Line Drawing Approach Based on Visual Curvature Estimation

Transcription

1 Lne Drawng Aroach Based on Vsual Curvature Estmaton Jun Lu, Mngquan Zhou, Guohua Geng, Feng Xao, Defa Hu Abstract In order to effectvely extract the feature lnes of the three-dmensonal model of the surface wth nose, the reasons for the loss of texture detals n the rerocessng stage are dscussed and a new method of lne drawng based on vsual curvature estmaton of the cultural relcs s roosed. Frst, estmate the dscrete curvature on trangular mesh vertex and dvde the cultural relc model nto the flat regon and the non-flat regon accordng to the curvature dstrbuton; then, conduct the sharenng flter on the vertex of the non-flat regon to calculate the new mesh vertex coordnates; fnally, basng on the vsual curvature, extract the curved contour lne to acheve automatc lne drawng of cultural relcs of the trangular mesh model. The exermental results show that the non-flat contour lnes based on the vsual curvature reman the detals of the surface texture of the 3D model and avod the (?)uneven drawng lnes by usng the drected rdge lne and valley lne drawng. Keywords cultural relcs, lne drawng, feature contour lne,3d model, vsual curvature. I. INTRODUCTION HE lne drawng s a fundamental work n the reservaton of cultural relcs. In the archeologcal exloraton, Tarchaeologsts should draw the lne drawngs for the fragment of cultural relcs and dect ts sze, shae, structure, attern and texture. A hgh-qualty lne drawng of cultural relcs can be taken as the llustraton n evacuaton reorts, dssertatons, monograhs and textbooks, as well as exhbton charts, and can be used for archve storage, auxlary rears and reservaton of cultural relcs, archaeologcal researches and cultural ublshng []. The lne drawng of cultural relcs should be done accordng to the measured values based on manual baselne drawng, mesh dvson and ont selecton and measurement wth a ruler n a tradtonal orthograhc Ths work was suorted by the Natonal Natural Scence Foundaton of Chna (grant number 63737, , , ), by the Natonal Natural Scence Foundaton n Shaanx Provnce of Chna (grant number 5JK247), by Natural Scence Basc Research Plan n Shaanx Provnce of Chna (grant number 27JC2-8), by the Natural Scence Foundaton of Wenan Normal Unversty (grant number 7YKF2). Jun Lu s wth the School of Informaton and Technology, Northwest Unversty, X'an 769, Chna. Jun Lu s also the School of Informaton and Technology, Wenan Normal Unversty, Wenan 7499, Chna. Mngquan Zhou s wth the School of Informaton and Technology, Northwest Unversty, X'an 769, Chna (corresondng author; e-mal: mqzhou@bnu.edu.cn). Guohua Geng s wth the School of Informaton and Technology, Northwest Unversty, X'an 769, Chna. Feng Xao s wth School of Comuter Scence and Engneerng, X an Technologcal Unversty, X an 72, Chna. Defa Hu s wth the School of Comuter and Informaton Engneerng, Hunan Unversty of Commerce, Changsha 425, Hunan, Chna roecton manual method, shown n Fg.. The whole rocess features numerous work rocedures, slow drawng, low-recson drawng and dversfed drawng qualty, and n artcular, when archaeologcal workers contnuously overturn and measure the cultural relcs n lne drawng, they nevtably cause secondary damages to cultural relcs wth cracks. (a) Baselne method (b) Mesh method Fg.. Manual drawng method of archaeologcal lne drawng To mrove the drawng effcency and qualty, archaeologcal deartments have tred to draw lne drawngs by usng dgtal hotograhy technology. Frst, cultural relcs whch are to be drawn are laced n a secfc envronment for dgtal hotograhy, then hgh-qualty cultural relcs mages obtaned n hotograhy are morted nto mage rocessng software such as Photosho and CorelDraw to mark the contour lne of cultural relcs by usng the human-machne nteracton mode, and searate the cultural relcs and ts background through mattng technology. Next, mages of matted cultural relcs are decolorzed, transformng them nto black and whte drawngs, and then are denosed and stylzed, and fnally acheve the lne drawng of cultural relcs. Wth ths method for hotograhy, the background of cultural relcs should be ure n color, so that there s an obvous contract wth the man color of the catured cultural relcs. The lght n hotograhy should be dffused lght or natural lght to ensure that the contrast between the lght and shades on the cultural relcs s not very shar. strong. In fact, t s very dffcult to obtan orthograhc roect mages of cultural relcs n the feldwork. In addton, manual mattng s not wdely used due to ts consumton of tme and energy. The method of contour detecton and extracton has been gradually aled to automatc drawng of lne drawng of cultural relcs n recent years. Tycal methods are dvded nto three, namely, mage-based edge detecton, mage-based non-hotorealstc drawng and sace-based contour lne detecton [2]. The roect team dscovers n the engneerng ractces that the extracted feature lnes are nosy, nconsstent and not deal when classc oerators such as Sobel, Prewtt, Log and Canny are used to detect the edges of dgtal mages of ISSN:

