Study on plane feature extraction in registration of laser scanning data sets for reverse engineering

Transcription

1 Bulletin of the JSME Journal of Advanced Mechanical Design, Systems, and Manufacturing Vol.9, No.5, 2015 Study on plane feature extraction in registration of laser scanning data sets for reverse engineering Muslimin*, **, Jiang ZHU*, Hayato YOSHIOKA*, Tomohisa TANAKA*** and Yoshio SAITO * * Department of Mechanical and Control Engineering, Tokyo Institute of Technology I1-35, , Ookayama, Meguro-ku, Tokyo, , Japan ** Department of Mechanical Engineering, Jakarta State Polytechnic Jl. Prof. G.A Siwabessy, Kampus Universitas Indonesia, Depok, 14425, Indonesia muslimin.a.aa@m.titech.ac.jp ***Department of Micro-nano System Engineering, Nagoya University Furo-cho, Chikusa-ku, Nagoya, , Japan Received 3 July 2015 Abstract This paper proposes a study on plane feature extraction in registration of multiple laser scanning data sets for reverse engineering (RE). The objective of this proposed method is to solve 3D registration problem with different form and distribution data sets, to acquire an accurate 3D CAD model so that the purpose of reverse parts accurately can be obtained, and to speed up the computation time. The registration process is carried out in two steps: rough registration and continued by fine registration which is combined with plane features extraction. Firstly, two or more point cloud data sets yielded from different scanning position are registered roughly by using transformation process (rotation and translation) to obtain the best initial position. Secondly, grid reconstruction of pairwise data sets and grid data pattern identification are applied. Thirdly, plane features of pairwise grids are extracted and validated by using some certain criteria. The aim of the validation is to convince only validated plane data involved in the fine registration process. Finally, the fine registration of pairwise data sets is conducted by using the selected validated plane data. In this fine registration, iterative closest point (ICP) process is applied based on both point-to-point and plane-to-plane with brute-force and kd-tree scenarios. Root mean square (RMS) of pairwise point distance and computation time are obtained over the process for all scenarios. To check the behaviour of validation process in fine registration, computation in each validation steps is also performed. The experiment result shows the extraction and validation planes improved the precision in both point-to-point and plane-to-plane registration in entire scenarios while kd-tree yields faster convergence. The benefits of the proposed method compared with existing methods are simpler and user-friendly, more applicable for RE of many manufacturing products, more accurate 3D CAD model result and shorter computation time. Key words: Reverse engineering, Laser scanning, Registration, Plane feature extraction, ICP, 3D CAD model 1. Introduction In conventional reverse engineering (RE), besides CCD cameras and coordinate measuring machines (CMMs), laser scanners are devices commonly used in both industrial applications and research purposes to acquire dense data in short time (Sokovic and Kopac, 2006). Current laser scanners have been meticulously scaled in micrometre and become viable to build up an accurate 3D CAD model. In laser scanning process, multi-view scanning is often applied in order to get whole surface data of reversed object such as the bottom side and the other area which is difficult to obtain in one step measurement (Lai, et al., 1999). Data registration is then applied to unify those different data sets in order to reconstruct a 3D CAD model (Tao and Jiyong, 2007). The goal of data registration process is to obtain the best transformation parameters such as rotation and translation that make the best coincidence and fitting between the pairwise data sets. The registration process is very important in RE because it directly influences a final reconstructed 3D CAD model. Furthermore, the final 3D CAD model has important roles to the further engineering process such as computer-aided engineering (CAE), computer-aided manufacturing (CAM) and other applications in order to realize reversed parts accurately. The more accurate 3D CAD model reconstructed, the more accurate reversed part can be realized. Paper No

