A Brief Introduction Of Point Cloud Registration Method 杨哲杨哲 1732821732822 Point Cloud Registration MethodPoint Cloud Registration MethodPoint Cloud Registration With Target ControlPoint Cloud Registration With Target Control3 34 4Quaternion Method Quaternion Method 2 21 1Iterative Closest Point(ICP) AlgorithmIterative Closest Point(ICP) Algorithm 4 Outline Outline Two point cloud sets of A and B, Two point cloud sets of A and B, are conformations of the same points in different coordinate systems are conformations of the same points in different coordinate systems Rigid transformation:Rigid transformation: Objective function: Objective function:1. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control4 4面面 （a a）Leica standard rotation plane targetLeica standard rotation plane target（b b） Mensi plane target Mensi plane targetFigure 1 Different kinds of plane target Figure 1 Different kinds of plane target （d d） Mensi plane target Mensi plane target（c c）FARO standard plane target FARO standard plane target 51. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control6 spatial similarity transformation parameters6 spatial similarity transformation parameters3 angle elements: 3 angle elements: 3 translation3 translation elements:elements: Adjustment model: Adjustment model: Or Or61. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control Rotation matrix:Rotation matrix: 71. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control The expansion of Taylors formula:The expansion of Taylors formula: Error Equation: Error Equation: 8 G G1. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control Derivative value: Derivative value: Suppose that: Suppose that:91. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control Error equation matrix:Error equation matrix: Gravity-centralize:Gravity-centralize:101. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control N pairs of corresponding points:N pairs of corresponding points: Order:Order:111. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control Error equation:Error equation:1. 1. Point Cloud Registration With Target ControlPoint Cloud Registration With Target Control12 New approximate value:New approximate value: Iteration:Iteration: Finally, we get the values of parameter: Finally, we get the values of parameter: 2. Iterative Closest Point(ICP) Algorithm2. Iterative Closest Point(ICP) Algorithm1313Basic thought:Basic thought:Firstly, from a point set, a bar curve, or a surface to find the Firstly, from a point set, a bar curve, or a surface to find the closest point that corresponds to one point, and then uses closest point that corresponds to one point, and then uses this result to find two corresponding point sets. Finally, we this result to find two corresponding point sets. Finally, we find out the corresponding point set and the corresponding find out the corresponding point set and the corresponding transformation matrix.transformation matrix.Basic steps:Basic steps:Step1:Search for the nearest pointsStep1:Search for the nearest pointsStep2:Solve transformation relationsStep2:Solve transformation relationsStep3:Application transformationStep3:Application transformationStep4:Repeated iterationStep4:Repeated iteration3 Quaternion Method 3 Quaternion Method n n What is Quaternion ?What is Quaternion ? 1414n n Unit quaternions Unit quaternions n n Rotation matrix R Rotation matrix R 3. Quaternion Method 3. Quaternion Method Definite translation vector:Definite translation vector: 1515Complete registration station:Complete registration station: Assume that:Assume that: Minimum objective function: Minimum objective function: The centroid of the set of basic points : The centroid of the set of basic points :3. Quaternion Method 3. Quaternion Method 1616 Orthogonal covariance matrix of point set: Orthogonal covariance matrix of point set: Antisymmetric matrixs cyclic components: Antisymmetric matrixs cyclic components: Construct a symmetric matrix: Construct a symmetric matrix:3. Quaternion Method 3. Quaternion Method 1717 Translation matrix: Translation matrix:The unit eigenvector corresponding to the maximum The unit eigenvector corresponding to the maximum eigenvalue of matrix :eigenvalue of matrix : Conclusions Thank you！1818