2 cultural relcs, as shown n Fg. 2. The mage-based, non-hotorealstc drawng method, whch can roduce the ntegral regon of the flter by constructng the edge tangental flow, can better rotect the structure wth drectonal features n the mages, and ensure the consstence of the outut feature lnes. The feature lnes of cultural relcs extracted by ths method are relatvely consstent, but too many rrelevant feature lnes to the lne drawng are left on the flat regon of ths model, as shown n Fg. 3. connectng the rdge lnes or valley lnes wll show sharenng. (a) 3D model (b) Based on mage sace (c) Based on obect sace Fg. 4 Effect of contour lne detecton method of 3D model II. RELATED RESEARCH (a)sobel oerator(b)prewtt oerator(c)log oerator(d)canny oerator Fg.2. Exermental effect of feature extracton of cultural relcs of classc oerators (a) Illustraton of feature lne flow feld of cultural relcs (b) Extracted feature lne of cultural relcs Fg. 3. Exermental effect of non-hotorealstc drawng of feature lne of cultural relcs The rerequste for the contour lne detecton algorthm based on obect sace s the 3D model of cultural relcs based on ont cloud data. The drect detecton method can detect f a gven edge belongs to the contour lne or a contour lne asses through ths trangular mesh sheet by traversng each edge or each trangular mesh n the 3D model. When the vewont of the observer changes, all contour lnes wll be recalculated. For non-statc 3D model, ths algorthm has very low effcency. The random detecton algorthm s used to detect contour lne wth local contnuty or contour lne mantanng contnuous whle the vewont changes but ths algorthm does not detect all edges of the 3D model. When a small art of contour edges are found, the adacent edges of these contour edges need detectng whether they are the contour edges, and then n recurson, kee on searchng tll the number of searched contour edges s bgger than the threshold. Ths algorthm has the advantages of easy mlementaton and hgh seed, but has the dsadvantages of ncaable of detectng all contour edges elow-recson n contour detecton and local detals loss, as shown n Fg. 4. In fact, dfferent from smle and geometrc model-based featurng lne extracton, the archaeologcal lne drawng manly dects the structure and texture of the cultural relcs. However, the exstng methods cannot meet the requrements automatc drawng n comuter-asssted archaeologcal lne drawng [3] For examle, the excessve nose smoothenng wll lead to detals loss on the 3D model surface of cultural relcs, global sharenng wll make the flat regon retan some dsturbance featurng lnes, and the lne drawng by smly A. Feature lne related to vewont The feature lne related to the sght lne ndcates the need to frst dentfy the vewont ror to calculatng the feature lne. The searched feature lne s related to the oston of the vewont. The reresentatve feature lnes are descrbed as follows: () Slhouettes Contours It ndcates the set of onts on the curvature n whch the vewng drecton s erendcular to the normal drecton. The slhouettes contours s the boundary between the vsble surface and nvsble surface n 3D model and dects the 3D model shaes vewed from vewonts wth dfferent angles. When the vewonts change, the slhouettes contours wll change. At ths tme, the dot roduct of the vewng drecton and normal drecton on the curvature should be recalculated. (2) Suggestve Contours[4] Suose that the sght lne vector v s set, vector w s the roecton on the tangent lane of the ont of the sght vector v on the curvature, and the lane formed by the vector w and the normal vector n s called the radal lane, as shown n fgure 5. The radal lane ntersects wth the curvature to form a curve, whch s called a radal curve. The curvature of the radal curve on the ont s called the radal curvature of ont, whch s marked as kw. ( ) (a) w s the roecton of v on the tangent lane of ont (b) Radal lane and radal curvature Fg. 5 Related concets of subectve contour The suggestve contour ndcates the set of onts on the curvature, n whch the radal curvature s and the dervatve s more than n w drecton. Ths set s reresented as follows: kw ( ) = () Dkw w ( ) > The suggestve contour, roosed by Decarlo n 23, s Slhouettes contour that s found after the sght lne drecton s slghtly changed. The suggestve contour can show more 3D model detals and better reflect the shae features of 3D ISSN:

3 models. The suggestve contour found by ths algorthm s the convex regon n the vsble regon. (3) Aarent Rdges[5] The aarent rdge s defned as the set of the onts that are the maxmum values of aarent curvatures on the surface of the 3D model. Judd et al. roected the normal vector of each ont on the surface of the 3D model to the aarent surface and defned the aarent curvature for each ont. The aarent curvature can reflect the curvature change of each ont on the surface of the 3D model from the vewont, as shown n fgure 6. In general, comutng workload for these feature lnes related to the sght lne s heavy. When the vewonts change, the curvature related to vewont should be comuted agan, for whch much tme s needed. When the trangular meshes are lentful, the comutng effcency s low. Fg. 6 Aarent curvature sze dagram C D θ Fg. 7 Crease lne B. Feature lne unrelated to vewonts The feature lnes unrelated to the vewonts ndcate that these feature lnes are related to geometrc features of the 3D model but not the oston of vewonts. The reresentatve feature lnes are descrbed as follows: () Crease Lnes The crease lnes ndcate