of the lens (c). It is lso possile to view individul mesh renderings (d). mx mx

6 Fig. 8: Hot-spot explortion. This figure shows model rendered in hot-spot mode (Section 4.5) with three different hot-spot exmples (different position nd extend). 4.6 Dt Summriztion in the Detil View To del with sclility, nd to provide condensed overview of the dt, we decided to integrte dt summriztion into the detil view (Figure 7c). When hovering with the mgic lens over the mesh, the user should detils out the underlying dt, s well s comined summry. The purpose of the summry is to quickly inform the user out the vriility of the dt t the current lens position, nd indicte whether further inspection would e necessry. We propose to clssify the reconstructions ccording to their ccumulted error t the current lens position. The vrince t the current lens position indictes the numer of clsses which re needed. After detiled discussions with our collortors we cme to the conclusion tht dividing the dt into three clsses (est/middle/worst) is very intuitive wy of presenting summry of the dt. Therefore, mximum of three clsses is llowed. We use two fixed thresholds tht define the finl numer of clsses. An verge imge is used s clss representtive to disply the dt. Figure 9 gives n exmple of how the dt summriztion could look like. If the vrince t the current lens position is low, only one clss is creted contining ll meshes (Figure 9). This shows tht ll reconstruction lgorithms produced the sme result t this position. The higher the vrince, the more clsses re creted (Figure 9). Such positions on the mesh, where the reconstruction lgorithms produced very different results, might need further inspection y the user. The proposed dt summriztion provides good overview of the dt, where the user cn quickly decide out further locl inspection of the dt. In ddition to this level of strction, the verge imges representing the clsses still revel the underlying informtion IMPLEMENTATION The pre-processing step, consisting of compring the meshes nd clculting the vrinces, ws implemented in C++. We used MeshDev [26] to clculte the differences. The cost of the preprocessing step, consisting of the clcultion of the vrince mp nd the loction of the hot-spots, depends on the numer of meshes in the input dt set. No user input is required during the pre-processing step. The interction itself, which works in rel-time, hs een implemented in C++ nd OpenGL/GLSL. The ppliction ws tested on mchine with n Intel i7 CPU, 12 GB of RAM nd n NVIDIA GeForce GTX 580 grphics crd. A comprison of the computtion times nd memory requirements during the nlysis cn e found in Tle 1. A more detiled description of the dtsets cn e found in Section 6. Tle 1: Runtime nd memory requirements. The first column gives the nme of the dtset. The second column shows the numer of meshes in this dtset. The next column contins the runtime for the pre-processing, which consists of the clcultion of the vrinces nd the locliztion of the hot-spots. The lst column shows the mount of memory used on the grphics crd. Dtset Meshes Pre-Processing Memory Grgoyle s 82.6m Dncing-Children s 797.5m Drtech s 131.4m 6 RESULTS We used dt from the field of point-cloud reconstruction to test our pproch (see lso Section 4). The dt ws produced y different lgorithms, for exmple Poisson Surfce Reconstruction (Poisson), Algeric Point Set Surfces (APSS) nd Multi-level Prtition of Unity Implicits (MPU). The reder is referred to the survey y Berger et l. [6] for more detiled description of the reconstruction lgorithms. We pplied our pproch to three different dtsets. The first dtset, clled Grgoyle, comprises ten mesh reconstructions from virtul point cloud scn of crved stone figure. The second dtset, clled Dncing-Children, consists of 100 mesh reconstructions from virtul point cloud scn of n ornment. The third dtset, clled Drtech, comprises 15 mesh reconstructions from scn of n industril workpiece. Figure 10 shows renderings of the reference meshes of the three dtsets nd further informtion out the mesh dimensions. Different reconstruction lgorithms perform with different ccurcy on different prts of surfce. The prllel coordintes plot in conjunction with the hot-spot thumnils (Section 4.3) enles the user to understnd the reltive performnce of different lgorithms on prticulr prt of surfce, nd t the sme time llows him/her to visully inspect the reconstructed surfce nd its qulity. In Figure 11, YMCA visulizes n utomticlly identified rtifct in the Drtech dtset produced y the Wvelet lgorithm (wrong mesh vertices highlighted red), nd clerly clssifies this lgorithm s n individul outlier on the Vertices: Fces: Vertices: Fces: Vertices: Fces: Fig. 9: Dt summriztion. This figure shows two exmples for dt summriztion in the detil view when hovering over res of low () nd high () vrince. Fig. 10: Dtsets used to evlute YMCA. All dtsets consist of mesh reconstructions from point cloud scns. The first one () is clled Grgoyle, the second dtset () is clled Dncing-Children, nd the nme of the third dtset (c) is Drtech. c