2 In the registration process, iterative closed point (ICP) (Besl and McKay, 1992) and its variants (Rusinkiewicz and Levoy, 2001, Yan and Bowyer, 2007, and so on) are commonly used in practical purposes. The ICP and its variants work well only if the preliminary relative position of pairwise data sets is in a good manner. Therefore, the ICP algorithms always need the good initial condition to be a basis of the iterative process in order to refine all corresponding point of pairwise data sets. The best parameters of translation and rotation that minimize the error is obtained in this iterative process (Zexiao, et al., 2005). Although ICP results in high accuracy and effectiveness in many terms, nevertheless it suffers at least in three key points: it needs a good initial guess so that the preliminary transformation (rough registration) is needed, fails due to a local minimum because of improper data or noisy, and slow computation. In the case of RE aim to generate an accurately reversed 3D CAD model, registration process using ICP becomes complicated and uneconomical when pairwise data sets are different form and distribution. This difficulty is mainly in determining the pairwise data sets involved in ICP registration. Nevertheless, in the measurement process, there will be part of an object measured twice as the overlapping area. The pairwise data of the overlapping area are utilized as a basis of ICP registration. Feature forms such as plane, point, edge, curvature and so on can be extracted and utilized to conform pairwise data sets suitability (Wang, et al., 2009). The grid method (Li, et al., 2013, Angelo, 2011) can be applied in order to obtain only suitable corresponding features extracted from overlapping data involved in ICP process. The extracted features in each grid must be validated in order to convince only the validated feature data sets are selected. The validated features are then utilized in ICP to enhance the accuracy of reversed 3D-CAD model and reduce computation time. In this paper, we propose a study on plane feature extraction in registration method of 3D point cloud data sets for RE process. The registration process is applied into two steps: rough and fine registration. Firstly, two point cloud data sets obtained from different scanning position are aligned or registered roughly using matrix transformation. Secondly, grid reconstruction and grid data pattern classification are applied in both registered point cloud data sets. Thirdly, plane feature and normal are then extracted from point sets of the plane data pattern in each grid. Extracted plane features are then validated using some certain criteria to assure that only validated plane data are selected for ICP registration process. Finally, the ICP processes using those pairwise validated plane data are applied with different fitting scenarios. The fitting scenarios of ICP in this proposed method are point-to-point ICP based and projected plane-to-plane ICP based with brute- Force and kd-tree scenarios. Fitting error and convergence time of registration are obtained over computing for the overall data sets. The experiment using real models was applied to evaluate the performance of the proposed method in order to examine which scenario contributes to rapid convergence and yields an accurate 3D CAD model with the lowest error (root mean square, RMS). The lowest RMS error has the contribution in producing a smooth surface and solid of 3D CAD model, mainly in 3D mesh model in which each commonly three nearest points of point cloud data is triangulated and then meshed. This proposed model is prospectively used for RE of moulding product, casting product, forging product, machining product or common manufacturing product in which plane features are available. This paper is organized in four sections. In the first section, we discuss the basic knowledge of registration and previous research correlated with the proposed method. In the second section, we briefly describe the proposed method and the implementation in the reverse engineering field to generate a 3D CAD model. In the third section, we apply the method to the real case using two existing models. In this section, experiment result and discussion, some performances of proposed method behaviour is noted and discussed briefly. The last section concludes the whole research result. 2. The Utilization of Feature Extraction in Registration Process 2.1 Rough Registration Rough registration is a preliminary process of alignment between two or more 3D point cloud data sets (Wang, et al., 2009). The purpose of rough registration is to obtain the best position and orientation of transformed data sets relative to reference data set. In common, the rough registration is applied in three steps: Selecting the corresponding features of pairwise data sets (reference and transformed); Generating vectors from those corresponding features to be a basis of transformation; and Applying the transformation matrix to transform transformed data into reference data in a coordinate system (local coordinate system). In the selection of basis of transformation, some researchers proposed the pairwise of 3-points to 3-points, 3-spheres to 3-spheres and 3-planes to 3-planes (Lai, et al., 1999). Pairwise corresponding vectors can be generated from those pairwise of corresponding 3-points to 3-points (Tao and Jiyong, 2007), 3-planes to 3-planes, 3-spheres to 3-spheres, and directly generated by using the principal component analysis (PCA) (Li et.al, 2013). In this proposed method, Let P be reference data set and Q be transformed data set. Q is transformed into P by using transformation matrix, M (consist of translation matrix, t and rotation matrix, R) based on the pairwise of transformation vectors. Three points or set data points of certain pairwise features of P and Q can be used to generate pairwise vectors 2

