Method for high-precision true color three-dimensional reconstruction of a mechanical component

A method for high-precision true color three dimensional reconstruction of a mechanical component, comprising:

• (1). image acquisition
• 1.1). fixing a left high-resolution grayscale camera and a right high-resolution grayscale camera on a support device, where the right high-resolution grayscale camera and the left high-resolution grayscale camera are at the same height and spaced at a certain distance;
• fixing an optical transmitter between the left high-resolution grayscale camera and right high-resolution grayscale camera and a low-resolution color camera above the optical transmitter;
• 1.2). adjusting the left high-resolution grayscale camera, the right high-resolution grayscale camera, the optical transmitter and the low-resolution color camera, so that a measured high-precision mechanical component can be completely and clearly captured by the cameras and the optical transmitter can completely and clearly project non-coded light and coded light on the surface of the measured high-precision mechanical component;
• adjusting a calibration plate and using Zhang's calibration method to complete a camera calibration;
• 1.3). placing the measured high-precision mechanical component at a suitable position in the view of the cameras, then rotating the measured high-precision mechanical component in a fixed direction and acquiring images of J poses:
• for the measured high-precision mechanical component of the jth pose, firstly the optical transmitter projects a non-coded light on the surface of the measured high-precision mechanical component, the low-resolution color camera takes image which is denoted by low-resolution color image CIj, the left high-resolution grayscale camera takes an image which is denoted by left high-resolution grayscale image LIj, then the optical transmitter projects N frames of encoded light on the surface of the measured high-precision mechanical component, the left high-resolution grayscale camera and right high-resolution grayscale camera respectively take a grayscale image which are respectively denoted by LIjn and RIjn, n=1, 2, . . . , N;
• (2). image processing
• 2.1). reconstructing a three-dimensional point cloud of the measured high-precision mechanical component of each pose:
• based on the principle of binocular camera, reconstructing a three-dimensional point cloud Pj of the jth pose by using the grayscale images LIj1, LIj2, . . . , LIjN and RIj1, RIj2, . . . , RIjN of the jth pose, where j=1, 2, . . . , J;
• 2.2). performing registrations on 3D point clouds to calculate a rigid body transformation matrix Wj by using the three-dimensional point cloud Pj as a target point cloud and the three-dimensional point cloud Pj+1 of the (j+1)th pose as a source point cloud, where j=1, 2, . . . , J−1:
• 2.2.1). respectively performing voxel down sampling on the target point cloud Pj and the source point cloud Pj+1, where the voxel down sampled target point cloud is denoted by the target point cloud Pj_down and the voxel down sampled source point cloud is denoted by the source point cloud Pj+1_down, and respectively performing 3D-SIFT key point extraction on the target point cloud Pj_down and the target point cloud Pj+1_down, where the extracted target point cloud is denoted by a target point cloud Pj_key, the extracted source point cloud is denoted by a source point cloud Pj+1_key;
• 2.2.2). initializing iteration number k=1, setting a maximum iteration number Kc_reg, setting an iteration number Kpp which is used for shifting a point-to-plane error function to a point-to-point error function, initializing transformed source point cloud Pj+1_key_1 to the source point cloud Pj+1_key;
