Feature Estimation and Registration of Point Clouds in Reverse Engineering

Transcription

1 Amercan Journal of Mechancal and Materals Engneerng 017; 1(4): do: /j.ajmme Feature Estmaton and Regstraton of Pont Clouds n Reverse Engneerng Hongguang Zhu, Xu Zhang College of Mechancal Engneerng, Shangha Unversty of Engneerng Scence, Shangha, Chna Emal address: @qq.com (Hongguang Zhu), @qq.com (Xu Zhang) To cte ths artcle: Hongguang Zhu, Xu Zhang. Feature Estmaton and Regstraton of Pont Clouds n Reverse Engneerng. Amercan Journal of Mechancal and Materals Engneerng. Vol. 1, No. 4, 017, pp do: /j.ajmme Receved: March 4, 017; Accepted: Aprl 8, 017; Publshed: July 1, 017 Abstract: Cultural relc s the carrer of nformaton, such as producton, lfe, scence and technology, art and so on. However, due to natural and man-made reasons, artfacts are often destroyed. Excavaton ste s the most common varety of cultural relcs, the need for cultural relcs repar. Because the artfacts are generally made on the rotatng dsk, so the object of ths study s the rotatng debrs. The geometrc characterstcs of the rotatng body are the rotaton axs, the contour lne, the radus of rotaton and the angle of ft. Estmate the overall characterstcs of the rotary body have mportant reference value for computer aded restoraton of cultural relcs. The effcency and precson of the axs of rotaton, contour s estmated by dfferent methods are dfferent, whch wll drectly affect the follow-up work of ths paper focuses on the sttchng, from the axs of rotaton estmaton, contour calculaton, rotaton radus and central angle calculaton s dscussed. Keywords: Cultural Relc Restoraton, Revolvng Body, Rotaton Axs, Contour, Radus of Gyraton 1. Introducton Antqutes s an mportant research object of archaeologsts, through the study of ancent artfacts can have a further understandng of ancent culture. But because of the natural and human destructon, the excavaton ste s often a pece of cultural relc, need further work before sttchng t possble to recreate the orgnal. Because most of the cultural relcs are made on the turntable, the object of ths paper s to study the splcng of the fragments of the rotatng body. The vbraton envronment test of electronc equpment to the sne test and random vbraton test test. The general approach s to fnd out the structure resonance frequency or drect defnton of the vbraton frequency, the frequency of ant resonance tests. [3] Structures n the resonant state of local dsplacement wll produce, caused by the local bendng deformaton, resultng n fatgue damage. It can quckly assess the structure strength, structural defects, and evaluaton In ths paper, the dynamc characterstcs of the specmen are tested, and the dynamc characterstcs of the low voltage crcut breaker are studed. In ths paper, the rotaton of the body fragments of the splcng process s as follows: (1) preprocessng: 3D pont cloud feature nformaton obtaned by 3D scanner; () classfcaton: accordng to the characterstcs of the 3D pont cloud of the obtaned fragments, the fragments from the same cultural relcs are classfed nto one class; (3) splcng: on the bass of classfcaton, local matchng and global matchng; (4) repar: geometrc and texture nformaton complete the lost. The axs of rotaton, rotaton, rotaton radus and contour matchng angle s an mportant feature of the rotatng body, so the use of more accurate estmates of the approprate method of these features for the sttchng precson rotatng body peces of cultural relcs s very mportant. Classfcaton s the premse of the effcency of the rotaton of the artfacts, and the use of approprate classfcaton methods, so that the fragmentaton of the work wth half the effort. Proper sttchng algorthm has a great nfluence on the accuracy and effcency of the sttchng. Fnally, the repar of cultural relcs can complete the sttchng work. To solve the above problems, ths paper manly through the rotaton of the body peces of cultural relcs n the process of sttchng estmaton of rotaton axs, the contour lne of the rotatng radus and central angle calculaton, the calculaton s dscussed.