common edges n whch the angle between two trangular meshes s less than 9, as shown n fgure 7. The edge AB s the common edge of ABC and ABD. If the edge AB s determned as the crease lne, the relaton between ABC and ABD should satsfy the formula (2) n n < cosθ = < ε < (2) n n In whch θ s the angle between two adacent trangular meshes, n and n are the normal vector of two adacent trangular meshes and ε s the restrcton threshold. For the 3D model of some secfc tyes of cultural relcs, a secfc threshold can be set to obtan an effectve crease lne. (2) Boundary Lnes The boundary lne ndcates the edge of the trangular mesh outsde the model boundary, namely, the set of edges n one trangular mesh. Not all 3D models have boundary lnes, e.g., the enclosed 3D model has no boundary lne. (3) Rdge Lnes and Valley Lnes To draw the rdge lnes and valley lnes of a 3D model, frst dentfy the rdge and valley onts of the 3D model. A B emn = kmn / tmn = emn / t > mn kmn < kmax In the two formulas (3) and (4), k max and k mn are the maxmum rncal curvature and mnmum rncal curvature of the vertexes, t max and t mn are the corresondng man drectons, and e max and e mn are called the extreme ont coeffcents. After calculaton accordng to the formula (3) and (4), the onts on the 3D model are dvded nto rdge onts, valley onts and other onts. The onts satsfyng the condtons n formula (3) are called rdge onts and the onts satsfyng the condtons n the formula (4) are called valley onts. The rdge onts are connected wth the valley onts accordng to the certan connecton strategy to obtan the rdge lnes and valley lnes of the 3D model. C. Aarent curvature of curves The lengths of the arc of the lane curve can be reresented as c ( s) = ( x( s), y( s)), whch has sgnfcant geometrc meanng. To any ont v on the curve, x (s) reresents the dstance from such ont to y axs and s called the heght n drecton; y (s) reresents the dstance from such ont to x axs and s called the heght n 9 drecton. In fact, t defnes the functon Hα : C R, n whch α reresents the angle and s called the heght functon n α drecton. A seres of heght functons can be obtaned by rotatng the coordnate axs to form a functon sace H α and ths sace ncludes nfnte heght functons. It s aarent that an nfnte set cannot be rocessed, so the functon sace H α should be samled. The frequent method s the unform samlng, namely takng samles at α = π, =,,..., N N to get N heght functons to comose a set { Hα, =,,..., N } wth N elements. The Fg. 8(b), (e), (d) and (e) are the heght functons of the fve-onted star contour n fgure 8(a) n the drectons of, 45, 9 and 35. Each heght functon ncludes artal nformaton of the orgnal curve. For a gven ont on the curve, the more heght functons take ths ont as the extreme ont of, the bgger the curvature of the curve at ths ont s, and the bgger the curvature value s. Ths ndcates that the curvature can be estmated by calculatng the number of drectons n whch the onts are the extreme ont. (4) emax = kmax / tmax = emax / tmax < kmax > kmn (3) Fg. 8 Heght functon of fve-onted star contour n 35 drecton, 45, 9 and Defnton l: Vsual curvature: For a ont v on the curve C, ISSN:

4 S (v) reresents that ths ont s wthn the S wde neghborhood on the curve. The vsual curvature at ths ont s K N, S In ths defnton, #[ ( S( v)) ] N [ H ( S( v)) ] # α = π (5) N S H α reresents the number of extreme onts, regardless of maxmum or mnmum [6], wthn the neghborhood S (v) of the ont v n the heght functon H α. Ths defnton ndcated how to calculate the vsual curvature. For a ont v on the curve, frst the extreme onts of ths heght functon Hα n ts neghborhood are calculated, then the sum of extreme onts n all heght functons n ths neghborhood s calculated, and fnally the vsual curvature of ths ont va the formula (5) s calculated. D. Aarent rncal curvature of curved surface The rncal curvature of the curved surface s one mortant ntrnsc shae of a 3D obect and lays a crtcal role n the rogressve reresentaton, curved surface analyss, and shae analyss based on vsual features of a 3D model. The classcal rncal curvature defnton s alcable to the normal curved surface and s not defned for most frequently used 3D models. Many scholars roose to use a calculaton method of the rncal curvature based on dfferent scales. One method s to convolve the curved surface and a kernel functon wth local smoothenng effect and obtan a mult-scale rncal curvature by changng arameters of ths kernel functon. Such methods wll contnuously change the orgnal curved surface, but the geometrc meanng of the scale arameters s not aarent, whch makes t not easy to set the scale arameters. Another method s to smlfy the model and estmate the rncal curvature on the smlfed model. In essence, these methods belong to local estmaton, are senstve to noses, and make t dffcult to elmnate small shae detals n large scale. The rncal curvature of one ont on the curved surface s closely assocated wth the normal lne of ths ont on the curved surface. In general, the normal lne n the dfferental geometry s frst defned and then the rncal curvature s defned. The normal lne of the curved surface s local and s suscetble to noses. To overcome ths contradcton, ths aer wll smultaneously estmate the normal lne drecton and the mnmzaton and maxmzaton rule of