3 to be a basis of transformation (Jiyong and Tao, 2007) (Fig. 1). If the final position of transformation Q is Q in which the position and orientation of Q are closest enough to P as the following equation: Q P (1) Transformation Q into the position and orientation of P (Q ) is using the following steps: 1.) Generate three set vectors (v 1, v 2, v 3) from corresponding features P and Q to be a basis of transformation (Fig. 1). Vector v 1 and v 2 can be directly generated from three points or group points in selected corresponding areas while v 3 can be obtained by cross product multiplication of v 1 and v 2 (v 3 = cross (v 1, v 2)). 2.) Transform P into origin (0,0,0) of global coordinate systems (G). One of vectors P (arbitrary, example v 3P as shown in Fig. 1) is then coincided with one arbitrary of axis G (example Z-axis) by rotating about the X-axis into the XZ plane, rotating about the Y-axis onto the Z-axis, and rotating as needed about the Z-axis respectively. G The transformation matrix of P to origin of G and coincide vector v 3P into Z-axis, P T is formulated as follow: G PT = R ZP ( ). R YP ( ). R XP ( ). t P (t x, t y, t z ) (2) where R ZP ( ), R YP ( ), R XP ( ) are rotation of,, and radian of vector v 3P about the X-axis, Y-axis and Z-axis respectively, and t P (t x, t y, t z ) is translation of P to origin (t P = O P G) (Fig. 1). 3.) Make coincidence Q into P in the global coordinate system using the following steps: Translate Q into origin by using Eq. (2) based on the translation vectors. Transform Q into P by coincide vectors (v 1Q, v 2Q, v 3Q) of Q to vectors (v 1P, v 2P, v 3P) of P. Transformation Q to P has the same step as the step 2.). Transformation matrix Q into P, P Q M (t, R) is formulated as: Q P M(t, R) = t Q P (t x, t y, t z ). R Q P (R ZQ P (δ), R YQ P (θ), R XQ P (φ)) (3) where t Q P (t x, t y, t z ) is a translation matrix of transformation Q into P, R Q P (R ZQ P (δ), R YQ P (θ), R XQ P (φ)) is set rotation matrix of transformation Q into position and orientation of P, and R ZQ P (δ), R YQ P (θ), and R XQ P (φ) are rotation of δ, θ, and φ radian about the X-axis, Y-axis and Z-axis respectively. 4.) Return the data sets into initial position by using the inverse transformation matrix as the following equation: G P T = t P (t x, t y, t z ) 1. R XP ( ) 1. R YP ( ) 1. R ZP ( ) 1 (4) The entire transformation process for set data P and set data Q, see Eq. (1), are as the following equation: P = P G T. G P P T. P and Q = G T. P QM (t, R). G P T. Q (5) (A) Note: (A) = Top position measurement result data P (as reference data) (B) = Front position measurement result data Q (as transformed data) (B) v 3 P v 3P,v 3Q v 3 P Rough registration v 1 P v 1 P O p v 2 P v 1P,v 1Q v 2P,v 2Q Fig. 1 Model 1 with the direction of scanning position, A and B; Data Q and data P before rough registration and their transformation vectors; (c) Data Q and data P after rough registration (Q and P). The RED color is data P and the BLUE color is data Q (and Q ). Unit of axes is [mm] (c) 23

4 In this case, we use two real models in order to demonstrate the effectiveness of the proposed method in reverse and reconstructing a 3D CAD model accurately with economic time. Those two models are Model 1 (a 3D-printing product) and Model 2 (Shinkansen toy as an injection moulding product) as shown in Fig. 1 and Fig. 11 respectively. Figure 1 shows Model 1 and its direction of laser scanning positions: top and front view position (A and B respectively). The top view position (A) yields data P as references data while the front position (B) yields data Q as transformed data. Figure 1 shows the position of data Q (blue color) relative to data P (red color) in one coordinate system. By applying for rough registration, data Q is transformed using transformation matrix, P Q M (t, R) into position and orientation of reference data P ( Q ). Figure 1 (c) shows the result of rough registration (P and Q ). The result of rough registration will be further processed using fine registration combined with plane extraction in grids. 2.2 Fine Registration The purpose of fine registration is to find fine optimum transformation parameters by using ICP (fine translation, t f and fine rotation, R f) which yield the best alignment and fitting between data Q (rough registration result) and data P. The best fitting is obtained by iteratively minimizing an error metric of distance between each corresponding Q and P, e(t f,r f) (Zexiao, et al., 2005, Wang et al., 2009). Fine registration in this proposed method consists of the following steps: 1.) Construct grids of data set P and Q and specify the index of each grid. A grid index is written as Grid_ID [i][j][k] in which index [i],[j] and [k] represents the position a grid in X, Y, and Z-position respectively (Fig. 2). 2.) Classify data pattern in each grid (Fig. 3). a. Identify and classify the data distribution (pattern) in every grid (Fig. 3). The only plane pattern will be utilized. b. Cluster data for a grid with more than one plane pattern data by using clustering method (Fig. 3 and 3(c)). 3.) Extract plane feature from the data pattern in each grid by using LSP (least square plane) fitting method. By this method, plane and normal of the data pattern in each grid are calculated (Fig. 4 and Fig. 5). 4.) Find the intersection of the pairwise grid between Q and P (Fig. 7(d)). 5.) Validate all pairwise extracted plane features candidates using the following criteria (Fig. 7(e) and 7(f)): a. Validation 0: check whether the points in a grid equal or more than 26 points (Li et.al, 2013). b. Validation 1: check the data distribution in each plane by checking the distance of points to its extracted plane. c. Validation 2: check whether there any neighbour s plane surrounding an extracted plane of a grid or not. d. Validation 3: check the angle of the pairwise corresponding plane in the intersection grid. 6.) Fine registration process based on ICP using pairwise extracted plane data. In this case, matching process of ICP use the following scenarios (Fig. 9 and Fig. 10): a. ICP based: point-to-point and plane-to-plane registration. b. Scenario of fitting process: brute-force and kd-tree Grid Reconstruction and Grid Index Identification Grid method, in this case, is used to divide huge point cloud data into small localized data set in order to simplify the handling of the point cloud data. Grid size of data P is firstly calculated as a reference, then grid size of data Q is set equal to the grid size of P. Grid with and without data of P and Q is classified and the data pattern of each grid is identified. Cluster method is used to split data for a grid consisted two or three data patterns. Only grid with plane data pattern will be selected and validated, and the only validated plane will be used in the further computation. Every grid is identified by a grid index, Grid_ID [i][j][k]. Grid method in this research is modified from some references (Zhongmin et.al, 2012, Li et.al, 2013, Diangelo and Giaccari, 2011). Grid reconstruction parameters are calculated by using the following steps. 1.) Determine x max, x min, y max, y min, z max and z min of X, Y, and Z-direction data set respectively. 2.) Calculate grid size (d g ). Grid size of data set depends on the density of point cloud data and expected number of point in each grid. In this research, grid size (d g ) is approximated using the following equation (Li et.al, 2013, Diangelo and Giaccari, 2011): d g = α ( (x max x min )+(y max y min )+(z max z min ) ) (6) 3 3 ( n p nm )( 1 r0 ) where: d g = Grid size. Grid size of Q is set equal to the grid size of P. 24