• 2.2.3). for the kth iteration, to each point of the source point cloud Pj+1_key_k, finding the nearest point in the target point cloud Pj_key as its corresponding point by using KD tree to obtain a corresponding point-to-point set Cj+1_key_k, then removing the point and its nearest point whose distance is great than threshold Thres to obtain a optimized point-to-point set Cj_key_k′;
• 2.2.4). homogenizing the ith point pj+1_key_ki of the source point cloud Pj+1_key_k in point-to-point set Cj_key_k′ to obtain its corresponding vector pj+1_key_ki=(xj+1_key_ki,yj+1_key_ki,zj+1_key_ki,1)T, finding corresponding point pj_key_i of the target point cloud Pj_key in point-to-point set Cj_key_k′ and homogenizing it to obtain its corresponding vector pj_key_i=(xj_key_i,yj_key_i,zj_key_i,1)T, where i=1, 2, . . . , Ncj_key_k, Ncj_key_k is the number of point-to-point set Cj_key_k′;
• if iteration number k is less than Kpp, then constructing a point-to-plane error function Fjk by using the distance from the point pj+1_key_ki to the tangent plane of point pj_key_i of target point cloud Pj_key, where the error function Fjk is:
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• where nj_key_i is the normal vector corresponding to point pj_key_i, Wjk is the transformation matrix of the kth iteration;
• if iteration number k is nor less than Kpp, then constructing a point-to-point error function Fjk according to the sum of the squares of the distances between the corresponding points, where the error function Fjk is:
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• 2.2.5). calculating the transformation matrix Wjk that makes the value of error function Fjk minimum, and then applying a transformation to the source point cloud Pj+1_key_k by using error function Fjk to obtain a source point cloud Pj+1_key_(k+1) and recording the value of error function Fjk at the kth iteration;
• 2.2.6). judging whether the variation |Fjk−Fj(k−1)| of the value of error function of two consecutive iterations is less than a threshold e or iteration number k reaches the maximum iteration number Kc_reg;
• if yes, then recording the point-to-point set Cj_key_k′′ at the k′th iteration, where k′ is the iteration number when the judgment condition is met, and calculating the optimal rigid body transformation matrix Wj=Wjk, Wj(k′−1) . . . Wj1, where the optimal rigid body transformation matrix Wj is a matrix of 4×4, its formation is:
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• where Rcloud_j is a rotation matrix of 3×3 which registers the source point cloud Pj+1_key to the target point cloud Pj_key, Tcloud_j is a translation vector of 1×3, {right arrow over (0)} is a row vector of 3×1;
• if no, k=k+1, and returning step 2.2.3);
• 2.3). fusing the left high-resolution image LIj with the low-resolution color image CIj of the jth pose, j=1, 2, . . . , m
• 2.3.1). calculating a projection matrix Hj for registering the low-resolution color image CIj to the left high-resolution image LIj:
• 2.3.1.1). respectively extracting SURF feature points from the low-resolution color image CIj and the left high-resolution image LIj, and taking the extracted SURF feature points as key points;
• 2.3.1.2). to each key point of the low-resolution color image CIj, finding the closest key point and the next closest key point in the left high-resolution image LIj according to Euclidean distance, if the ratio of the distance of the closest key point to the distance of the next closet key point is less than a set threshold θ, then determining the closest key point in the left high-resolution image LIj as the matching point, thus a matching point pair set Ccl_j is obtained;
• 2.3.1.3). setting a maximum iteration number Kp_reg and an error threshold φ, initializing iteration number k=1, then optimizing the matching point pair set Ccl_j through random sampling consistency (RANSAC) algorithm to obtain the projection matrix Hj:
• 2.3.1.3.1). for the kth iteration in the process of optimizing the matching point pair set Ccl_j, randomly selecting four point pairs, which are denoted respectively by {qcj_1, qlj_1}, {qcj_2, qlj_2}, {qcj_3, qlj_3} and {qcj_4, qlj_4}, and homogenizing them to obtain four point pairs {qcj_1, qlj_1}, {qcj_2, qlj_2}, {qcj_3, qlj_3} and {qcj_4, qlj_4}, then calculating a projection matrix Hjk between the four point pairs, which satisfies the following relationship:
• qlj_i=Hjk·qcj_i, 1, 2, . . . , 4
• 2.3.1.3.2). homogenizing a point pair {qcj_i, qlj_i} other than the selected four point pairs from the matching point pair set Ccl_j to obtain point pair {qcj_i, qlj_i} then calculating a mapping error εjk_i=∥qlj_i,Hjkqcj_i∥ according to the projection matrix Hjk, where i=5, 6, . . . , Ncj, Ncj is the number of point pairs of the matching point pair set Ccl_j, and selecting the point pair which mapping error εjk_i<φ to form a interior point set Sjk;
• 2.3.1.3.3). if the last iteration has been performed, namely k=Kp_reg, then comparing Sj1, Sj2, . . . , SjKp_reg to select the projection matrix Hjk as the projection matrix Hj when the interior point set Sjk is the largest, or k=k+1 and returning step 2.3.1.3.1;
• 2.3.2). registering the low-resolution color image CIj to the left high-resolution image LIj according to the projection matrix Hj to obtain a high-resolution registered color image CIj_r:
• 2.3.2.1). creating a empty high-resolution registered color image CIj_r which has the same size with the left high-resolution image LIj, then performing coordinate transformation on the pixels of the low-resolution color image CIj to obtain a color image CIj;
• 2.3.2.2). determining the interpolation range:
• the pixel points of the high-resolution registered color image CIj_r which are located on color image CIj and other than the matching points in matching point pair set Ccl_j are the points which are needed to be interpolated, namely interpolation points;
• 2.3.2.3). using the bilinear interpolation method to interpolate the pixel values of all interpolation points:
• to the ith interpolation point qcj_r_i(xcj_r_i, ycj_r_i), performing a inverse transformation according to the projection matrix Hj to obtain a pixel point ρcj_i(xcj_ρ_i, ycj_ρ_i) located on the low-resolution color image CIj, and finding four nearest pixel points which are denoted respectively by pcj_ρ_i11(xcj_ρ_i1, ycj_ρ_i1), pcj_ρ_i12(xcj_ρ_i1, ycj_ρ_i2), pcj_ρ_i21(xcj_ρ_i2, ycj_ρ_i1) and pcj_ρ_i22(xcj_ρ_i2, ycj_ρ_i2);
• firstly interpolating in the x direction to obtain the following:
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• then interpolating in the y direction to obtain the following pixel value:
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• letting the pixel value CIj_r(xcj_r_i, ycj_r_i) of the interpolation point qcj_r_i(xcj_r_i, ycj_r_i) be CIj(xcj_ρ_i, ycj_ρ_i);
• 2.3.2.4). to the pixel points of the high-resolution registered color image CIj_r which are located on color image CIj and are the matching points in matching point pair set Ccl_j, directly using the pixel values of their corresponding matching point in the low-resolution color image CIj to assign;
• and to the pixel points of the high-resolution registered color image CIj_r which are not located on color image CIj, directly using preset RGB value to assign, thus the high-resolution registered color image CIj_r is obtained;
• 2.3.3). fusing the left high-resolution image LIj with the high-resolution registered color image CIj_r:
• 2.3.3.1). performing Nl-layer Laplacian pyramid decomposition on the left high-resolution image LIj to obtain Nl layers of image LIj_w, performing Nl-layer Laplacian pyramid decomposition on each channel of the high-resolution registered color image CIj_r to obtain Nl layers of image CIj_rw on R channel, Nl layers of image CIj_gw on G channel and Nl layers of image CIj_bw on B channel, where w=1, 2, . . . , Nl and represents the serial number of image;
• 2.3.3.2). respectively performing bilateral filter on the top-layer images CIj_rNl, CIj_gNl, CIj_bNl and LIj_Nl to obtain top-layer images CIj_rNl_b, CIj_gNl_b;