the rncal curvature [6]. vector of the ntersectng lne of P and P 2 lane. P and P 2 smultaneously rotate around L and roduce a seres of orthogonal lane grou ( P, P2 ) α. The ntersectng lne between these lanes and curved surface S s the lane curve. For these lane curves, the mult-scale vsual curvature s calculated. When the scale s, the ntersectng lne between the lane grou ( P, P2 ) α wth L as the common lne and curved surface S has a curvature at the ont v, wth K L(v) as the maxmum. Based on the dfferental geometry knowledge, when L s the normal lne of the curved surface S at the ont v, K L(v) s the mnmum. Therefore, K L(v) can reach the global mnmum by searchng the L sace and the normal drecton and rncal curvature can be obtaned. Defnton 2: Mnmzaton and maxmzaton rule: Suort that C s the ntersectng lne of the lane P and curved surface S and K C(v) s the vsual curvature of C at ths ont, the vsual rncal curvature of the curved surface s defned as follows: For any ont v on the curved surface S, K s the maxmum of the vsual curvature of L (v ) the ntersectng curve of the lane wth L and curved surface S at the ont v n case of scale. When K L (v ) reaches the global mnmum, the corresondng L s the vsual normal of the curved surface S at ont v and s reresented as N. K s one vsual rncal N (v ) curvature and s reresented as ar k l, seen n the followng formula mn max k l = K C (6) L( v) C( v) The formula (6) s called the mnmzaton and maxmzaton rule. Ths rule s the method to calculate the vsual normal and vsual rncal curvature of the curved surface. III. PROBLEM ANALYSIS A. Smooth Transton leads to loss of texture detals Most ont cloud models of the cultural relcs are coarse and full of noses due to low recson, slhouettes and scannng envronment. The roect team reduces noses for the 3D model of the head of Terra-cotta Warror by usng the Taubn smoothng algorthms, but the effect s not deal, as shown n Fg.. Fg. 9 Orthogonal lane grou ntersectng wth the curved surface va the ont v As shown n fgure 9, v s one ont on the curved surface S, L s a unt vector wth the ont v as the startng ont, P and P 2 are two lanes whch nclude L and L v s the drecton ntersect wth each other orthogonally, and ( ) (a) =.97 ror to smoothng (b) =.93 ror to smoothng (c) =.97 for slght smoothng (d) =.97 for heavy smoothng Fg. Comarson of smoothng effect of Taubn algorthm for Terra-cotta Warror model ISSN:

5 Fg. (a) shows the feature lnes extracted before smoothng treatment of the cultural relc model. Fg. (c) and (d) are the feature lnes extracted after smoothng treatment of cultural relc models usng Taubn smoothng algorthm. The roect team dscovered that the change n value can reduce the mxed and dsorderly feature lnes and the boundary lnes wll not change the shae, but the texture detals lke the texture detals of eyes cannot be drawn n the exerment, as shown n Fg. (a) and (b). The comarson of Fg. (a), (c) and (d) shows that f the cultural relc model s not smoothed, a large number of mxed and dsorderly feature lnes wll be extracted due to nose nfluence. However, slght smoothng cannot fully remove nfluences of noses on extracton of the feature lnes and excessve smoothng wll lead to loss of the texture. So, how to avod texture detal loss of culture relcs n excessve smoothenng becomes urgent n the research. The exerment shows that generally the aarent concave and convex arts have bgger curvature on the curved surface. These aarent concave and convex regons are also the mortant regon for detaled drawng n the lne drawng. The Gauss curvature and mean curvature calculated usng the Vorono method roosed by Meyer have smaller errors and the feature regon of the detected trangular mesh model s more accurate. Therefore, the extracted feature lne has better effect and can better dstngush the regon (namely feature regon) and flat regon where the normal vector of the curved surface changes quckly. Defnton 3: The feature regon s the regon on the 3D model of the cultural relc where the curvature changes sgnfcantly and the absolute curvature s bgger. Defnton 4: The flat regon s the regon on the 3D model of the cultural relc where the curvature changes slghtly and the absolute curvature aroxmates to zero. Defnton 5: Mean of feld s the reference threshold for the local smoothng of cultural relc model of secfc tye as dentfed by referrng to the archaeologcal exerences and analyzng exermental statstcs. The archaeologcal ersons focus on the curves whch reflect geometrc change on the surface of cultural relcs n comletng the cultural relc lne drawng. Although the rdge lnes and valley lnes occur at the extreme ont of the 3D model curvature of cultural relcs and the mortant structural roertes of cultural relcs can be catured, the lne drawng wll be shar and unable to form the natural and vsual lne drawng of the cultural relcs because the rdge lne and valley lnes are embedded n the obect s surface and wll not slde wth the changes of vewonts. B. Introducton of mnmzaton and maxmzaton rule The vsual curvature and the classc curvature measure the bendng degree of the curve at a ont. The vsual curvature uses the N-samle set { Hα, =,,..., N } of the functon sace H α, whch ndcates that the vsual curvature deends on the samlng rate. The samlng rocess can