5 = A user defined scalar factor (Diangelo and Giaccari, 2011). The value of for reference data P is 1 ( (reference) =1) while the value of for transformed data Q will be adjusted based on the value of d g grid P. n p = A total number of point in a data set. n m = Expected number of data in a grid. We expected around 26 points in a grid. r 0 = The ratio of number grid that represents the ratio of points to total grid number. In this case, we choose r 0 = ) Calculate number of grid along X-direction, Y-direction, and Z-direction using the following equation: { N x = x max x min d g N y = y max y min d g N z = z max z min d g where N x, N x, N z are the number of the grid in X, Y, and Z-direction respectively. 4.) Assign every point p i(x i, y i, z i) in a set point belong to Grid_ID [i][j][k], where [i], [j] and [k] are calculated using the following equation: [i] = x i x min d g [j] = y i y min d g [k] = z i z min { d g 5.) Identify the grid index, Grid_ID each grid. The position of a grid in a data set, Grid_ID [i][ j][k], is calculated using the following equation: Grid_ID [i][j][k] = (x min + [i]d g, y min + [j]d g, z min + [k]d g ) (9) where i = 1, 2, 3,, N x ; j = 1, 2, 3,.., N y; and k = 1, 2, 3,.., N z. We calculate grid reconstruction parameters both data P and Q by using Eq. (6) to Eq. (9). Figure 2 shows the grid reconstruction for data Q of Model 1 as an example of computation. In this Fig. 2, we can find that only grid contained data points appeared. Based on the computation, both data set P (reference) and data Q (transformed) have 25 grids in X- direction, 15 grids in Y- direction, 12 grids in Z-direction, and the same grid size ( mm). (7) (8) Grid_ID [1][1][1] Fig. 2 Grid reconstruction for data Q of Model 1. Unit of axes is in [mm] Data Pattern Classification and Plane Extraction In this step, the data pattern of each grid is identified and classified. Based on the data pattern classification, we obtain six possibilities of data pattern forms in a grid as follows (Fig. 3): 1) A grid consists of data with one plane pattern form, example: Grid_ID [1][7][3] (Fig. 3 ). 2) A grid consists of two plane pattern forms, example: Grid_ID [1][1][4] (Fig. 3 ). 3) A grid consists of three plane pattern forms, example: Grid_ID [1][10][5] (Fig. 3 (c)). 4) A grid consists of free form pattern, example: Grid_ID [1][7][2] (Fig. 3 (d)). 5) A grid consists of irregular data, it can be interpreted as noise, uncompleted data, or data separated by grid process, example: Grid_ID [1][6][7] (Fig. 3 (e)). 6) A grid without points or less than 26 points, example: Grid_ID [1][1][1] (Fig. 3 (f)). 25

