Sharp Feature Detection as a Useful Tool in Smart Manufacturing

In e na ional Jou nal o Geo-In o ma ion A icle Sha p Fea u e De ec ion as a Use ul Tool in Sma Manu ac u ing Jana P ochazko a 1,* , Da id P ocházka 2and Ja omí Landa 2 1Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, 616 69 B no, Czech Republic 2Facul y o Business and Economics, Mendel Uni e si y in B no, 613 00 B no, Czech Republic; [email p o ec ed] (D.P.); ja omi [email p o ec ed] (J.L.) *Co espondence: p [email p o ec ed].cz Recei ed: 12 May 2020; Accep ed: 27 June 2020; Published: 30 June 2020   Abs ac : Indus y 4.0 comp ises a wide spec um o de elopmen al p ocesses wi hin he managemen o manu ac u ing and chain p oduc ion. P esen ly, he e is a huge e o o au oma e manu ac u ing and ha e au oma ic con ol o he p oduc ion. This in en ion leads o he inc eased need o high-quali y me hods o digi iza ion and objec econs uc ion, especially in he a ea o e e se enginee ing. Commonly used scanning so wa e based on well-known algo i hms can co ec ly p ocess smoo h objec s. Ne e heless, hey a e usually no applicable o complex-shaped models wi h sha p ea u es. The numbe o he poin s on he edges is ex emely limi ed due o he p inciple o lase scanning and some imes also low scanning esolu ion. The e o e, a co ec edge econs uc ion p oblem occu s. The same p oblem appea s in many o he lase scanning applica ions, i.e., in he ep esen a ion o he buildings om ai bo ne lase scans o 3D ci y models. We ocus on a me hod o p ese a ion and econs uc ion o sha p ea u es. We p o ide a de ailed desc ip ion o all h ee key s eps: poin cloud segmen a ion, edge de ec ion, and co ec B-spline edge ep esen a ion. The ea u e de ec ion algo i hm is based on he con en ional egion-g owing me hod and we de i e he op imal inpu alue o cu a u e h eshold using loga i hmic leas squa e eg ession. Subsequen edge ep esen a ion s ands on he i e a i e algo i hm o B-spline app oxima ion whe e we compu e he weigh ed asymme ic e o using he golden a io. The se ies o examples indica es ha ou me hod gi es be e o compa able esul s o o he me hods. Keywo ds: edge de ec ion; poin cloud; e e se enginee ing; spline; indus y 4.0; 3D scanning; 3D model MSC: 65D10 1. In oduc ion Indus y 4.0 is he end owa ds au oma ion and da a exchange in manu ac u ing echnologies and p ocesses. Indus y 4.0 ac o ies ha e machines which a e augmen ed wi h wi eless connec i i y and senso s, connec ed o a sys em ha can isualize he en i e p oduc ion line and make decisions on i s own. Sma manu ac u ing is a b oad ca ego y o manu ac u ing ha employs compu e -in eg a ed manu ac u ing, high le els o adap abili y and apid design changes, digi al in o ma ion echnology, and mo e lexible echnical wo k o ce aining [1,2]. Ou wo k co e s he pa o au oma ion in manu ac u ing and e e se enginee ing o design changes. The widesp ead a ailabili y o cheap comme cial dep h senso s o mul i-came a se ups leads o hei common usage in manu ac u ing enginee ing, especially in apid p oduc de elopmen [ 3 ]. The e o e, he poin cloud has become he egula ype o he ep esen a ion used e.g., in e e se ISPRS In . J. Geo-In . 2020,9, 422; doi:10.3390/ijgi9070422 www.mdpi.com/jou nal/ijgi ISPRS In . J. Geo-In . 2020,9, 422 2 o 18 enginee ing (RE) and apid p o o yping (RP). The p ecision, scanning speed and a ie y o p ocessing algo i hms c ea e sui able condi ions o i s common usage. A key p oblem in he RE/RP in eg a ion, as men ioned in [ 4 ], is he ans o ma ion o a se o dense poin s ob ained in he RE p ocess o a i ing model ha can be used. In Figu e 1, he e e se enginee ing p ocess is desc ibed. Figu e 1. Re e se enginee ing p ocess. Usually, 3D scanne s a e p o ided wi h so wa e ha c ea es a physical objec in he wo-phase se up: econs uc ing CAD model om he scanned poin da a, and subsequen STL model ou pu . Howe e , he implemen ed me hods a e usually su icien only o simple and smoo h objec s. Mo e complex objec s wi h holes, sha p edges o co ne s o en equi e p io knowledge o how o edi he scanned da a. The da a pos -p ocessing is ime-consuming and can po en ially lead o e o s. We p esen an algo i hm ha au oma ically de ec s sha p ea u es in a bi a y poin cloud da a. Ou algo