reduce nformaton. If the samlng rate s hgher, the calculated vsual curvature s more recse. In theory, when the number of the heght functon aroxmates to nfnte number, the more recse vsual curvature can be obtaned. All extreme onts, regardless of ther sgnfcance, wll be counted and generate same contrbuton n the defnton of the vsual curvature,, so the curvature s suscetble to noses. Fg. 8 shows that f the curvature of a ont s bgger, ths ont s the extreme ont n the heght functon n more drectons. It s mortant that sgnfcance of dfferent extreme onts s dfferent n heght functons. Noses can generate a large amount of extreme onts on the curve, but generally these extreme onts corresond to smaller eak or valley n ther heght functons and the end onts n bgger convex regon or concave regon corresond to bgger eak or valley n many heght functons. It ndcates that the shae detals can be measured by measurng the corresondng eak or valley sze of the extreme onts va the heght functon, whch s a new method to dstngush the shae detals of dfferent scales. Defnton 6: Mult-scale vsual curvature: for any ont v on the curve C, f S s the S wde neghborhood, the mult-scale vsual curvature at the ont v s reresented as follows: K N, S [ H ( S( v)) ] N # α = π (7) N S In the formula, s the scale factor, #[ ( S( v)) ] α reresents the number of extreme onts, whose scales are not less than, of the heght functon Hα wthn the neghborhood S. In the mult-scale vsual curvature, only relatvely mortant extreme onts are counted and the extreme onts whose scale s less than wll be gnored. The rncal curvature of the 3D lane s a local dfferental comonent and s suscetble to noses. In general, calculaton deends on the normal lne of the curved surface and the normal lne of the curved surface s suscetble to noses, so t s dffcult to be accurately estmated. Therefore, the calculated rncal curvature error s bgger. To solve ths roblem, ths aer ntroduces the mnmzaton and maxmzaton rule. In essence, the mnmzaton and maxmzaton rule gets the best normal drecton by searchng all ossble normal drectons of the curved surface and calculate mult-scale vsual curvature of the ntersectng lnes of the lane and curved surface assng ths normal lne n each ossble normal drecton. All ossble normal drectons wll be searched and the mult-scale vsual curvature of the ntersectng lnes of the lane and curved surface assng ths normal lne wll be calculated n each ossble normal drecton, so ths algorthm s very comlcated. Suose there are t ossble normal drectons, for each ossble normal drecton, m lanes asses through ths drecton. The mean number of onts on the ntersectng lne of these lanes and curved surface s n. For each ntersectng lne, the mean number of heght functons s k. The comlexty of the mnmzaton and maxmzaton rule 2 s o ( tmkn ). To reduce the number of normal drectons to be searched, one normal drecton s roughly estmated and the samles are taken around ths normal drecton n order to ensure t mnmzaton under the rerequste of ensurng the normal recson and reach maxmal recson at mnmal cost. For each ossble normal drecton, nfnte lanes wll ass through H ISSN:

6 ths normal lne. Generally, m lanes assng through ths normal lne can be obtaned va the unform samlng. For each ntersectng lne, N heght functons can be obtaned va the unform samlng for the angle nterval [,π ] by referrng to the vsual curvature calculaton formula of the lane curve. For each heght functon, calculate the scale of each vertex and gnore smaller extreme onts to estmate the vsual curvature. Fnally, the best normal drecton of the curved surface s selected and the vsual rncal curvature of the curved surface s obtaned usng the mnmzaton and maxmzaton rule. IV. ALGORITHM DESIGN A. Basc flow Frstly, the vsual curvature of the 3D model vertex s calculated by countng the number of heght functons n whch the vertex s the extreme ont for each vertex based on the N samle set { Hα, =,,..., N } of the functon sace H α. Secondly, then the model s dvded nto a flat regon and a feature regon based on the vsual curvature dstrbuton of vertexes under the scale constrant. Thrdly, the vertexes n the feature regon are sharened and fltered based on the mean of the archaeologcal feld and the vertex coordnates of new trangular mesh model are calculated. Fnally the feature contours of the cultural relc model are extracted and the lne drawng of the cultural relcs s drawn whch can satsfy the vsual erceton of the archaeologcal ersons and effectvely reserve the texture detals. B. Estmaton of vsual curvature To calculate the vsual curvature, dscretzaton s the key and frst ste. To comrehensvely analyze the erformance of the estmaton method of dscrete curvature [7], ths aer estmates the dscrete curvature of the trangular mesh model usng the Vorono method roosed by Meyer et al. The detaled stes are descrbed as follows: Store neghbored onts and facets of each vertex and record the total neghbored onts (n) and neghbored facets (m) of each vertex. () Calculate the normal vector each trangular facet. v N v m v v 2 (a) Normal vector v + of vertex N... n v v 3 - n A 2 ; (b) mxed area M and regon of vertex A Fg.. Normal vector and mxed area of vertex s of + A As shown n Fg. (a), suose that the vertex ncludes m neghbored trangles, the