6 (c) Fig. 3 (d) (e) (f) Six pattern possibilities in a grid: Grid with 1 plane; Grid with 2 planes; (c) Grid with 3 planes; (d) Grid with free form; (e) Grid with irregular form and (f) and Grid with less than 26 points. Unit of axes is [mm] We only consider grids consists of at least 26 points (in accordance with Validation 0). A grid without a point, a grid with only one point or a grid with less than 26 points, a grid with free form surfaces and curves pattern, and a grid with irregular data will not be considered in the further computation. In a grid with one plane pattern data, the plane will be directly extracted from this grid. Grid consists of two or three plane pattern forms, data is firstly clustered using clustering method and then extracted based on the clustered data group (Zhou, et al., 2009). In case clustering process, if a grid has two or three patterns it will be considered as two or three separated data although has the same grid ID. The plane of a grid with plane pattern form data is then extracted in the next step. In the plane extraction process using the least square plane (LSP) fitting method, first we computed mean (μ) and centred data (C) of n-points in a grid. The single value decomposition (SVD) is used to calculate fitted plane and normal in each grid. The least square plane always passes through the mean of the group of points and normal always orthogonal to the plane. The brief explanation of the LSP fitting using SVD method is as the follows: a) Let p i be points of set data in a grid to which the LSP needs to be fitted. n b) Mean, = mean( i=1 p i ), where n is number of point p i in a grid (Fig. 4). c) Centred data, C = {(p i - ) i=1: n}. d) Singular Value Decomposition (SVD) is performed on C: [U, S, V] = svd(c) Mean point ( ) of data sets (shown as the red dot) is as shown in Fig. 4. The vector V corresponding to the minimum singular value in S gives the desired normal vector. The normal to a plane of the point sets (shown by the green arrow) in a grid is shown in Fig. 4. The plane, normal plane, and mean of points in each grid, and angle of pairwise data sets between data P and data Q (ϕ) is shown in Fig. 4(c). (n ) (ϕ) ( ) ( ) (n P) (n Q) (c) Fig. 4 Point set with its mean point in a grid; LSP fitted to n-neighbours and its normal (n ); and (c) Pairwise planes and their normal (n P and n Q) and the angle between two normal (ϕ). Unit of axes is [mm] 26

7 Figure 5 shows a plane and normal extracted from a grid with one plane data pattern (Fig.3). Figure 5 and Fig. 5(c) shows planes and normal in a grid extracted from a grid with two plane pattern (Fig.3) and three plane patterns (Fig.3(c)) respectively. (c) Fig. 5 Extraction a plane and normal in a grid; Extraction two planes and two normal in a grid; and (c) Extraction three planes and three normal in a grid. Unit of axes is [mm] Intersection and Validation Plane Features The intersection of plane features refers to the corresponding grid between P and Q with equal index (Grid_ID). In this step, we identify all intersection grid of P and Q. Furthermore, we extract and validate plane features from the intersections grid in order to select the appropriate data involved in fine registration. The following steps describe the intersection and validation process of pairwise extracted plane features: 1) Find all intersection grid between data sets P and Q. 2) Validate all extracted planes on the intersection grids P and Q. We use three criteria of plane validation as following: a. Validation 0: check the number of data in each grid. A grid is validated or accepted if it has at least 26 points. b. Validation 1: check the distribution all points relative to its extracted plane. If all points meet the acceptance criteria, extracted plane in a grid is accepted. On the contrary, extracted plane in a grid is ignored. Criteria of acceptance Validation 1 is as following: - All points must be within the lower limit (μ σ) and the upper limit (μ + σ) as the following equation: μ σ d pi μ + σ (10) where d pi is a distance of point p i to its extracted (fitted) plane in a grid, μ is mean of all distance of data points, and σ is a standard deviation of all distance of data points. - All distance of points to its extracted plane (d pi ) must be lower than 0.2 mm ( d pi 0.2) to select the only plane with the high fit. If there is distance point higher than 0.2 mm, the plane is ignored (Fig. 4(c)). c. Validation 2: check the neighbours. If there is, at least, one neighbour s plane, the plane is accepted and merged, in contrary it is ignored. In computation, Validation 1 and Validation 2 are combined to simplify the calculation. d. Validation 3: check the pairwise plane angle (ϕ). We use angle threshold 15 degrees. The angle of the pairwise plane must be in the range -15 o ϕ 15 o and 165 o ϕ 195 o (Fig. 4(c)). Theoretically, we can choose any value ϕ in the range until -45 o ϕ 45 o and 135 o ϕ 225 o depends on the effectiveness of validation process. Only validated plane features that met all criteria will be utilized in the fine registration process. The result of the validation process is provided in Table 2 and Fig. 7 for Model 1 and Table 4 and Fig. 11 for Model Fine Registration Process In this proposed method, the fine registration process is applied using ICP based on point-to-point based and planeto-plane based registration using brute-force and kd-tree scenarios. In ICP point-to-point based, every point in the data sets Q in every grid registers with points in data P (reference data). In the ICP plane-to-plane based registration, all points in a grid are firstly projected into the plane then projected points are used in ICP process in the same way as in ICP based point-to-point registration process. In the brute-force scenario, points from transformed data (data set Q ) is forced to be fit (register) with points in reference data (data P), while in kd-tree pairwise point is registered based on kd-tree algorithm (Moore, 1991). Fine fitting data sets using ICP based on point-to-point registration and plane-to-plane registration using brute-force and kd-tree scenarios is according to the following steps: 27