2 84 Hongguang Zhu and Xu Zhang: Feature Estmaton and Regstraton of Pont Clouds n Reverse Engneerng. Calculaton of Rotatng Shaft The rotatng shaft s an mportant geometrc feature of the rotatng body. Yacoub [1] and Sablatng [] proposed the axs of rotaton estmaton based on Hough transform fragments, specfc dvded nto 3 steps: (1) plane fttng method based on vector estmaton; () Hough transform; (3) by usng prncpal component analyss method to estmate the shaft. Ths method s robust to nosy data, but slower. The optmzaton method proposed by Halr [3] s more accurate than the prevous one, but t s not good enough to use the least square method. Zhang Zongxa [4] of Shandong Unversty uses the method of two surface fttng to calculate the normal vector, and uses the method of lnear geometry to calculate the rotaton axs of [5]. In ths paper, the author calculates the normal vector by three methods (1 wth average method adjacent trangles as vector vectors; plane vector method based on fttng calculaton; 3 two quadrc surface fttng method based on vector calculaton), and draw the followng conclusons: n the absence of nose under the condton of normal vector obtaned by varous methods are approxmately equal, when addng nose, calculated by two quadrc surface fttng method of vector method s lower than the other two has strong ant-nterference ablty, but the speed s slow. Based on the calculaton method of the vector author estmate the rotaton axs, the experments show that: the method of vector trangle method to calculate the axs of rotaton s smple and fast, plane fttng method to get the speed of a rotatng shaft was obtaned by two quadrc surface fttng method of vector rotaton speed s slow, but the accuracy s hgh. Based on the calculaton of the lnear geometrc axs of rotaton by the rotatng axs and normal all vertces of the ntersecton, so the rotaton axs and normal n PLUCKER coordnates of 6 tuple, may be the axs of rotaton s X = (X, x ), L = (l, l ), I = 1,... k, k s the total number of vertces. Object functon: F(x) = Constrant condton : Among: k x l x l = 1 ( + + ) =. (1) x = X T DX = 1 T X MX T M=, [ l l l l l l ] A A A = ( ) ( ) ( ) ( ) ( ) ( ), D = dag (1, 1, 1, 0, 0, 0). The objectve functon based on the constrants of the mnmum soluton s PLUCKER axs coordnate X = (x, x ). Accordng to the pont lne coordnates P = ( X X ) / X, drecton vector x, spatal rotaton axs lnear equaton expresson. Fgure s the result of usng the lnear geometry method to obtan the rotaton axs: Fgure 1. Vase pont cloud. Fgure. The axs of rotaton n lne geometry. 3. Contour Calculaton The contour lne s also an mportant cultural relcs geometrc features of the rotatng body, the B-Splne curve s nvarant n geometry, convex hull, convexty and reduce varaton, local support, and many other excellent propertes, often usng B-Splne curve to ft the contour lne [6]. In recent years scholars related theory of splne were studed: the Parkof ordered B splne approxmaton method, the method of control ponts gven n advance of the curve, and the ntal feature pont selecton, usng the least squares technque to approxmate the orgnal curve. Sant-Marc proposed the method of usng four B splne to represent and judge the shape symmetry [7]. L W n the process of nterpolaton of B splne curve fttng, s proposed accordng to the characterstcs of the orgnal data of the arc length and curvature, the method of adaptve selecton of nodes, but ths method not to estmate the approxmaton error and s senstve to nose [8]. On the curve of the dscrete samplng ponts usng B splne curve fttng, the commonly used methods of nterpolaton and approxmaton of two. Interpolaton method s to select the samplng control ponts on the orgnal curve, wth a certan degree of B splne to connect each control pont, the formaton of a number of pecewse contnuous B splne curve. The advantages of splne nterpolaton wth mnmum curvature, the nterpolaton curve fttng, can ncrease the shape of the edge pont to adjust the contour data, fnally get the smplfed shape. The approxmaton method needs less parameters, and the change of local functon does not affect the representaton of the whole shape. It s not senstve to the nose. The B-Splne curve s used to represent the contour lne of n foregn

3 Amercan Journal of Mechancal and Materals Engneerng 017; 1(4): countres, but the samplng pont s only obtaned from the ntersecton of a plane and a fragment of the axs of rotaton, and the estmated contour of the s not accurate [9]. Based on PDM (Pont Dstance Mnmzaton) the B-Splne curve fttng method, 3D pont cloud data of the method usng only one plane and debrs ntersecton pont obtaned are sparse, the samplng ponts and use the dstance as error crteron fttng method s relatvely poor, and due to the presence of nose, samplng pont may all the features can not be completely retaned the contour lnes, and the fttng part of the lack of nformaton [10]. Based on SDM (Square Dstance Mnmzaton) of the B-Splne curve fttng method, the method of control polygon frstly wth four bnary tree to calculate the ntal curve, then accordng to the curve between pont cloud data and two-dmensonal square dstance control polygon adjustment curve contnuously, fttng curves by two-dmensonal pont cloud data of the [11]. Ths method s a good method to ft the data of two-dmensonal pont cloud, whch has fast speed and stable convergence [1]. Based on the SDM method, the outlne of the outlne of the general steps are: frst of all the cultural relcs of the three-dmensonal pont projecton to a plane, x = ( P - P ) I, y = ( P -P) I. 0 0 Among: P 0 s based on a pont calculaton of rotaton axs lne geometry n the calculaton of the shaft; I s the unt drecton vector of the rotaton axs; I s the moment vector of the rotaton axs; P 3D ponts for fragmentaton; x, y for the three-dmensonal pont cloud data to the plane after the projecton of the two-dmensonal coordnates. The x calculated by the formula s actually the dstance from each vertex P to the axs of rotaton, and y s the projecton of the P to the axs of rotaton. The projecton results n the same crcle (vertcal axs of rotaton and rotaton of plane crossed by the parts of the crcle s called the crcle) correspondng to the same pont n the plane coordnate system, so to get a set of D pont clouds [13]. Then, the SDM method s used to ft the pont cloud wth the B-Splne curve to get the contour lne. Fgure 3 s the fttng of the rotated contour lne by the SDM method: 4. The Radus of Gyraton and the Calculaton of the Angle of Ft 4.1. Calculaton of Radus of Gyraton The axs of rotaton and rotaton of the contour lne s calculated to calculate the rotaton radus of rotaton, frst to calculate the rotaton of the contour nterval samplng (slcng), a rotatng axs perpendcular to the axs of rotaton of a seres of equdstant lne, the lne and the ntersecton of the rotary contour ntersecton of straght lne wth the axs of rotaton the dstance (that s the center of a crcle) s that each layer correspondng to the radus. 4.. Matchng Angle Calculaton Judgng Pont Cloud Shape Fgure 4. Regular wdth pont cloud. Fgure 5. Irregular wdth pont cloud. Fgure. 3 Rotary contour. As shown n Fgure 4 and 5, you need to take a number of

4 86 Hongguang Zhu and Xu Zhang: Feature Estmaton and Regstraton of Pont Clouds n Reverse Engneerng ponts along the vertcal drecton of the cloud layer (the yellow horzontal lne represents a layer, that s, F1F and I1I1 layer), and then on each layer of the pont cloud projecton data ponts. In addton, need to fnd the mddle poston of each lne segment cloud pont E1E (the bus), to calculate each layer on the bus to the farthest pont on both sdes of the central angle (matchng angle) [14]. In Fgure, due to the symmetry of the pont cloud, the center of a data pont can be selected as the segmentaton pont when selectng the center lne. As for the pont cloud as shown n Fgure 3, s to choose the lne G1G or H1H, you need to frst determne the shape of the pont cloud. For the pont cloud n Fgure 3, f you choose the subsecton lne H1H, t does not pass through the pont cloud of the lower part of the cloud, n the calculaton of the two sdes of the angle of cooperaton, there wll be errors, thus affectng the coordnaton effect. The pecewse lne G1G s a better choce, t can ensure that each slce layer through the pont cloud nsde, t can be calculated from the pont of vew of the ponts on both sdes of the coordnaton, so as to ensure the feasblty of subsequent calculatons. In the judgment of the pont cloud shape process, manly through the judgment ponts to judge the whole part of the layer of pont cloud shape trend, so as to select ts horzontal center poston as segment ponts n proper wdth, calculaton prncple such as formula (): n η = ( = 1,, 3) () N In the formula, N s the total number of teratons plus 1, n s for the whole of the 10 layer (from the begnnng of the twenteth layer, each layer of the ncrease n the number of ponts) to meet the number of cases ( = 1,, 3) under the number of layers, η s correspondng to the proporton of n accounted for N. The algorthm steps are as follows: (1) determne the number of teratons need N: accordng to a pont cloud of layers, and set the 10 layer s calculated from the teraton step, the number of teratons of N. () set the ntal teraton varables: make the tenth level ponts s n 0, and n 1, n and n 3 are zero. (3) to determne the search rules and search: from the begnnng of twenteth, every 10 ncrease of the number of layers and calculate the layer data ponts, when the layer ponts number was two tmes larger than n 0, n 3 automatcally add 1; when the layer ponts number s less than half of n 0, n 1 automatcally add 1; otherwse, n automatcally add 1. (4) accordng to the formula (), Calculatng the proporton of n 1, n and n 3 n N, so as to determne the shape of the pont cloud, select the approprate locaton of the narrow segment as a whole pont cloud segmentaton lne Calculaton of Pont Cloud Coordnaton Angle Fgure 6 s a layer of pont cloud projecton, n the calculaton of the matchng angle, t s necessary to fnd the pont cloud n the plane of the pecewse pont C, and then calculated by the two part segment ponts correspondng to the pont cloud segmentaton angle 1 and. Among them, A ponts to the left of the pecewse pont central angle correspondng to the maxmum when the data ponts, and B ponts to the rght end of the data ponts wth pecewse pont maxmum angle. Fgure 6. Coordnaton angle of a certan pont cloud. 5. Usng the Radus of Gyraton and the Angle of Cooperaton to Coordnate the Pont Cloud For the two ponts and dvded nto n1 and n layers of cloud ponts, each layer of the radus of gyraton and ft angle data are as follows: (1) the value of the radus of the two groups can be obtaned from the two pont clouds R 1 ( = 1,, 3 n1) and R j (j = 1,, 3... n). Among them, R 1 and R j are the radus for the pont cloud 1 and pont cloud n the and j layer. () n addton, the correspondng values of the four groups can be obtaned angle 1 and angle ( = 1,, 3 n1 ), angle 3j and angle 4j (j = 1,, 3... n). Angle 1 and angle are the angle of ft on the layer on the frst pont cloud; Smlarly, angle 3j and angle 4j are the angle of ft on the other layer of the pont cloud. Usng (1) and () n several groups of data, whch can be calculated by the radus of features, so as to search two pont cloud layer dfference ξ, then use the matchng angle features ultmately determne whether they are n the correspondng layer can be matched. 6. Summary In ths paper, through calculatng the rotatng body rotaton axs, pont cloud contour lne, turnng radus and angle wth the characterstcs of nformaton, and complete the regstraton of cultural relc of pont cloud, rotaton axs and contour precson wll be obtaned drectly affects the rotaton radus and angle wth precson n the use of half sze and wth the pont of the pont cloud regstraton n the process, through the method of moble two pont cloud to determne the relatve

5 Amercan Journal of Mechancal and Materals Engneerng 017; 1(4): poston of the matchng effect of each match, untl the search results wth the need, to get the matchng layer, the angle value s checked, the realzaton of pont cloud regstraton fragments. References [1] S. Ben Yacoub and Ch. Menard, Robust axs determnaton for rotatonal symmetrc objects out of range data. Burger and Burge [Burge97], pages [] R. Sablatng and M. Kampel, Model-Based Regstraton of Front-and Backvews of rotatonal symmetrc objects, Computer Vson and Image Understandng, 00. [3] R. Halr Estmaton of the axs rotatonal of fragements of archaeologcal pottery, Burger and Burge [Burge97], pages [4] Zhang Zongxa. Research and mplementaton of classfcaton and retreval of cultural relc. Master Thess of Shandong Unversty, 005. [5] Pottmann, H., Peternell, M., Ravan, B., An ntroducton to lne geometry wth applcatons, Computer Aded Desgn 31, 1999, [6] Park H, Lee J. H. B-splne curve fttng based on adaptve curve refnement usng domnant ponts [J]. Computer Aded Desgn, 007, 39(6): [7] Sant-Marc P., Rom H., Medon G., B-splne contour representment and symmetry detecton [J]. IEEE Transactons on Pattern Analyss and Machne Intelgence, 1993, 15(11): [8] L W., Xu S., Zhao G., et al. Adaptve knot placement n B-splne curve approxmaton [J]. Computer Aded Desgn, 005, 37(8): [9] R. Sablatng and M. Kampel, Model-Based Regstraton of Front-and Backvews of rotatonal symmetrc objects, Computer Vson and Image Understandng (S ), 00, 87(1-3): [10] Schndler K, Kampel M, Sablatng R. Fttng of a Closed Planar Curve Representng a Profle of an Archaeologcal Fragement [C]. Proceedngs of Proceedngs of the 001 conference on Vrtual realty, archeology, and cultural hertage. Glyfada: ACM Press, 001: [11] Wenpng wang, Helmut Pottmann, Yang Lu. Fttng B-splne Curves to Pont Clouds by Square Dstance Mnmzaton [M]. ACM Transactons on Graphcs (S ), 006, 5: [1] Ouyang Leguang. Cultural debrs classfcaton mosac and parallel algorthm. Master's degree thess of Shandong Unversty [13] Zongfang Zhang. The estmaton of the overall characterstcs of the rotatng object artfacts from pont clouds. [J] Journal of Bejng Electroncs Scence and Technology Insttute, 008. [14] Qan Lu. Research and applcaton of 3D contour lne matchng peces of cultural relcs mosac algorthm based on master's degree thess of Northwestern Unversty, 013. Bography Zhu Hongguang was born n October 1991 n Henan Provnce. He has got a bachelor s degree of Mechancal Manufacturng and Automaton n Xnxang Unversty n 015 and now he s a postgraduate n Shangha Unversty of Engneerng Scence. Zhang Xu manly engaged n reverse engneerng, CAD & CG, precson detecton and other aspects of the study for many years, In September 008, she receved a doctorate degree n mechancal manufacturng and automaton from Zhejang Unversty. Partcpated n the study of the "410 project" of the major mltary project, partcpated n the GE nternatonal cooperaton project, and partcpated n the research and development of large scale reverse software n chna; She publshed more than and 10 papers n the hgh level academc journals and nternatonal conferences, ncludng 7 SCI/EI papers.