corresondng vertex ncludes m neghbored vertex v ( m), n s the normal vector of the trangle v v +, and N s the normal vector of vertex The calculaton formula s descrbed as follows:. n = ( v ) ( v+ ) ( v ) ( v+ ) The trangle area s formed by calculated as follows:, ( v ) ( v+ ) v and (8) v + s s = (9) 2 Wheren m (2) Calculate the normal vector of each vertex. The normal vector of the vertex s estmated takng the neghbored trangle area at the vertex as the wegh factor. The calculaton formula s descrbed as follows: m m N (/ s) ns = () = = (3) Calculate the total roecton area AM of neghbored trangles of each vertex. a) If the trangle s the acute trangle, lnk the crcumcenter of the trangle to the mdont of two edges connected wth vertex and get the area A as shown n Fg. (b). b) For the rght angled trangle or obtuse angled trangle, lnk the mdont of the ooste edge of the rght angle or obtuse angle to the mdont of two edges connected wth the vertex and obtan the area A as shown n Fg.. 2 A M s the whole mxed area calculated usng the above two methods, shown as the shadow area n Fg.. (4) Traverse all vertexes of the trangle mesh model, and calculate the Gauss curvature kg( ), mean curvature kh ( ), maxmal rncal curvatures k ( ) and mnmal rncal curvatures k2 ( ) of the vertex [8]. The Gauss curvature of the vertex s calculated as follows: kg( ) = 2π θ A () M N( ) The mean curvature of the vertex s calculated as follows: kh ( ) = ( cotα + cot β )( ) N (2) 4AM N( ) In the above formula, A M s the mxed area of the trangle, θ ndcates the angle between the edge and +, α ndcates the angle between the edges and, β ndcates the angle between the edge + and +, and N s the normal vector of the vertex. The maxmal rncal curvature and mnmal rncal curvature of the vertex can be drectly calculated by the Gauss curvature and mean curvature of the vertex va the followng formula: 2 k = k + k k (3) ( ) ( ) ( ) ( ) H H G ISSN:

7 2 ( ) ( ) ( ) ( ) k = k k k (4) 2 H H G The unform samlng method s used based on the dscrete curvature calculaton and the vsual rncal curvature of the vertex n the model s calculated usng formula (5) and rule (6). C. Detecton of feature regon The feature regon of the 3D model s detected to hghlght the sharenng oeraton of the detals feature and revent noses n the flat regon from beng exanded due to global sharenng. Generally, the normal vectors or curvature of the nose onts n the flat regons are not contnuous but solated. To determne f a ont s wthn the flat regon of the model, t s necessary to determne f the absolute curvature of ths vertex aroxmates to zero and calculate the absolute curvature of the vertexes n the neghborhood of ths vertex. If the absolute curvature of more than two neghbored vertexes of ths vertex does not aroxmate to zero, ths vertex s regarded as solated noses of the flat regon and belongs to the flat regon. D. Local sharenng Local sharenng ams to amlfy the feature detals of the 3D model of the cultural relcs. If the vertexes n the feature regon of ths model are locally sharened, t can effectvely revent global sharenng from amlfyng the model noses. The stes are descrbed as follows: () Traverse all vertexes of the model and determne the regon of the vertexes. (2) If the vertex belongs to the flat regon, sk to ste (). (3) If the vertex belongs to the feature regon, sk to ste (4). (4) If the vertexes n the feature regon of ths model are locally sharened, the new coordnates of the vertexes n ths regon wll be recalculated. a) For the vertex and ts neghbored vertex sharened n the trangular mesh model, the oston offset of the vertex calculaton formula: to be must be calculated va the followng = w ( ) (4) In the formula, w s the weght functon and satsfes w =. For easy calculaton, the value s /n, namely recrocal of the number of neghbored onts of the vertex ; b) ' Calculate the new coordnate of the vertex va the followng formula: ' = + µ v µ (5) ( ) ( ) Here, µ and are the scale arameter and meet < < µ < v. ( ) reresents a vector and s the square root of three comonents of the vertex. If the calculated result s = ( xyz,, ) v( ) = ( x, y, z ), then. Smoothng wll make the 3D model shrnk toward the center. On the contrary, sharenng wll make the 3D model exand outward. The formula (5) changes the mark + of the fnal tem on the rght sde of the Taubn smoothenng formula nto mark - to get the effect ooste to the smoothng, thus hghlghtng the local features of the model. To revent such exanson from affectng extracton of the feature lne, ( µ ) v( ) s added to the formula (5), whose symbol s contrary to the thrd µ, whch can effectvely reduce outward exanson degree of the 3D model, and ensure that the local features of the 3D model can be amlfed [9]. If stes -4 are erformed once, the rocedure s called sharenng. The sharenng tme s dentfed by the model tye tll the extracted feature lnes are suffcent to descrbe the detals of cultural relcs. E. Extracton of feature lnes The contour extracton s the core element n the drawng of the lne drawng of cultural relc, ncludng outer contour and nternal detals. The nternal detals nclude the anted ornamentaton on the surface of the cultural relc and aarent rdges. The crease lnes and boundary lne manly descrbe the detals nsde the cultural relc and can