8 1) Involve points in selected pairwise extracted planes for the point-to-point fitting scenario and pairwise projected points onto selected extracted planes for the plane-to-plane scenario. 2) Registration pairwise points in each plane candidate in each grid with the same grid index (data sets Q and P) is applied by minimizing the Euclidian distance of two pairwise points. Distance between arbitrary transformed point Q i (Q ix, Q iy, Q iz ) into the point in reference data P j (P jx, P jy, P jz ) is formulated as the following equation: d(q i, P j ) = (P jx Q ix ) 2 + (P jy Q iy ) 2 + (P jz Q iz ) 2 (11) and minimizing the Euclidian distance between those two points is defined as: d(q i, P j ) = min d(q i, P j ) i N g (12) where N g is the amount points of all intersection grid between P and Q. 3) Registration is searching fine transformation parameter until the limit minimum distance reached with minimum error metric of translation and rotation, e(t f,r f) using following equation: N s e(t f,r f) = i=1 P j M(t, R). Q i (13) 4) The root mean square (RMS) of alignment error is calculated by the following formula: N RMS = P j Q i 2 s i=1 (14) where P j Q i is distance point-to-point (or distance projected plane-to-plane) To evaluate the performance of proposed method, we give an example of fine registration between the pairwise grid of data set P j and data set Q i. Figure 6 shows the example of fine registration of validated plane data points in the pairwise grid with the same grid index Grid_ID [2][3][3] in which each point of data set Q i are fitted with data set P j based on the point-to-point ICP based registration. Data set of a grid P Data set of a grid Q Data set of a grid P Data set of a grid Q Fig. 6 Fine registration in pairwise grids: Before fine registration, and After fine registration. Unit of axes is [mm] 3. Experiment Result and Discussion We use two models of existing products to evaluate the effectiveness of the proposed method. Model 1 (a 3D printer model) and Model 2 (an injection moulding product) are shown in Fig. 1 in Fig. 11 respectively. Some cases of the experiment are designed in order to study the behaviour of proposed method into the cases as shown in Table 1. Case 0 is ICP fine registration based on point-to-point with brute-force and kd-tree scenario using all data without plane features extraction. Case 1 is ICP fine registration based on both point-to-point and plane-to-plane registration with brute-force and kd-tree scenario using pairwise plane feature data sets of intersection grid without validation (Validation 0). Case 2 is the same treatment as Case 1 for pairwise plane feature data sets of intersection grid after Validation 1 and 2. Case 3 is the same treatment as Case 1 for pairwise plane feature data sets of intersection grid after Validation 1, 2 and 3. In the Case 0, ICP fine registration is directly applied using all data of P and Q, while in Case 1 to Case 3, the fine registration parameters (translation, t f and rotation, R f) are firstly calculated by applying ICP using only pairwise validated plane data sets, then those parameters t f and R f are used to transform all data Q into P. 28

9 Table 1. Case of experiment scenarios for fine registration #Case 0 #Case 1 #Case 2 #Case 3 ICP point-to-point based with brute-force and kd-tree scenario using pairwise data sets before intersection process (using all data P and Q ), ICP point-to-point and plane-to-plane based with brute-force and kd-tree scenario using intersection of pairwise data sets before validation process (Validation 0) ICP point-to-point and plane-to-plane based with brute-force and kd-tree scenario using intersection of pairwise data sets after Validation 1 and 2 ICP point-to-point and plane-to-plane based with brute-force and kd-tree scenario using Intersection of pairwise data sets after Validation 1,2 and Model 1: A 3D-Printing Product Model 1 is a 3D-printing product (Fig. 1). Laser scanning data sets and rough registration result are shown in Fig. 1 and Fig. 1(c) respectively. The computation result of intersection and validation of pairwise data sets P (red color) with its grids (green color) and data sets Q (red color) with its grids (magenta color) is shown in Table 2 and Fig. 7 (f). Table 2. Intersection and validation result between P (top view position) and Q (front view position) Data P (reference data) Data Q (transformed data) Number of point [points] 16,384 13,096 Size of grid [mm] Number of grid with data [grids] After intersection and validation 0 [grids] 407 (374 validated) 407 (365 validated) After Validation 1 and 2 [grids] After Validation 1,2 and 3 [grids] (c) (d) (e) Fig. 7 Data P; Data Q ; (c) Data P and Q ; (d) Intersection of data P and Q before validation; (e) Intersection data P and Q after validation 1 and 2; (f) Intersection data P and Q after validation 1, 2 and 3. Unit of axes is [mm] (f) 29