• CIj_bNl_b and LIj_Nl_b;
• 2.3.3.3). to the top-layer images of three channels of the high-resolution registered color image CIj_r, calculating the difference before and after bilateral filtering to obtain detail layer images CIj_rNl′=CIj_rNl−CIj_rNl_b, CIj_gNl′=CIj_gNl−CIj_gNl_b and CIj_bNl′=CIj_bNl−CIj_bNl_b, which have rich details of image;
• 2.3.3.4). performing Gaussian filter on the top-layer image of the left high-resolution image LIj to obtain a overall smooth image LIj_Nl_g, then calculating the difference between the top-layer image LIj_Nl_b and the overall smooth image LIj_Nl_g to obtain a layer image LIj_Nl′=LIj_Nl_b−j_Nl_g which has rich edge information;
• 2.3.3.5). calculating top-layer fusion images, where the top-layer fusion image of R channel is:
• Fuj_Nl_r=CIj_rNl+αCIj_rNl′+βLIj_Nl′, the top-layer fusion image of G channel is:
• Fuj_Nl_g=CIj_gNl+αCIj_gNl′+βLIj_Nl′, the top-layer fusion image of B channel is:
• Fuj_Nl_r=CIj_rNl+αCIj_rNl′+βLIj_Nl′;
• 2.3.3.6). to the layer fusion images other than the top-layer fusion images, for the reason of retaining the rich color information, assigning the layer fusion images of R channel according to equation Fu=j_w_r=CIj_rw, the layer fusion images of G channel according to equation Fuj_w_g=CIj_gw and the layer fusion images of B channel according to equation Fuj_w_b=CIj_bw, where w=1, 2, . . . , Nl−1;
• 2.3.3.7). based on all layer fusion images of each color channel, performing Nl-layer Laplacian pyramid composition to obtain fusion images of each color channel, thus the color fusion image of the jth pose is obtained and denoted by Fuj;
• 2.4). reconstructing a color point cloud:
• 2.4.1). performing color reconstruction on point cloud of each pose to obtain color point clouds {tilde over (P)}1, {tilde over (P)}2, . . . , {tilde over (P)}m:
• 2.4.1.1). to each point pji(xji, yji, zji) of the three-dimensional point cloud Pj of the measured high-precision mechanical component of the jth pose, performing a coordinate system conversion from three-dimensional point to pixel point:
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• where zc is a scale factor, fx and fy are respectively the focal lengths of camera in the x and y direction, u0 and v0 are respectively the coordinates of camera's main point on pixel plane, Rc and Tc are respectively the rotation matrix and the translation vector in camera calibration parameters, (aji,bji) are the coordinates of the pixel point qij corresponding to the point pji(xji, yji, zji) of the three-dimensional point cloud Pj, i is the serial number of the point;
• 2.4.1.2). obtaining pixel value R(aji,bji) of R channel, pixel value G(aji,bji) of G channel and pixel value B(aji,bji) of B channel of pixel point at coordinates (aji,bji) on the color fusion image Fuj, then assigning pixel values to the point pji(xji, yji, zji) of the three-dimensional point cloud Pj according to the following equations:
• R(xji,yji,zji)=R(aji,bji), G(xji,yji,zji)=G(aji,bji) and B(xji,yji,zji)=B(aji,bji) to obtain color point cloud {tilde over (P)}j, j=1, 2, . . . , m, where R(xji, yji, zji), G(xji, yji, zji) and B(xji, yji, zji) are respectively the point values of R, G and B channel of point pji(xji, yji, zji) of color point cloud {tilde over (P)}j;
• 2.4.2). registering the color point clouds of all poses:
• based on the series of rigid body transformation matrices W1, W2, . . . , Wm−1 which are obtained according to step 2.2, performing registration by respectively converting the color point clouds {tilde over (P)}2, {tilde over (P)}3, . . . , {tilde over (P)}m to the coordinate system of the color point cloud {tilde over (P)}1, where the color point clouds after conversion are respectively denoted by {tilde over (P)}2*, {tilde over (P)}3*, . . . , {tilde over (P)}m*, there have:
• {tilde over (P)}2*=W1{tilde over (P)}2
• {tilde over (P)}3*=W1W2{tilde over (P)}3
• . . .