7 Wvelet RBF Fig. 13: Mesh oundries. The summry view in the detil view enles users to identify regions where the reconstruction lgorithms produce lmost the sme () or different () mesh oundries, indicted y color nd. Fig. 11: Outlier detection. The visul nlysis tools of YMCA llow users to quickly detect outliers, which might e cused y noise in the dt () or y certin lgorithm ehvior like over-smoothing (). prllel coordinte xis, with reltively high reconstruction error. At different prt of the model, the RBF lgorithm stnds out y flsely closing hole, where ll remining lgorithms perform correctly (Figure 11). By giving this integrted overview of the lgorithms reltive performnce on different surfces res (sttisticlly nd visully), the hot-spot locliztion nd the prllel coordintes plot llow the users to quickly clssify lgorithms nd judge their eligiility. A mnul comprison of ll meshes is fr more tedious nd leds to prticulr rtifcts eing esily missed. In ll three dtsets, prts of the vrince mp exhiit rectngulrshped rtifcts. We used the overview imge nd the mgic lens (Section 4.4) to further inspect those res. With our tools we could find out tht these rtifcts re lwys produced y the Poisson reconstruction lgorithm (Figure 12). Apprently, this rtifct is cused y the limited resolution of the octree employed y the Poisson lgorithm for reconstruction. With the visul nlysis tools of YMCA, this rtifct could quickly e relted to the Poisson lgorithm nd explored visully. It is clerly visile in which prt of the model the octree resolution hs to e djusted to gurntee smooth reconstruction. With the dt summriztion used in the detil view (Section 4.6), differences t the reconstructed mesh oundries cn e explored. Blending the lens view of meshes of the sme clss llows direct comprison nd visuliztion of the geometric vrince of their oundries. In Figure 13, two exmples of different oundries cn e seen. Prts of the oundry of the Grgoyle model hve een reconstructed in similr wy y ll lgorithms (Figure 13), wheres in other prts the oundries of the reconstructed meshes differ more strongly (Figure 13). The differences in the oundries ecome visile s color nd in the imges. Different reconstructions my produce different oundries, due to different pproches to fit surfce to the point cloud dt. With YMCA it is now possile to explore these effects in detil. The regions where oundries differ re clerly visile when inspecting the mesh with the mgic lens. This helps the user to judge which reconstruction would etter represent the dt. The prllel coordintes plot of YMCA lso proved to e very helpful in the nlysis of lrge dtsets. If such dtsets shll e inspected, it is very importnt to quickly nrrow down the serch spce to suitle reconstructions. Reconstruction lgorithms tht perform either generlly very good, or very d, in most cses cn e identified. It is lso possile to eliminte lgorithms from further nlysis, if they do not meet certin reconstruction requirements. An exmple is given y the inspection of the Dncing-Children dtset, consisting of 100 meshes. The resulting prllel coordintes plot cn e seen in Figure 14. Here it ws possile to, for exmple, identify one lgorithms (Fourier-3) with low error rte, nd one lgorithm with high error rte (SPSS- 7) in ll hot-spot regions. We lso found one lgorithm (Scttered-2) tht exhiits vrying error rte. 0 Fourier-3 Scttered-2 SPSS Poisson min Fig. 12: Artifct nlysis. In ll dtsets rectngulr-shped rtifcts could e identified in the overview imge (). With the mgic lens tool it is possile to find out tht these rtifcts re cused y the Poisson reconstruction lgorithm (). Fig. 14: Anlyzing lrge dtsets. The prllel coordintes plot is very helpful tool when nlyzing lrge dtsets. One lgorithm with low error rte (Fourier-3), one with high error rte (SPSS-7) nd one with vrying error rte (Scttered-2) in the hot-spot regions could e identified very quickly.