10 In fine registration, only validated plane data are used for ICP process to find fine transformation parameters (t f and R f), and then using those parameters (t f, R f) to transform overall data Q into P. Figure 8 shows the result of fine registration using ICP based point-to-point registration with the brute-forces scenario. Figure 8 shows fine registration by using only validated intersection data (validation 1,2 and 3) in order to find the transformation parameters (t f, R f). Figure 8 shows the fitting of overall data Q into data P by using t f and R f obtained in previous step, and Fig. 8(c) shows the performance of computation. Figure 9 shows the same computation result as Fig. 8 for ICP based plane-to-plane using kd-tree scenario. (c) Fig. 8 ICP point-to-point with brute-force scenario: Using validated intersection data (Validation 1,2 and 3); Transformation all data Q into P ; and (c) Performance of computation. Unit of axes in, and drms in (c) is [mm] (c) Fig. 9 ICP plane-to-plane with kd-tree scenario: Using validated intersection data (validation 1,2 and 3); Transformation all data Q into P ; and (c) Performance of computation. Unit of axis in, and in (c) is [mm] 210

11 All cases of experiment scenarios are computed using the same computation as the previous calculation (resulted in Fig. 8 and Fig.9). The computation result for overall scenarios is shown in Table 3 and Fig.10. Table 3. Computation result for different case experiment scenarios of Model 1 2. Point-to-Point Fine Registration Brute-Force kd-tree #Cases #Case , #Case #Case #Case Plane-to-Plane Fine Registration Brute-Force kd-tree #case #Case #Case #Case kd-tree kd-tree (c) (d) Fig. 10 Resume of computation result in overall scenarios: Case 0; Case 1; (c) Case 3; and (d) Case 4. Unit of is [mm] 211

12 3.2 Model 2: A Bullet Train Toy as Injection Moulding Product (Shinkansen Toy) Model 2 is a bullet train toy (Shinkansen toy) which is manufactured by injection moulding process. This product mainly consists of plane and free form features. In the case of RE by using our proposed method, the same as Model 1, we use two positions of measurement and apply two steps of registration: rough registration using transformation method and fine registration using the ICP-based method. In this fine registration, we utilize only validated extracted plane features from data sets in pairwise grids involved in ICP process. The same as Model 1, we use the point-to-point and the plane-to-plane with brute-force and kd-tree scenarios. Data of laser scanning after rough registration of P and Q (Q ), grid reconstruction parameters, intersection and validation data computation are as shown in Table 4. Table 4. Intersection and validation result between P (top view position) and Q (front view position) Model 2 Data P (reference) Data Q (transformed) Number of point [points] 37,233 26,905 Size of grid [mm] Number of grid with data [unit grids] 1,624 1,385 Intersection (grid with data in same index) [unit grids] and validation (771 validated) 835 (760 validated) Validation 1 and 2 [unit grids] Validation 1,2 and 3 [unit grids] Figure 11 shows Model 2 a Shinkansen toy model with two position of scanning measurements. Figure 11 shows data Q relative to data P before validation in a coordinate system. By using rough registration, data Q transformed into position and orientation of data P (Q change into Q )(Fig. 11(c)). Figure 11 (d) shows the fine registration result that used ICP point-to-point based with brute-force using transformation parameter obtained in ICP of pairwise validated data sets (Validation 1, 2 and 3). The result of computation for overall cases of experiment scenario is shown in Table 5 and Fig. (12). Reference data sets P is plotted in RED color and transformed data set Q is plotted in BLUE color. Top Position Front Position (c) (d) Fig. 11 Model 2 (a Bullet train toy) and its measurement position; Data Q and data P before rough registration; (c) Data Q and data P after rough registration; and (d) Fine registration ICP for Case 3. Unit of axes is [mm] 212

13 Table 5. Computation result for different case experiment scenarios of Model 2 1. Point-to-Point Fine Registration Brute-Force kd-tree #Cases #Case , #Case #Case #Case Plane-to-Plane Fine Registration Brute-Force kd-tree #case #Case #Case #Case Point-to-Point, kd-tree (c) (d) Fig. 12 Resume of computation in overall scenarios of experiments: Case 0; Case 1; (c) Case 2; and (d) Case 3. Unit of is [mm] Based on the result of the experiment using both real models, we can see that the proposed method increases the accuracy (yield the lower error, ) and decrease computation time. It can be proved from every stage of computation for the different case of experiments. In Case 0 (before using this proposed method), the error of registration () is around 3.54 mm for Model 1 (Table 3 #Case 0 and Fig. 10) and around 2.35 mm for Model 2 (Table 5 #Case 0 and Figure 12). In Case 1 (after using the intersection data set before validation), the error of registration () decrease to be around 0.21 mm for Model 1 (Table 3 #Case 1 and Fig 10) and around 1.05 mm for Model 2 (Table 5 #Case 1 213