i hm is based on a modi ied egion-g owing me hod. The inpu alue o he algo i hm is only one pa ame e — he no mal ec o h eshold θN (op imal s a alue and he desc ip ion is p esen ed in Sec ion 2.1). Region-g owing algo i hm elimina es he plana poin s and he emaining poin s a e p obably edge poin s. Be o e he inal manu ac u ing p ocess o 3D p in ing, a co ec model is essen ial o STL gene a ion [ 5 ] and subsequen slicing [ 4 , 6 ]. Figu e 2shows he common p oblema ic pa (jagged and inaccu a e bo de s) ha occu s equen ly. To sol e his p oblem, in Sec ion 3.2 we p opose he no el edge ep esen a ion based on B-spline app oxima ion. The asymme ic e o e alua ion is based on bell unc ion wi h weigh ing using golden a io [ 7 ] o imp o e he edge ep esen a ion o he models. Mo eo e , ou B-spline app oxima ion is also su icien o di ec STL slicing om poin clouds ha ex ac s he sec ional con ou s (cu es) di ec ly wi hou model econs uc ion. The o e iew o hese me hods is e.g., in [ 8 ]. The p esen ed B-spline app oxima ion can be used wi hou limi a ions in his slicing p ocedu e because i ob iously i e a i ely minimizes he shape-e o o he laye cu es. Figu e 2. P oblema ic pa s on he edges. P io Wo k Poin cloud segmen a ion and classi ica ion plays a key ole in poin cloud p ocessing in RE/RP usage. Segmen a ion is he p ocess o g ouping poin clouds in o mul iple homogeneous egions wi h simila p ope ies whe eas classi ica ion is he s ep ha labels hese egions. Segmen a ion me hods a e di ided in o many ca ego ies and he choice o he me hods depends on he a ea o in e es , sampling ISPRS In . J. Geo-In . 2020,9, 422 3 o 18 densi y, da a quali y and explici s uc u e o poin cloud. We can use he ca ego iza ion desc ibed in [9,10]: egion-g owing, edge-based me hods, model i ing, and hyb id me hods. Mos o he me hods s a wi h egion g owing ha was pu posed by Besl [11] o segmen a ion o images. The egion-g owing algo i hm was la e expanded in o 3D in wo di e en e sions: unseeded [ 12 ] and seeded [ 13 ]. Region g owing is applied in plen y o di e en applica ions, e.g., ex ac ing ea u es and plana su aces om 3D ou c op poin clouds [ 14 ], su ace segmen a ion, and edge ea u e lines ex ac ion om ac u ed agmen s o elics [ 15 ] o u ban en i onmen modelling [16] and also 3D ci y modelling (li e a u e su ey e.g., in [17]). Region g owing is equen ly imp o ed. Fo example, Dema is e al. [ 18 ] de ec he closed sha p edges using he egion g owing wi h no mals gi en by building a local mesh and leas -squa es planes h ough he nea es neighbo hood poin s. The co ec edge de ec ion in p o ided by g aph heo y (minimum spanning ee). In [ 16 ], egion-g owing s ep is pe o med on an oc ee-based oxelized inpu poin cloud ep esen a ion o ex ac majo segmen s. The edge-based me hods a e usually used wi h poin clouds ans o med in o he ange images [ 19 ]. Using he high-le el ea u es (scan line g ouping echnique) as segmen a ion p imi i es ins ead o indi idual pixels ensu e he high compu a ional speed. Howe e , his edge de ec ion is no applicable o noisy da a. Model i ing me hods assume ha a su ace can be desc ibed as a composi ion o simple, canonical geome ic shapes (wa e igh econs uc ion). Elemen a y me hods use RANSAC o obus ly ind planes, sphe es, cylinde s, cones, and o ii [ 20 ]. Howe e , he e occu s a p oblem wi h noise, any ine-g ained de ails a e likely o be ea ed as noise wi h he p imi i e p io , i hey a e unable o be ep esen ed as a union o smalle p imi i es (a su ey is desc ibed in [ 21 ]). The pa ial solu ion is hyb id me hods ha employ p imi i es wi h o he p io [22]. Region-g owing, edge-based me hods and model i ing do no need p e-p ocessing, bu he e exis o he segmen a ion me hods based on p e-p ocessing. These algo i hms a e capable o econs uc ing da a incomple eness [ 23 , 24 ] o cons uc a iangula mesh o gi en poin cloud [25–27]. A e wa ds, he o med mesh can be p ocessed using e.g., he disc e e di e en ial geome y whe e local ex eme o he su ace de ec he edge lines [ 25 ] o algeb aic me hods based on bi a ia e polynomials [ 27 ]. We mus no e ha some o hese me hods wo k wi h he machine lea ning me hods [28]. A e he poin cloud segmen a ion and classi ica ion, we need a co