8 7 EVALUATION To evlute our pproch, we hve collected qulittive feedck from users experienced in working with meshes. From this feedck we wnted to find out how useful the proposed visul nlysis is for the users, nd we lso discussed possile pplictions for future work. Every feedck session lsted etween 30 nd 45 minutes. First the motivtion nd the technique itself were explined to every prticipnt. Then they got trining dtset where they could test the interction possiilities. Afterwrds they were presented new dtset, nd were sked to nme one or more reconstruction lgorithms tht produce pproprite results for the given point cloud. They were lso sked to explin their decision. For this tsk they hd ten minutes time. At the end, we sked them to fill in questionnire with four questions (descried in Figure 15 nd Figure 16). We sked seven prticipnts (six men, one womn) to prticipte in our feedck study. Three of the prticipnts hve een working in the field of point-cloud reconstruction for yers, nd therefore hve lot of experience. Two other prticipnts re experienced computer scientists in the rendering field, where they re working with mesh opertions like filtering or simplifiction. Two prticipnts re students from the field of computer grphics. All prticipnts greed tht nlyzing point cloud reconstructions is n importnt tsk, nd tht existing methods do not provide sufficient ssistnce for this. Six out of seven prticipnts hd no prolem to solve the tsk of finding n pproprite reconstruction lgorithm for the given point cloud. One prticipnt rn out of time while solving the tsk. We compred the results with reconstructions tht were previously selected y domin experts. It turned out tht prticipnts selected the most suitle reconstruction lgorithms in ll cses. With the first three questions in the questionnire we wnted to find out more out the prcticility of the system: 1. Does the system help to spot point cloud regions which re prolemtic for reconstruction? 2. Does the system help to decide which reconstruction lgorithm should e used? 3. Does the system help to etter understnd the strengths nd weknesses of certin reconstruction lgorithms? The nswers to these three questions cn e seen in Figure 15. The prticipnts greed tht YMCA helps to spot the most prolemtic regions in the reconstruction from point cloud (Question 1). They lso lrgely greed tht the system cn help to identify the most pproprite reconstruction lgorithms for given point cloud (Question 2). However, they were discordnt out whether YMCA helps to etter understnd how the reconstruction lgorithms work (Question 3). Some prticipnts stted tht lgorithms cn e judged in visul wy, ut for detiled nlysis dditionl informtion out the point cloud (i.e., noise level) would e necessry. For future work, it would e interesting to nlyze the lgorithms pipelines in more detil, nd to lso tke into ccount the influence of different prmeter settings. The fourth question in the questionnire concerned which elements of the user interfce the prticipnts found helpful during the nlysis. We sked which of the following elements they used the most: Vrince mp (i.e., overview imge) Prllel coordintes (i.e., visuliztion of reconstruction results in the prllel coordintes plot) Hot-spot locliztion (i.e., the possiility to click on hot-spot thumnils in the prllel coordintes plot nd the hot-spot rendering mode) Detil view nd dt summriztion (i.e., detil view with closeup views nd rnking, nd dt summriztion) The nswers to this question cn e found in Figure 16. The overview imge showing the vrince mp ws rted to e the most helpful interfce element for the users. This is not surprising, since t the one hnd this is the centrl interction element of the system, nd on the other hnd most users re lredy fmilir with interpreting color het mps on 3D models. The prllel coordintes plot ws very helpful for the prticipnts to compre the overll nd locl performnce of individul lgorithms. They used this interfce element especilly to eliminte reconstructions from further nlysis. Although ll users were convinced out the fct tht list of hot-spots is lredy prepred when strting the nlysis, some of them did not like the hot-spot rendering technique. They stted tht it is confusing t the eginning nd needs more experience to e interpreted in the right wy. The prticipnts lso used the detil view to