14 and Fig 12). In Case 2 (after using Validation 1 and 2), the error of registration () significantly decreases into around 1.12 mm for Model 1 (Table 3 #Case 2 and Fig. 10(c)) and around 0.9 mm for Model 2 (Table 5 #Case 2 and Fig 12(c)). In Case 3 (after using Validation 1, 2 and 3), the error of registration () decrease to be around 0.55 mm for Model 1 (Table 3 #Case 3 and Fig 10(d)), and around 0.85 mm for Model 2 (Table 5 #Case 3 and Fig 12(d)). time decrease significantly related to the validation stage as shown in Table 3 for Model 1 and Table 5 for Model 2. All validation scenarios show the significant contribution in increasing the accuracy of the 3D-CAD model in which the error of RMS significantly decrease and decrease the computation time. In common, both point-to-point and plane-to-plane fine registration makes the same accuracy (value of the error, ) in both brute-force and kd-tree scenario. However, the kd-tree scenario can make much faster computation than brute-force scenario as shown in Table 3 and Table Conclusion This paper proposes a study of plane features extraction in registration of laser scanning data set in reverse engineering. Plane features are extracted and then validated by using certain criteria base on the pairwise grid with the same ID. Fine registration using ICP is applied only using the selected validated planes by point-to-point and plane-toplane ICP with brute-force and kd-tree scenario. Based on the registration result, we make some conclusions as bellow: b) The method can be used to solve 3D registration problem of the pairwise data sets with different form and distribution data sets. c) Plane feature extraction combined with ICP yields the accurate CAD model and economic. The result shows that the proposed method significantly improve the accuracy (results lower error of RMS) and reduce computation time (faster convergence) in all scenarios. The smallest RMS will produce smooth surface or solid of 3D CAD model. d) The performance of kd-tree can improve convergence and computation time better than brute-force. However, the accuracy resulted from both of them is not different much. e) Some criteria of validation process significantly influence CAD model accuracy and computation performance. References Andrew Moore, 1991, An introductory tutorial on kd-trees, Extract from PhD Thesis: Efficient Memory-based Learning for Robot Control PhD Thesis, Technical Report No. 209, Computer Laboratory, University of Cambridge. Hong Zhou, Yonghuai Liu, Longzhuang Li, Baogang Wei, 2009, A clustering approach to free form surface reconstruction from multi-view range images, Image and Vision Computing 27, pp Jin Tao and Kuang Jiyong, 2007, A 3-D point sets registration method in reverse engineering, Computer & Industrial Engineering 53, pp J.Y. Lai, W.-D. Ueng and C.-Y. Yao, 1999, Registration and Data Merging for Multiple Sets of Scan Data, International Journal of Advanced Manufacturing Technology, Vol. 15, Springer-Verlag London Limited, pp Lirong Wang, Fang Xu, Ichiro Hagiwara, 2009, An Efficient Registration Algorithm of Multi-view Three-dimension Images, World Congress on Computer Science and Information Engineering. Luca Di Angelo and Luigi Giaccari, 2011, An Efficient Algorithm for the Nearest Neighborhood Search for Point Cloud, IJCSI International Journal of Computer Science Issues, Vol. 8, Issue 5. M. Sokovic, J. Kopac, 2006, RE (reverse engineering) as necessary phase by rapid product development, Journal of Materials Processing Technology 175, pp Paul J. Besl and Neil D. McKay, 1992, A method for registration of 3D shapes, IEEE Transactions on Pattern Analysis and Machine Intelligence 14 (2), pp Ping Yan, Kevin W. Bowyer, 2007, A Fast Algorithm for ICP-based 3D Shape Biometrics, Computer Vision and Image Understanding 107, pp Rusinkiewicz S., Levoy M., Efficient variants of the ICP algorithm, In Proceedings of Third International Conference on 3-D Digital Imaging and Modeling, 2001, pp Xie Zexiao, Wang Jianguo, Zhang Qiumei, Complete 3D measurement in reverse engineering using a multi-probe system, International journal of machine tools & 1manufacture 45 (2005) Xudong Li, Wei Li, Hongzhi Jiang, Huijie Zhao, 2013, Automatic evaluation of machining allowance of precision castings based on plane features from 3D point Cloud, Computers in Industry 64, pp