ec model ep esen a ion and essella ion (usually STL) wi h subsequen slicing o ex ac laye -based addi i e manu ac u ing [ 29 ]. The e exis a ious app oaches ha combine di e en echnologies. T adi ional STL app oach is desc ibed e.g., in [ 30 ]. B-spline o NURBS su aces a e used equen ly, e.g., au ho s in [ 31 , 32 ] p esen s di ec slicing om NURBS wi hou STL. Also, B-Rep model composed o planes, sphe es, cylinde s and cones om a 3D mesh is i ing o slicing [ 33 , 34 ]. Some o he au ho s omi he model econs uc ion and make he di ec gene a ion o sec ional con ou . Fo example, au ho s in [ 35 ] employ he cu e skele on o he model o slice h ough he su ace mesh edges. B-spline cu e i ing o he laye s whe e he cu e cu a u e is de e mined by a ci cle i ing p ocedu e is p esen ed in [8]. The de elopmen o neu al ne wo ks and deep lea ning also ouches he esea ch in poin cloud analysis. Some me hods a e p omising bu he e is s ill no one-size- i s-all app oach. Re iews o he me hods a e co e ed e.g., in [36–38]. P esen li e a u e con ains mos o he ecen ly known p inciples. Main scien i ic con ibu ion is in hei imp o emen s and applica ions. Fo example, wo k [ 39 ] (published 2020) uses B-spline ep esen a ion and no mal compu a ion using no mal cu a u e di ec ly compu ed by pa ial de i a i es o he su ace. The omi ing o he p e-de ined h eshold alue is he main idea in [ 40 ] (published 2019). The au ho s sugges he composi ion o spa ial FFT-based il e ing and bounda y de ec ion, which oge he allow o di ec gene a ion o low noise essella ed su aces om poin cloud da a. Re [ 41 ] p esen s he ea u e sensi i e poin cloud simpli ica ion ha is based on insensi i e suppo ec o eg ession. ISPRS In . J. Geo-In . 2020,9, 422 4 o 18 The ad an ages o he well-known me hods ( egion-g owing o PCA) a e ob ious— obus ness, compu ed easiness, s able algo i hms. Because o ha , we chose hese classical me hods and ou main idea was (1) he simpli ica ion and au oma ic se ing o inpu alues (desc ibed in Sec ion 2.1) (2) ind op imal e o e alua ion in B-spline ep esen a ion ha is sui able o enginee ing objec s. The p oblem o e o compu a ion is desc ibed in Sec ion 2.2 and we p oposed asymme ic weigh ing based on golden a ion. 2. Me hods and Ma e ials The common indus ial enginee ing componen s consis o la , smoo h o cu ed su aces. A measu able di e ence in su ace no mals o cu a u e is ela i ely small on mos o he model su aces. Con a y o ha , in he neighbo hood o a sha p ea u e, such as a sha p edge o co ne , he e is a signi ican change in he su ace no mal and cu a u e. Thus, i we emo e all poin s o he la , smoo h o cu ed su aces, he emaining ones a e he poin s on he sha p ea u es. Wi h his idea in mind, we build ou me hod, simila ly o [ 42 ], on he analysis o he eigen alues o he co a iance ma ix o e e y poin ’s k -nea es neighbo . We use egion g owing no o ind plana su aces o egula models [43] bu o emo e he poin s wi h low cu a u e (Sec ion 2.1). The impo an inpu alues o egion g owing a e no mal and cu a u e h esholds. Thei se ing subs an ially changes he segmen a ion esul s, bu hei choice is unin ui i e and di icul especially o beginne s. We ind he geome ic co ela ion be ween hese wo alues and we compu e he op imal ini ial alue ha is applicable in he case o egula enginee ing objec s. This is desc ibed in he ollowing subsec ions. This app oach is obus o he noise and is sui able o subsequen B-spline app oxima ion. The B-spline app oxima ion was chosen due o i s good p ope ies and well-known compu a ion. The i e a i e p ocess ensu es su icien quali y. The e o compu a ion is based on he asymme ically weigh ed dis ance (asymme ic dis ance is p esen ed in [ 44 ]) bu in ou case, he weigh is desc ibed wi h he golden a io. The asymme ic measu emen eplaces he ou lie s and p o ec s he cu e om he zig-zag e ec . This app oach is desc ibed in Sec ion 2.2. Compu ed B-spline cu e can ep esen edges in poin clouds. Mo eo e , desc ibed B-spline app oxima ion is also possible o use in he me hods o di ec slicing. 2.1. Edge Poin s De ec ion The p ocessing o a gi en poin cloud s a s wi h he egion-g owing segmen a ion. Su ace no mal compu a ion is based on P incipal Componen Analysis (PCA) [ 45 ] ha uses an o hogonal ans o ma ion o con e a se o obse a ions o possibly co ela ed a iables in o a se o alues o linea ly unco ela ed a iables. The desc ip ion is in Sec ion 2.1.1. Edges can be also classi ied by Gauss mapping [ 42 , 46 , 47 ]. The poin no mal ec o s a e p ojec ed on he Gauss sphe e and subsequen clus e ing dis inguish he poin ype (co ne , edge, plana ). This me hod is ime-consuming so ha we use he egion g owing. 2.1.1. PCA—No mal Es ima ion The i s s ep in he PCA algo i hm is he compu a ion o he co a iance ma ix C o each poin P in he poin cloud. C=1 k k ∑ i=1 (Pi−¯ P)·(Pi−¯ P)T, (1) whe e ¯ P is he cen oid o k -nea es neighbo hood poin s Pi , i= 1, 2, . . . k o a poin P . Eigen alues ( λ0 , λ1 , λ2 ) and eigen ec o s ( ~ 1 , ~ 2 , ~ 3 ) o his ma ix de ines he co a iance ellipsoid. We dis inguish be ween hese h ee cases: 1. (λ0≤λ1≤λ2)∧(λ1≈λ2) 2. (λ0≤λ1≤λ2)∧(λ0≈λ1) ISPRS In . J. Geo-In . 2020,9, 422 5 o 18 3. (λ0≤λ1≤λ2)∧(λ0≈λ1≈λ2). These ypes o co a iance ellipsoids de ine he neighbo hood o he gi en poin (Figu e 3a–c). In he case o an obla e ellipsoid ( (λ0≤λ1≤λ2)∧(λ1≈λ2) ), he poin is ob iously on an almos plana a ea and he eigen ec o co esponding wi h he smalles eigen alue is poin no mal. λ0 λ1 λ2 (a) λ2 λ0λ1 (b) λ2 λ0 λ1 (c) Figu e 3. Types o he co a iance ellipsoid (a) obla e (b) p ola e (c) simila o a sphe e. 2.1.2. Region G owing—Ini ial No mal Th eshold Value h θN Region-g owing segmen a ion algo i hm usually equi es inpu pa ame e s: minimal and maximal clus e size, k -nea es neighbo poin s, no mal h eshold h θN and cu a u e h eshold h θC . Value θN is he angle be ween wo-poin no mals and θC is cu a u e. They s ongly a ec he segmen a ion esul s and geome ically, hey a e igh ly connec ed. The se ing o he ini ial alues is unin ui i e and no use - iendly so ha we ocus on he op imal au oma ic es ima ion o θN. Figu e 4a shows he de ini ion o he cu a u e θ o he cu e l a he poin P1 . In he limi as ∆ →0, we ob ain: θ=lim ∆ →0 ∆α ∆ (2) In he case o a poin cloud, we conside he pa ame e ∆ as he minimal dis ance dmin o he line be ween wo adjacen poin s (Figu e 4b). The cu a u e θCis compu ed by θC=θN dmin . (3) l Δα Δα Δ P1 n1n2 2 1 P2 (a) dmin θN θN P1 n1n2 2 1 P2 (b) Figu e 4. (a) Cu a u e o he cu e, (b) cu a u e es ima ion in a poin cloud. The e o e, he egion-g owing segmen a ion can be con olled only by one pa ame e — he no mal ec o h eshold h θN. The ollowing pa desc ibes he p ocess o he ideal ini ial alue o h θN. We p epa ed a se o es ing poin clouds Mi , i= 1, 2, . . . , 6 o co e he spec um o di e en shapes om simple one o he complex ones (Figu e 5). These poin cloud da a we e acqui ed by ATOS ISPRS In . J. Geo-In . 2020,9, 422 6 o 18 Compac Scan 2M.We se a es ing ange o maximal alues o no mal ec o h eshold h θN= 1, . . . , 15. I means ha he segmen a ion emo es all poin s in clus e s whe e he no mal ec o h eshold is lowe han h θN . Le nou be a numbe o he emo ed poin s and nin be se e al poin s in a poin cloud. We applied he egion-g owing algo i hm on ou da a-se s wi h pa ame e s h θN and we compu ed he numbe o emo ed poin s nou . The pe cen age o emaining poin s is de ined as: pe cN=nou nin ·100. (4) We no ice ha he dependence be ween h θN and pe cN has loga i hmic p og ess, he loga i hmic eg ession is he bes choice o compu e he dependence: h θN=b1ln(pe cN) + b0,b0,b1∈R. (5) The g aphs and inal esul s a e in Sec ion 3.1. ( a ) ( b ) ( c ) ( d ) ( e ) ( ) Figu e 5. Tes ing poin clouds: (a)M l, (b)M2, (c)M3, (d)M4, (e)M5, ( )M6. 2.2. B-Spline Edge Rep esen a ion B-spline i ing belongs o he a o i e ools o p ocessing o a se o uno ganized, possibly noisy da a poin s in compu e g aphics, compu e ision and CAD/CAM. The main ad an age o B-spline app oxima ion is based on he well-known o mula ion o B-spline [48]: C(u) = n ∑ i=0 Bi,p(u)Pi, (6) whe e Bi,p(u) is he B-spline basis unc ion o deg ee p wi h con ol poin s Pi . The pa ame e u is om he nonpe iodic and nonuni o m kno in e al u=<u0 , u1 , . . . , un+p+1> . We se u0= 0 and un+p+1=1. Le {Qk}m k=0 be he se o inpu poin s. The i ing algo i hm sea ch o con ol poin s Pi , kno ec o u o he spline cu e de ined in Equa ion (6) and also he pa ame e s b u={b uk}m k=0 ha sa is ied he equa ion: Qk= n ∑ i=0 Bi,p(b uk)Pi(7) and C(u0) = C(0) = Q0,C(un+p+1) = C(1) = Qm. Fi s , we compu e he ini ial cu e shape. The au ho s in [ 44 ] wo k wi h he ini ial ci cle (cen e o he ci cle is a he mean o he poin cloud, he adius o he maximal dis ance o a poin o cen e ) o an ellipse which he main axes a e compu ed by PCA. We s a wi h equen ly used cho dal and cen ipe al me hod. The cho dal me hod compu es he pa ame e s as: b u0=0; b um=1; b uk=b uk−1+|Qk−Qk−1| d(8) whe e d=∑m k=1|Qk−Qk−1| . Cen ipe al me hod is simila , we only add squa e oo o he line leng h. Cen ipe al me hod is mo e ele an in case ha he da a akes sha p u ns. ISPRS In . J. Geo-In . 2020,9, 422 7 o 18 Secondly, we se he kno ec o u wi h condi ion ha e e y kno span con ains a leas one b uk . The in e nal kno spans a e de ined by [49]: i= loo (jd),α=jd −i, up+j= (1−α)b ui−1+αb ui,j=1, . . . , n−p(9) and unc ion loo is he la ges in ege such i≤jd. Subsequen ly, coo dina es o he con ol poin s Pi a e app oxima ed by he s anda d echnique o linea leas -squa es i ing [48]. We minimize he unc ion: =| m−1 ∑ k=1 Qk−C(b uk)|2(10) We can desc ibe he solu ion in ma ix o m ( he sys em o n−1×n−1 equa ions) as: (BTB)P=R(11) whe e ma ix B B ep esen s he B-spline unc ion o deg ee p e alua ed o all b uk , k= 1, . . . , n− 1. Ma ix Pa e wan ed con ol poin s and ec o Ris he ec o o n−1 poin s: R=   ∑m−1 k=1B1,p(b uk)Rk . . . ∑m−1 k=1Bn−1,p(b uk)Rk   (12) and Rk=Qk−B0,p(b uk)Q0−Bn,p(b uk)Qm,k=1, . . . , m−1. (13) The Equa ion (11) can be sol ed by Gaussian elimina ion because he ma ix BTB is posi i e de ini e and well-condi ioned. We mus deal wi h he main p oblem h oughou he i e a ion p ocess: a choice o he dis ance measu e o e o de e mina ion. The o mula ion o he p oblem is simple, we ha e uno ganized da a poin s (in ou case possible edge poin s) wi h non-uni o m dis ibu ion wi h conside able noise. This p oblem can be o mula ed as a nonlinea op imiza ion p oblem. Gi en inpu poin s {Qk}m k=0 , we wan o compu e con ol poin s Pi ha minimize a gene al objec i e unc ion [44]: =1 2 n ∑ k=1 d2(P(u),Qk) + λ s(14) d2(P(u) , Qk) is he dis ance o poin Qk o he cu e P( ) , s is egula iza ion e m o ensu e a smoo h cu e, λ is weigh o s . In ou algo i hm, we wo k wi h he asymme ic weigh ed poin dis ance measu e. We in oduce a no el e o e m in Equa ion (15) ha is based on golden a ion. I ensu es ha he inne poin s (on he same side as a no mal ec o ) ha e lesse in luence han he ou e . This ad an age elimina es he p oblema ic ou lie s and imp o es he shape o he cu e (Figu e 6). ou lie s Figu e 6. The example o he ou lie s. ISPRS In . J. Geo-In . 2020,9, 422 8 o 18 The dis ance dk is he signed dis ance o he poin Qk and he closes poin on he compu ed B-spline cu e. dk is posi i e i he poin Qk is on he same side as no mal nk —see Figu e 7a. This e o e m is: wϕ(dk) =          1 ϕ+ϕ−d2 k σ2 o dk<0 1 o dk≥0 (15) k= 0, 1, 2 . . . , m , whe e σ de ines he wid h o he ansi ion o he weigh ing unc ion wi h espec o he signed dis ance. The alue ϕis he golden a io 1.61803398875. The objec i e unc ion has a o m: ϕ= m ∑ k=0 wϕ(dk)d2 k, (16) The weigh ing unc ion wϕ(dk)and objec i e unc ion ϕa e modelled in Figu e 7b. C(k) nk Qk (a) -1.5 -1 -0.5 0 0.5 1 d 0 0.5 1 1.5 2 (b) Figu e 7. ( a ) No mal ec o is on he opposi e side o he poin Qk , dis ance dk is nega i e, ( b ) he g aphs o he unc ions wϕ( ed line) and ϕ(blue line). The asymme ic e o de ec s he pa s whe e he cu e accu acy is insu icien . The imp o emen is done by local kno inse ion. We know he pa ame e uk o he nea es cu e poin C(uk) o e e y Qk . The e o e, we inse all kno s uk in he insu icien pa s and ecompu e he cu e using kno inse ion scheme. I uk∈<uk,uk+1), hen he new con ol poin s Pia e: Pi=βiPi+ (1−βi)Pi−1(17) whe e βi=     uk−ui ui+p−ui o k−p+1≤i≤k 1 o i≤k−p 0 o i≥k+1 (18) In he pa s, whe e he e o is high, we add he new kno in he alue o he nea es cu e poin . We es ed he p oposed imp o emen on he se o poin clouds C1 , C2 , C3 , C4 and C5 . The es esul s and ho ough compa ison a e in Sec ion 3. 3. Resul s and Discussion This sec ion con ains wo main pa s: Es ima ion o no mal h eshold pa ame e and B-spline i ing wi h a no el asymme ic e o . In he i s pa , we made a se ies o es ing objec s— om almos plana ones o he complex ones wi h holes. We p oceeded hese models wi h egion-g owing ISPRS In . J. Geo-In . 2020,9, 422 9 o 18 algo i hm and using ou p oposed me hod (Sec ion 2.1.2) we es ima e he op imal alue o he no mal h eshold. This alue can be se as a uni e sal inpu h eshold alue. The inexpe ienced end-use s o he edge de ec ion algo i hm do no need any complex manual on how o con ol he esul s. The second s ep con ains a B-spline i ing algo i hm o he edge ep esen a ion. The inpu o his pa a e poin s de ec ed in he i s s ep. The asymme ic e o wi h he golden a io (Equa ion (15) ) is used in he i e a ion p ocess as desc ibed in he p e ious sec ion. On he se o di e en cu es (smoo h, complex) we show he esul s and we make a compa ison wi h me hod [44]. Fea u e de ec ion algo i hm was implemen ed in Mic oso Visual S udio C++ wi h Poin Cloud Lib a y 1.8.0. The B-spline app oxima ion was p og ammed in MATLAB R2018a. The poin cloud da a-se s we e ob ained by ATOS Compac Scan 2M. Tes ing was p o ided on he MacBook P o, 2.6 GHz In el Co e i7, 16 GB 1600 MHz DDR3, NVIDIA GeFo ce GT 750M 2048 MB, SSD. 3.1. Es ima ion o No mal Th eshold h θN The i s analyses examines he impac o pa ame e h θN . The se o es ing poin clouds Mi,i∈ h1, 6iis in Figu e 5. Le sin be se e al poin s in he gi en poin cloud (Table 1). Table 1. The poin clouds wi h numbe o poin s sin. Model M1M2M3M4M5M6 sin 87,848 67,394 195,815 123,112 103,534 90,209 We applied he egion-g owing algo i hm on ou da a-se s wi h he ini ial pa ame e s h θN∈N , h θN= 1, . . . , 15 and we ind he numbe o emo ed poin s nou . The pe cen age o emaining poin s is compu ed by: pe cN=nou nin ·100. (19) Table A1 p o ides he esul s ob ained by he analysis o di e en alues h θN . We can see ha he alue o pe cNis igh ly ela ed o he complexi y o he model. Table A2 (middle column) p esen s poin cha s o he alues h θN and pe cN . We can see ha independen ly on he model complexi y, i has he loga i hmic p og ess. The e o e, he dependence be ween h θN and pe cN can be gene ally desc ibed wi h loga i hmic eg ession using Equa ion (5) . The inal equa ions and g aphs a e in Table A2 (las column). We wan o de e mine he bes possible inpu alue h θN ha is applicable o common poin clouds o he enginee ing models. We s a wi h he a e age eg ession equa ion ( he a e age o he equa ions in Table A2): θST ≈R(x) = −2.45 ·ln(x) + 6.06. (20) The op imal alue o pe c is se empi ically as 1–6%. The e o e, he alues o h θN a e in in e al hR(1),R(6)i. Ob iously, we ge : R(1) = −2.45 ·ln(1) + 6.06 ≤θST ≤ −2.45 ·ln(6) + 6.06 =R(6) 6.06 ≤θST ≤1.67. (21) The a i hme ic mean o R( 1 ) and R( 6 ) is θop = 3.86 is se as a de aul ini ial alue in he p oposed ea u e de ec ion algo i hm. In he case o insu icien esul s, his alue can be changed inc emen ally. Table 2shows he segmen a ion esul s o models Mi , i= 1, 2, . . . , 6 using he de aul ini ial alue θop = 3.86. I is ob ious ha he esul s a e su icien and his alue helps inexpe ienced use s o s a segmen a ion wi hou any p io knowledge o cu a u e o no mal h eshold. By applying he inc emen al change o his alue, he esul s a e imp o ed o ob ain su icien quali y o ac ual use. ISPRS In . J. Geo-In . 2020,9, 422 16 o 18 Table A3. Compa ison o B-spline cu e app oxima ion o es ing clouds, CP is numbe o con ol poin s, wϕis a e age weigh ed e o . C1 CP 4 10 20 wϕ[mm] 2.35 1.15 0.83 C2 CP 4 10 20 40 80 wϕ[mm] 14.01 5.54 2.02 1.25 0.99 C3 CP 20 40 80 wϕ[mm] 3.96 0.96 0.85 C4 CP 80 100 160 wϕ[mm] 0.41 0.37 0.27 C5 CP 10 40 80 wϕ[mm] 2.19 0.67 0.33 Re e ences 1. Da is, J.; Edga , T.; Po e , J.; Be naden, J.; Sa li, M. Sma manu ac u ing, manu ac u ing in elligence and demand-dynamic pe o mance. Compu . Chem. Eng. 2012,47, 145–156. [C ossRe ] 2. Vaidya, S.; Ambad, P.; Bhosle, S. Indus y 4.0—A Glimpse. P ocedia Manu . 2018,20, 233–238. [C ossRe ] 3. Chua, C.K.; Leong, K.F.; Lim, C.S. Rapid P o o yping: P inciples and Applica ions. In Rapid P o o yping: P inciples and Applica ionse; Wo ld Scien i ic Publishing: Singapo e, 2010. 4. Qiu, Y.; Zhou, X.; Qian, X. Di ec slicing o cloud da a wi h gua an eed opology o apid p o o yping. In . J. Ad . Manu . Technol. 2011,53, 255–265. [C ossRe ] 5. Li esu, M.; Elle o, S.; Ma inez, J.; Le eb e, S.; A ene, M. F om 3D models o 3D p in s: an o e iew o he p ocessing pipeline. Compu . G aph. Fo um 2017,36, 1–24. [C ossRe ] 6. Choi, S.-H.; Sama edam, S. Modelling and op imisa ion o apid p o o yping. Compu . Ind. 2002,47, 39–53. [C ossRe ] 7. Sen, S.K.; Aga wal, R.P. Golden a io in science, as andom sequence sou ce, i s compu a ion and beyond. J. Compu . Ma h. Appl. 2008,56, 469–498. [C ossRe ] 8. Ja id ad, R.; Pou moayed, A.R. Con ou cu e econs uc ion om cloud da a o apid p o o yping. Robo . Compu . In eg . Manu . 2011,27, 397–404. [C ossRe ] ISPRS In . J. Geo-In . 2020,9, 422 17 o 18 9. G illi, E.; Menna, F.; Remondino, F. A e iew o poin clouds segmen a ion and classi ica ion algo i hms. In . A ch. Pho og amm. Remo e Sens. Spa . In . Sci. 2017,XLII-2/W3, 339–344. [C ossRe ] 10. Nguyen, A.; Le, B. 3D poin cloud segmen a ion: A su ey. In P oceedings o he 6 h IEEE Con e ence on Robo ics, Au oma ion and Mecha onics (RAM), Manila, Philippine, 12–15 No embe 2013; pp. 225–230. 11. Besl, P.J.; Jain, R.C. Segmen a ion h ough Va iable-O de Su ace Fi ing. IEEE T ans. Pa e n Anal. Mach. In ell. A ch. 1988,10, 167–192. [C ossRe ] 12. Naha , M.; Ali Sujan Rahman, M. Imp o emen o Single Seeded Region G owing Algo i hm on Image Segmen a ion. Glob. J. Compu . Sci. Technol. 2018,18, 15–22. 13. Adams, R.; Bischo , L. Seeded Region G owing. IEEE T ans. Pa e n Anal. Mach. In ell. A ch. 1994 ,6, 641–647. [C ossRe ] 14. Wang, X.; Zoua, L.; Shena, X.; Rena, Y.; Qina, Y. A egion-g owing app oach o au oma ic ou c op ac u e ex ac ion om a h ee-dimensional poin cloud. Compu . Geosci. 2017,99, 100–106. [C ossRe ] 15. Xu, J.; Zhou, M.; Wu, Z.; Shui, W.; Ali, S. Robus su ace segmen a ion and edge ea u e lines ex ac ion om ac u ed agmen s o elics. J. Compu . Des. Eng. 2015,2, 79–87. [C ossRe ] 16. Vo, A.V.; T uong-Hong, L.; Lae e , D.F.; Be olo o, M. Oc ee-based egion g owing o poin cloud segmen a ion. ISPRS J. Pho og amm. Remo e Sens. 2015,104, 88–100. [C ossRe ] 17. Ni, H.; Lin, X.; Ning, X.; Zhang, J. Edge De ec ion and Fea u e Line T acing in 3D-Poin Clouds by Analyzing Geome ic P ope ies. Remo e Sens. 2016,8, 710. [C ossRe ] 18. Dema is, K.; Vande s ae en, D.; Volodine, T.; Roose, D. De ec ion o closed sha p edges in poin clouds using no mal es ima ion and g aph heo y. Compu . Aided Des. 2007,39, 267–283. 19. Jiang, X.Y.; Bunke, H.; Meie , U. Fas ange image segmen a ion using high-le el segmen a ion p imi i es. In P oceedings o he Thi d IEEE Wo kshop on Applica ions o Compu e Vision, Sa aso a, FL, USA, 2–4 Decembe 1996; pp. 83–88. 20. Schnabel, R.; Wahl, R.; Klein, R. E icen Ransac o poin cloud shape de ec ion. Compu . G aph. Fo um 2007 , 26, 214–226. [C ossRe ] 21. Be ge , M.; Tagliasacchi, A.; Se e sky, L.M.; Alliez, P.; Guennebaud, G.; Le ine, J.A.; Sil a, C.T. A Su ey o Su ace Recons uc ion om Poin Clouds. Compu . G aph Fo um 2016,36, 301–329. [C ossRe ] 22. La a ge, F.; Alliez, P. Su ace econs uc ion h ough poin se s uc u ing. In Compu e G aphics Fo um; Benes, B., Chen, M., Eds.; Wiley: New Yo k, NY, USA, 2013; pp. 225–234. 23. Wang, M.; Ju, M.; Fan, Y.; Guo, S.; Liao, M.; Yang, H.; Komu a, T. 3D Incomple e Poin Cloud Su aces Recons uc ion Wi h Segmen a ion and Fea u e-Enhancemen . IEEE Access 2019 ,7, 15272–15281. [C ossRe ] 24. Yin, K.; Huang, H.; Zhang, H.; Gong, M.; Cohen-O , D.; Chen, B. Mo i : in e ac i e su ace econs uc ion om incomple e poin clouds wi h cu e-d i en opology and geome y con ol. ACM T ans. G aph. 2014 , 33, 202. [C ossRe ] 25. Hildeb and , K.; Pol hie , K.; Wa de zky, M. Smoo h ea u es lines on su ace meshes. In Eu og aphics Symposium on Geome y P ocessing; Desb un, M., Po mann, H., Eds.; Eu og aphics Associa ion: Ai e-la-Ville, Swi ze land, 2005; pp. 85–90. 26. Oh ake, Y.; Belyae , A. Au oma ic de ec ion o geodesic idges and a ines on polygonal su ace. J. Th ee Dimens. Images 2001,15, 127–132. 27. S ylianou, G.; Fa in, G. C es lines ex ac ion om 3D iangula ed meshes. In Hie a chical and Geome ical Me hods in Scien i ic Visualiza ion; Fa in, G., Hamann, B., Hagen, H., Eds.; Sp inge : Be lin, Ge many, 2003; pp. 69–81. 28. Too ooni, S.; Dsouza, A.; Dono an, R.; Rao, P.K.; Kong, Z.; Bo gesen, P. Classi ying he Dimensional Va ia ion in Addi i e Manu ac u ed Pa s F om Lase -Scanned Th ee-Dimensional Poin Cloud Da a Using Machine Lea ning App oaches. J. Manu . Sci. Eng. 2017,139, 142–149. 29. Benie e, R.; Subsol, G.; Gesqui e, G.; Le B e on, F.; Puech, W. A comp ehensi e p ocess o e e se enginee ing om 3D meshes o CAD models. Compu . Aided Des. 2013,45, 1382–1393. [C ossRe ] 30. Zhang, Z.; Sanjay, J. An imp o ed slicing algo i hm wi h e icien con ou cons uc ion using STL iles. In . J. Ad . Manu . Technol. 2015,80, 1347–1362. [C ossRe ] 31. Ma, W.; Bu , W.C.; He, P. NURBS-based adap i e slicing o e icien apid p o o yping. Compu . Aided Des. 2004,36, 1309–1325. [C ossRe ] 32. O opallo, W.; Piegl Les, A.; Rosen, P.; Rajab, K. Gene a ing poin clouds o slicing ee- o m objec s o 3-D p in ing. Compu . Aided Des. Appl. 2017,14, 242–249. [C ossRe ] ISPRS In . J. Geo-In . 2020,9, 422 18 o 18 33. Shi, K.; Cai, C.; Wu, Z.; Yong, J. Slicing and suppo s uc u e gene a ion o 3D p in ing di ec ly on B- ep models. Vis. Compu . Ind. Biomed. A 2019,2, 3. [C ossRe ] 34. Zhao, G.; Ma, G.; Feng, J.; Xiao, W. Nonplana slicing and pa h gene a ion me hods o obo ic addi i e manu ac u ing. In . J. Ad . Manu . Technol. 2018,96, 3149. [C ossRe ] 35. K esslein, J.; Haghighi, P.; Jaejong, P.; Ramna h, S.; Su adha , A.; Shah, J.J. Au oma ed c oss-sec ional shape eco e y o 3D b anching s uc u es om poin cloud. J. Compu . Des. Eng. 2018,5, 368–378. [C ossRe ] 36. Liu, W.; Sun, J.; Li, W.; Hu, T.; Wang, P. Deep Lea ning on Poin Clouds and I s Applica ion: A Su ey. Senso s 2019,19, 4188. [C ossRe ] [PubMed] 37. G i i hs, D.; Boehm, J. A Re iew on Deep Lea ning Techniques o 3D Sensed Da a Classi ica ion. Remo e Sens. 2019,11, 1499. [C ossRe ] 38. Guo, Y.; Wang, H.; Hu, Q.; Liu, H.; Liu, L.; Bennamoun, M. Deep Lea ning o 3D Poin Clouds: A Su ey. a Xi 2019, a Xi :abs/1912.12033. 39. Lee, D.; Quan, I.; Wu, C.; Wu, J.; Tami , D.; Rishe, N. Op imizing B-Spline Su ace Recons uc ion o Sha p Fea u e P ese a ion. In P oceedings o he 10 h Annual Compu ing and Communica ion Wo kshop and Con e ence (CCWC), Las Vegas, NV, USA, 6–8 Janua y 2020; pp. 359–364. 40. Mineo, C.; Pie ce, S.G.; Summan, R. No el algo i hms o 3D su ace poin cloud bounda y de ec ion and edge econs uc ion. J. Compu . Des. Eng. 2019,6, 81–91. [C ossRe ] 41. Ma ko ic, V.; Jako ije ic, Z.; Miljko ic, Z. Fea u e sensi i e h ee-dimensional poin cloud simpli ica ion using suppo ec o eg ession. Tech. Gaz. 2019,27, 985–994. 42. Bazazian, D.; Casas, J.R.; Ruiz-Hidalgo, J. Fas and Robus Edge Ex ac ion in Uno ganized Poin Clouds. In P oceedings o he In e na ional Con e ence on Digi al Image Compu ing: Techniques and Applica ions (DICTA), Adelaide, Aus alia, 23–25 No embe 2015; pp. 1–8. 43. Wang, Y.X.; Wang, J.; Chen, X.; Chu, T.; Liu, M.; Yang, T. Fea u e Su ace Ex ac ion and Recons uc ion om Indus ial Componen s Using Mul is ep Segmen a ion and Op imiza ion. Remo e Sens. 2018 ,10, 1073. [C ossRe ] 44. Mö wald, T.; Balze , J.; Vincze, V. Modeling connec ed egions in a bi a y plana poin clouds by obus B-spline app oxima ion. Robo . Au on. Sys . 2008,76, 141–151. [C ossRe ] 45. Jolli e, I.T. P incipal Componen Analysis; Sp inge : New Yo k, NY, USA, 1986; p. 487. 46. Bancho , T.; Ga ney, T.; McC o y, C. Cups o he Gauss Map. In Resea ch No es in Ma hema ics; Pi man: London, UK, 1982. 47. Webe , C.; Hahmann, S.; Hagen, H. Me hods o ea u e de ec ion in poin cloud. In Visualiza ion o La ge and Uns uc u ed Da a Se s–IRTG Wo kshop; Middel, A., Schele , I., Hagen, H., Eds.; Schloss Dags uhl–Leibniz-Zen um ue In o ma ik: Bodega Bay, CA, USA, 2010; pp. 90–99. 48. Piegl, L.; Tille , W. The NURBS Book; Sp inge : New Yo k, NY, USA, 1997. 49. de Boo , C. A P ac ical Guide o Splines; Sp inge : New Yo k, NY, USA, 2001. 50. Blake, A.; Isa d, M. The Ac i e Con ou s; Sp inge : New Yo k, NY, USA, 1998. 51. Wang, W.; Po mann, H.; Liu, Y. Fi ing B-spline cu es o poin clouds by cu a u e-based squa ed dis ance minimiza ion. ACM T ans. G aph. 2006,25, 214–238. [C ossRe ] c 2020 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h p://c ea i ecommons.o g/licenses/by/4.0/).