judge the locl ehvior of the lgorithms. Only one prticipnt stted tht the dt summriztion is sometimes hrd to interpret nd would need longer trining period. We lso sked the prticipnts out suggestions for future work. During these discussions it turned out tht the system inspired the users quite lot, nd they hd mny suggestions for dditionl fetures nd pplictions. For the overview imge, one prticipnt stted tht it Question 1 Vrince mp Prllel coordintes Question 2 Question 3 Hot-spot locliztion Detil view nd dt summriztion Yes No Yes No Fig. 15: Evluting the prcticility of YMCA. Question 1: Does the system help to spot point cloud regions which re prolemtic for reconstruction? Question 2: Does the system help to decide which reconstruction lgorithm should e used? Question 3: Does the system help to etter understnd the strengths nd weknesses of certin reconstruction lgorithms? YMCA proved to e very helpful for evluting point clouds nd finding the most suitle reconstruction. Fig. 16: Evluting the most helpful user interfce elements. With this question we wnted to find out which user interfce elements the users found the most helpful ones. All prticipnts liked the vrince mp nd rted it to e very useful. Also the prllel coordintes plot nd the detil view were used y most of the prticipnts. However, the hot-spot rendering ws sometimes confusing nd therefore not rted to e very useful in ll cses.

9 would e helpful to see the reference mesh rendered in colors ccording to the lgorithms which perform est t certin points. This could e vlule hint in the nlysis. Hving very colorful model mens tht lgorithms differ lot, wheres hving lrge uniformly colored prts mens tht one lgorithm performs etter thn ll others in those res. For the dt summriztion in the detil view, the prticipnts suggested tht sometimes it would e useful to e le to mnully djust the clss orders, or even do clssifiction y themselves (y mnully selecting lgorithms). The prticipnts experienced with point cloud reconstruction lso stted tht they liked the dt summriztion in the detil view, ecuse it quickly provides n overview of the dt t the current locl position. They lso pointed out tht summriztion lone is not helpful for them. To e le to judge which lgorithm performs etter thn the others, they still need to e le to ccess the individul input meshes. Therefore, they lso liked the possiility to depict ll close-up views of ll meshes from one clss in Smll Multiples disply. 8 DISCUSSION YMCA opertes on set of meshes which re compred to reference mesh nd nlyzes similrities nd differences mong them. Not mny suitle tool-sets exist tht llow the efficient comprison of multiple meshes. With YMCA it is now possile to quickly nd visully nlyze mesh reconstruction results nd depict the pproprite solution for the given point cloud dt. The system lso provides n overview of the criticl res in the ville point cloud dt, with respect to different reconstruction pproches. Our system nonetheless hs some limittions, which point to interesting directions for future work. For the dt in this pper, reference meshes were given which could e used to clculte the differences in the meshes. However, often this is not the cse when nlyzing point cloud dt (e.g., when scnning rel-world ojects). In this cse we propose to crete n verge mesh out of the input meshes, nd to compre the meshes ginst this verge. This provides n initil overview of the differences in the dt. If the user is not stisfied with compring the meshes ginst the verge, he/she cn exchnge the reference nd use some other input mesh insted, e.g., the mesh tht delivers the est reconstruction of certin prts of the input dt. YMCA lredy provides controls for exchnging the reference mesh. We used n ttriute devition metric [26] to clculte the mesh differences. This pper is primrily out the visul depiction of mesh differences, which mens tht the clcultion of the differences is decoupled from the visul representtion. The metric cn e exchnged with ny other mesh difference clcultion (e.g., curvture mesurements). We tested this y using geometric devition [26], which cn e seen in Figure 17. The vrince mp of YMCA gives n overview of the regions in the point cloud where the reconstructions produce different results. However, for some pplictions it might e interesting to see the glol error insted (i.e., regions where ll reconstructions fil). To test this, we used the men squred error to ggregte the different errors into one vlue per vertex. YMCA lredy provides mens for exchnging the metric, which cn e lso pplied to using the error vlues for Fig. 17: Chnging the metric from point distnces () to geometric devitions () results in n lterntive overview imge s well s different hot-spot loctions. visuliztion insted of the vrinces. At present this mens tht the system hs to e initilized with either the one or the other settings. The user cn only explore the results of one metric t time. This is something tht we wnt to chnge in the future. We would lso like to work on possiilities where the metric cn e chnged during nlysis, while the settings (like selections in the prllel coordintes plot) re still preserved for ll metrics. This wy it will e possile to select list of hot-spots (clculted y different metrics) nd use them for further nlysis. As pointed out during the evlution, YMCA provides limited support in understnding the strengths nd weknesses of individul reconstruction lgorithms. Our pproch enles the user to visully compre the results nd therefore judge them, ut domin experts stted tht dditionl informtion out the input dt (e.g., noise level) would e helpful. We pln to integrte this into the system in the future. Berger et l. [6] implemented surfce reconstruction enchmrk tool which cn e used to test severl reconstruction lgorithms ginst one point cloud dtset. Additionlly, the enchmrk tool provides scnning simultions which cn produce different point clouds of the sme model with different qulity (e.g., dd more or less noise to the dt). Then the enchmrk tool cn e used to pply the reconstruction lgorithms to different point cloud versions. This would spn prmeter spce for every reconstruction lgorithm showing its strengths nd weknesses (e.g., in the presence of noise). We lso would like to pply YMCA to other mesh dtsets, for exmple creted y different mesh re-smpling or simplifiction lgorithms. It would lso e interesting to explore other 3D dtsets. One possiility could e to explore differences in lgorithms for isosurfce construction. In the user interfce we would like to dd more complex shding models with the possiility to chnge the lighting y user-defined prmeters. For the nlysis we would like to provide mens tht the user cn define new reference (e.g., specific corner or shpe) the input meshes should e compred to. During the evlution, the domin experts lso rought up nother promising ide for future work. For them it would e very helpful to e le to export 2D flttened or unrolled representtion of the current model showing ll, or t lest the most importnt, hot-spots in one imge, together with smples of the reconstructed meshes. Up to now such illustrtions re generted mnully y rotting the model nd producing close-up views. 9 CONCLUSION In this pper we presented Your Mesh Comprison Appliction (YMCA), new visul nlysis ppliction for the comprtive visuliztion of multiple 3D meshes. Interctive tools re provided to present n overview of the differences in the dt, nd to explore locl res of interest in more detil. Our visuliztion pproch comines explicit encoding, juxtposition, nd prllel coordintes. It further ddresses the sclility prolem of previous mesh comprison tools. We pplied our pproch to meshes coming from different mesh reconstruction lgorithms tht were pplied to point clouds. With our method, differences etween severl resulting meshes cn e quickly identified, nd it is lso helpful to explore individul chrcteristics of the different mesh reconstruction lgorithms. In the future, it will e interesting to investigte other possile interction techniques. Especilly for lrge dtsets, we would like to improve the interction possiilities in the prllel coordintes plot (e.g., y ngulr rushing [17]). We would lso like to comine severl mesh comprison metrics into one system. Another direction for further reserch is the fine-grined nlysis of the prmeter spce of the ville mesh reconstruction lgorithms. With our tool it could e possile to identify strengths nd weknesses of the lgorithms when pplied to different point clouds. ACKNOWLEDGMENTS The work presented in this pper hs een prtilly supported y the ViML project (FWF Austrin Reserch Fund, no. P21695) nd y the AKTION project (Aktion OE/CZ grnt numer 68p11).