• {tilde over (P)}m*=W1W2 . . . Wm−1{tilde over (P)}m
• 2.4.3). fusing the overlapping part of the color point clouds:
• setting {tilde over (G)}1*={tilde over (P)}1*={tilde over (P)}1, then fusing the color point cloud {tilde over (P)}2* with the color point cloud {tilde over (G)}1* to obtain a color point cloud {tilde over (G)}2* to j=2, 3, . . . m−1, successfully fusing the color point cloud {tilde over (P)}j+1* with the color point cloud {tilde over (G)}j* to obtain a color point cloud {tilde over (G)}j+1*, and finally obtaining a fused overall color point cloud {tilde over (G)}m* that the high-precision true color three dimensional reconstruction is complete;
• where the fusion of the color point cloud {tilde over (P)}j+1* and the color point cloud {tilde over (G)}j* is:
• to the matching point pair in the point-to-point set Cj_key_k′′, directly taking it as a correspondence point pair and putting it into a correspondence point pair set Coj;
• to a non-matching point {tilde over (p)}j+1_i*({tilde over (x)}j+1_i*, {tilde over (y)}j+1_i*, {tilde over (z)}j+1_i*) of the color point cloud {tilde over (P)}j+1*, finding the nearest point in the color point cloud {tilde over (P)}j+1* by using KD tree, and then calculating the average value σ of all distances between non-matching points and their respective nearest points;
• simultaneously, to each non-matching point of the color point cloud {tilde over (G)}j*, finding the nearest point in the color point cloud {tilde over (P)}j+1* by using KD tree, if the distance of the nearest point is less than the average value σ, then the non-matching point of the color point cloud {tilde over (G)}j* and its nearest point in the color point cloud {tilde over (P)}j+1* are taken as a correspondence point pair and put into the correspondence point pair set Coj;
• weighting geometric coordinates of each correspondence point pair {{tilde over (p)}j+1_i*({tilde over (x)}j+1_i*, {tilde over (y)}j+1_i*, {tilde over (z)}j+1_i*), {tilde over (g)}j_i*({tilde over (x)}j_i*, {tilde over (y)}j_i*, {tilde over (z)}j_i*)} in the correspondence point pair set Coj with the weights αi and βi to obtain the coordinates of a fused point {tilde over (g)}j+1_i*:
• (αi{tilde over (x)}j+1_i*+βi{tilde over (x)}j_i*,αi{tilde over (y)}j+1_i*+βi{tilde over (y)}j+1_i*,αi{tilde over (z)}j+1_i*+βizj_i*)
• respectively weighting the point values of R, G and B channel of each correspondence point pair {{tilde over (p)}j+1_i*({tilde over (x)}j+1_i*, {tilde over (y)}j+1_i*, {tilde over (z)}j+1_i*), {tilde over (g)}j_i*({tilde over (x)}j_i*, {tilde over (y)}j_i*, {tilde over (z)}j_i*)} in the correspondence point pair set Coj with the weights (αri,βri), (αgi,βgi) and (αbi,βbi) to obtain the point values R({tilde over (g)}j+1_i*), G({tilde over (g)}j+1_i*) and B({tilde over (g)}j+1_i*) of R, G and B channel of the point {tilde over (g)}j+1_i* of the color point cloud {tilde over (G)}j+1*:
• R({tilde over (g)}j+1_i*)=αriR({tilde over (p)}j+1_i*)+βriR({tilde over (g)}j_i*)
• G({tilde over (g)}j+1_i*)=αgiG({tilde over (p)}j+1_i*)+βgiG({tilde over (g)}j_i*)
• B({tilde over (g)}j+1_i*)=αbiB({tilde over (p)}j+1_i*)+βbiB({tilde over (g)}j_i*)
• where, i=1, 2, . . . , Ncoj, Ncoj is the number of the correspondence point pairs, R({tilde over (p)}j+1_i*), G({tilde over (p)}j+1_i*) and ({tilde over (p)}j+1_i*) are respectively the point values of R, G and B channel of the point {tilde over (p)}j+1_i*, R({tilde over (g)}j_i*), G({tilde over (g)}j_i*) and B({tilde over (g)}j_i*) are respectively the point values of R, G and B channel of the point {tilde over (g)}j_i* of the color point cloud {tilde over (G)}j+1*.