be extracted accordng to related concets. The slhouettes lnes ndcate the outer contours of the cultural relcs. The extracton method [] s descrbed as follows: Frst, the trangles of the mesh model are dvded nto vsble trangle, nvsble trangle and contour trangle. Suose that the sght lne vector of the vertex s w = c, wheren c s the coordnate of the vewont. If the dot roduct of the normal vector of the vertex and the sght lne vector w of ths vertex are more than, ths vertex s vsble. If the value s less than, t ndcates that ths vertex s nvsble. If three vertexes of a trangle are vsble, ths trangle s vsble. If three vertexes of the trangle are not vsble, t s called an nvsble trangle. The contour trangle s the trangle n whch not all three vertexes are vsble or nvsble, as shown n Fg.3. w N > w N < w N < w N > w N = Fg. 2 Slhouettes contour extracted va lnear nterolaton method As shown n fgure 3, the contour trangle should nclude the assng Slhouettes contour. The contour trangle s found by traversng the trangular mesh model. Two vertexes wth dfferent nvsblty are lnearly nterolated as follows: t t = + (6) t + t t + t w N Here, t = w N, after w N = s found, lnk them together and draw them on the screen to obtan the Slhouettes contour of the 3D model. ISSN:

8 V. EXPERIMENTAL VERIFICATION The exermental data s the 3D model of the cultural relcs of Clesdra, a funeral obect of Zhangtang tomb n Western Han Dynasty, and Stone Horse of Emeror Xuanzong s Tomb, whch were collected va 3D laser scannng technology under cooeraton between the Natonal and Local Jont Engneerng Research Center for Cultural Relc Dgtalzaton, and Emeror Qn s Terra-cotta Warrors and Horses Museum and Shanx Archaeologcal Research Insttute, as shown n Fg. 3. the model vertexes. The red art s the feature regon of the model and the green art s the flat regon of the model, as shown n Fg. 6. The comarson of the curvature dstrbuton dagram of the corresondng model ndcates that the algorthm n ths aer can effectvely remove the nose onts n the flat regon. (a) Clesdra of Zhangtang tomb (b) Stone Horse of Emeror Tangxuan s Tomb Fg.6. Regon dvson dagram of cultural relc model (a) Clesdra of Zhangtang tomb (b) Stone Horse of Emeror Xuanzong s Tomb Fg. 3 Orthogonal roecton vew of exermental model Ste Estmate the vsual curvature of the vertexes of trangular mesh model of the cultural relc and draw the dstrbuton dagram of the curvature. Ste3 Based on the mean value of the archaeologcal feld, sharen and extract the feature contours of the trangular mesh mode to generate the lne drawng of the cultural relcs wth enough detaled features. (a) Gauss rate (b) Mean curvature (c) Maxmal rncle curvature (d) Mnmal rncal curvature Fg. 4 Curvature dstrbuton dagram of Clesdra (a) No sharenng (b) Four-tme global sharenng (c) Four-tme local sharenng (method n ths aer) Fg. 7. Plane lne dagram of Clesdra (a) Gauss rate (b) Mean curvature (c) Maxmal rncle curvature (d) Mnmal rncal curvature Fg. 5 Curvature dstrbuton dagram of Stone Horse Fg. 4 and Fg. 5 show the curvature dstrbuton dagram of the trangular mesh model n Fg. 3 (a) and (b) after dscrete curvature estmaton, of whch the green art shows that the curvature s assgned by the nterval aroxmate to the zero. Samlng curvatures more than zero are dvded nto two grous and are assgned n red and green colors based on the curvature. The samlng curvatures less than zero are dvded nto two grous and are assgned n green and blue colors. Ste2 Detect the feature regon, whch can fully embody the model detals accordng to the vsual curvature of the vertexes of the trangular mesh model under scale constrant. The trangular mesh model of cultural relc s dvded nto a feature regon and a flat regon based on the vsual curvature of (a) No sharenng (b) Fve-tme global sharenng (c) Fve-tme local sharenng (method n ths aer) Fg. 8. Feature lne extracton result of stone horse In the exerment, three ars of lne drawng are derved. Lne drawng drectly extracted from the trangular mesh model wthout sharenng n Fg. 8 (a) and Fg. 9 (a) s, ncomlete n extracton and ncaable of fully exressng the detaled features of the obects. The lane lne dagram extracted after global sharenng the trangular mesh model n Fg. 8 (b) and Fg. 9 (b) show rch lnes, bur the lnes are also drawn on a flat regon due to dsturbance of local noses, whch makes the whole lne drawng confused. Whle, the lne drawngs n Fg. 8 (c) and Fg. 9 (c) are extracted by usng the method n ths aer after feature regon detecton, based on the vsual curvature estmaton, and then local sharenng. These two lne drawngs ndcate that the method roosed n ths aer cannot only drawrch detals, but also effectvely revent the ISSN:

9 dsturbance of the noses n the flat regon. Fg. 2. The lne drawng of Terra-cotta Warrors debrs VI. CONCLUSIONS For the 3D model of cultural relc wth coarse surface and much nose, how to recsely select the feature regon for sharenng and extract the cultural relc drawng satsfyng the vsual features of human bengs s the man dffculty n fndng a soluton to automatc drawng for archaeologcal lne drawngs. The tradtonal rncal curvature estmaton deends on the estmaton of the normal lnes, whch are suscetble to noses. The normal lnes of the curved surface and rncal curvature are estmated n accordance wth the mnmzaton and maxmzaton rule to get the hghly robust normal lne and rncal curvature. The obtaned mult-scale vsual rncal curvature can dslay the shae detals of the obect n dfferent scales n the contnuous scale sace and satsfy the secfc vsual rocessng requrements n the drawng of the cultural relc lne drawng. (a) 3D model (b) Front vew (c) Left vew (d) To vew (a) 3D model (b) Front vew (c) Left vew (d) To vew Fg. 2. 3D vew of the Terra-cotta Warrors The ractce n our team work show that the method roosed n ths aer can reserve more detals, reduce nose lne n drawng, and effectvely revent massve calculaton resultng from vewont change. The lne drawng by usng our method can satsfy actual archaeologcal work requrements better and effectvely solve the roblems n manually drawng of the archaeologcal drawng such as low seed, low recson and heavy workload. In our future research work, the machne learnng method wll be ntroduced to solve the roblems of automatc settng of values n the mult-scale vsual curvature calculaton formula (6) and recse and automatc dvson of the model regon, whch wll rovde a techncal suort for the large-scale automatc and accurate drawng of the archaeologcal lne drawngs. REFERENCES [] Ma Hongzao, Feld archaeology drawng. Beng: Publshng House of Pekng Unversty, 2. [2] M. Q. Zhou, G. H. Geng, Z. K. Wu, Dgtal Preservaton Technology for Cultural Hertage. Srnger, 22. [3] F. Cole, K. Sank, D. Decarlo, A. Fnkelsten, T. Funkhouser, How well do lne drawngs dect shae?, ACM Transactons on Grahcs, vol.28, no.3, , 29. [4] L. T. DeCarlo, An alcaton of sgnal detecton theory wth fnte mxture dstrbutons to source dscrmnaton, Journal of Exermental Psychology: Learnng, Memory, and Cognton, vol.29, , 23. [5] T. Judd, F. Durand, E. Adelson, Aarent rdges for lne drawng. ACM Transactons on Grahcs (TOG). Proceedngs of ACM SIGGRAPH 27, vol. 26, No.9, 27. [6] H. R. Lu, Curvatrue Reresenton and Decomoston of Shae. Huazhong Unversty of Scence & Technology, 29. [7] H. L. Fang, G. J. Wang. Comarson and Analyss of Dscrete Curvatures Estmaton Methods for Trangular Meshes, Journal of comuter-aded desgn & comuter grahcs, vol.7, no., , 25. [8] S. R. Fan, S. F. Ru, M. Q. Zhou, G. H. Geng, A Method of Extractng Feature Contour from Trangular Mesh Surface Model of Fractured Sold. Journal of Comuter-Aded Desgn & Comuter Grahcs, vol.7, no.9, , 25. [9] M. Kolomenkn, I. Shmshon, A. Tal, Demarcatng curves for shae llustraton, ACM Transactons. on Grahcs, 28, vol.27, no.5, , 28 [] H. Jng, B. F. Zhou. A 3D model feature- lne extracton method usng mesh sharenng. Proceedng of Edutanment. Berln: Srnger, , 26. Jun Lu graduated from the School of Comuter Scence and Technology, Chengdu Unversty of Technology, for the degree of Bachelor n 995. He receved hs M.Sc degree n the School of Comuter Scence and Technology, Norhwest Unversty n 29. Snce 2 he worked toward hs Ph.D. degree at Northwest Unversty. He entered the Natonal-Local Jont Engneerng Research Center of Cultural Hertage Dgtzaton n Northwest Unversty, as an assstant researcher from 2 to 26. He s a member of Chna Comuter Federaton. Hs current research nterests nclude cultural hertage dgtzaton, attern recognton and machne learnng. Mngquan Zhou graduated from the School of Comuter Scence and Technology, Northwest Unversty, for the degree of Bachelor and Master. Now he s a rofessor of the School of Comuter Scence and Technology, and the Drector of Research Center for vrtual realty and vsualzaton technology, Beng Normal Unversty. He s a senor member of Chna Comuter Federaton. Hs research nterests nclude comuter grahcs, vrtual realty and Chnese nformaton rocessng. Guohua Geng graduated from the School of Comuter Scence and Technology, Northwest Unversty, for the degree of Bachelor and Master. Now she s a rofessor of the School of Comuter Scence and Technology, and the Drector of the Natonal-Local Jont Engneerng Research Center of Cultural Hertage Dgtzaton n Northwest Unversty. She s a senor member of Chna Comuter Federaton. Her research nterests nclude cultural hertage dgtzaton, attern recognton and ntellgent nformaton rocessng. Feng Xao receved hs B.Sc. and M.Sc. degrees n comuter scence from X an Technologcal Unversty n 2 and 23, resectvely. After the M.Sc. degree, he oned the faculty member of X an Technologcal Unversty. Snce 26 he worked toward hs Ph.D. degree at Northwest Unversty and receved ISSN:

10 hs Ph. D. degree n comuter scence from Northwest Unversty n 22. Hs research nterests nclude dgtal mage rocessng, attern recognton, mage retreval machne learnng. Defa Hu receved the PhD degree n comuter scence and technology from Hunan Unversty of Chna. Currently, he s a researcher (assstant rofessor) at Hunan Unversty of Commerce, Chna. Hs maor research nterests nclude nformaton securty and mage rocessng. He s nvted as a revewer by the edtors of some nternatonal ournals, such as Multmeda Tools and Alcatons, Internatonal Journal of Informaton and Comuter Securty, etc. He has ublshed many aers n related ournals. Table. The nformaton about Terra-cotta Warrors debrs Orgnal model Smlfed model Models Feature Mnmum Average Total Ponts Feature Mnmum Average Total Ponts onts d d Tme (s) onts d d Tme (s) Terra-cotta # Terra-cotta # Terra-cotta # Terra-cotta # ISSN: