Estimates a 3D affine transformation from two point sets. More...
#include <EstimateAffineTransformation3D.hpp>
Public Types | |
typedef super::VectorXT | VectorXT |
Column vector of arbitrary size with value type T. | |
typedef super::MatrixXT | MatrixXT |
Matrix of arbitrary size with value type T. | |
typedef super::Vector2T | Vector2T |
2D column vector with value type T. | |
typedef super::Vector3T | Vector3T |
3D column vector with value type T. | |
typedef super::Vector4T | Vector4T |
4D column vector with value type T. | |
typedef super::RowVector2T | RowVector2T |
2D row vector with value type T. | |
typedef super::RowVector3T | RowVector3T |
3D row vector with value type T. | |
typedef super::Matrix2T | Matrix2T |
2 x 2 matrix with value type T. | |
typedef super::Matrix3T | Matrix3T |
3 x 3 matrix with value type T. | |
typedef super::Matrix4T | Matrix4T |
4 x 4 matrix with value type T. | |
typedef super::ArrayXT | ArrayXT |
General-purpose array of arbitrary size with value type T. | |
enum | Error { NOT_ENOUGH_POINTS, UNEQUAL_NUMBER_OF_POINTS, UNKNOWN_ERROR, WRONG_POINT_SIZE } |
Public Member Functions | |
EstimateAffineTransformation3D () | |
Constructs a new instance of this class. | |
EstimateAffineTransformation3D (const std::vector< Coordinate< T > > &source_points, const std::vector< Coordinate< T > > &target_points) | |
Constructs a new instance of this class. | |
EstimateAffineTransformation3D (const std::vector< Vector3T > &source_points, const std::vector< Vector3T > &target_points) | |
Constructs a new instance of this class. | |
EstimateAffineTransformation3D (const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > &source_points, const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > &target_points) | |
Constructs a new instance of this class. | |
virtual | ~EstimateAffineTransformation3D () |
Deletes the instance. | |
virtual void | compute () |
Computes the transformation estimation. | |
Matrix3T | getLinearTransformationMatrix () const |
Vector3T | getTranslationVector () const |
virtual value_type | getRMS () const |
Returns the root mean square (RMS) error of the estimated transformation. | |
virtual const Matrix4T & | getTransformationMatrix () const |
void | setSourcePoints (const std::vector< Coordinate< T > > &) |
Sets the source points. | |
void | setSourcePoints (const std::vector< Vector3T > &) |
Sets the source points. | |
void | setSourcePoints (const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > &) |
Sets the source points. | |
void | setTargetPoints (const std::vector< Coordinate< T > > &) |
Sets the target points. | |
void | setTargetPoints (const std::vector< Vector3T > &) |
Sets the target points. | |
void | setTargetPoints (const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > &) |
Sets the target points. | |
Public Attributes | |
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef T | value_type |
Internally used value type (should be a floating point type). | |
Protected Attributes | |
MatrixXT | m_source_points |
MatrixXT | m_target_points |
Matrix4T | m_transformation_matrix |
Estimates a 3D affine transformation from two point sets.
This class estimates a 3D affine transformation between two point sets in terms of least squares. The point sets must have the same cardinality, and the points must correspond to each other. There must be at least four corresponding point pairs.
The algorithm estimates a transformation matrix as shown below:
\[ \begin{pmatrix} y_1 \\ y_2 \\ y_3 \\ 1 \end{pmatrix} = \begin{pmatrix} a_{11} & a_{12} & a_{13} & b_1 \\ a_{21} & a_{22} & a_{23} & b_2 \\ a_{31} & a_{32} & a_{33} & b_3 \\ 0 & 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \\ 1 \end{pmatrix} \qquad \qquad \text{or} \qquad \qquad y = Ax + b \]
The source points are the set of all \( x \) and the target points are the set of all \( y \).
Here is an more elaborate example to see, how to use the class:
#include <iostream> #include <vector> #include <TRTK/Coordinate.hpp> #include <TRTK/Transform3D.hpp> #include <TRTK/EstimateAffineTransformation3D.hpp> using std::cout; using std::endl; using std::vector; using namespace TRTK; int main() { // Construct an affine transformation. Transform3D<double> transform; transform.a12() = 1; transform.a14() = 1; transform.a31() = 2; transform.a34() = 3; // Construct two sets with source and target points, respectively. vector<Coordinate<double> > source_points; vector<Coordinate<double> > target_points; Coordinate<double> source_point1( 1, 2, 0); Coordinate<double> source_point2( 3, -2, 0); Coordinate<double> source_point3(-1, 1, 1); Coordinate<double> source_point4( 2, 0, -1); source_points.push_back(source_point1); source_points.push_back(source_point2); source_points.push_back(source_point3); source_points.push_back(source_point4); Coordinate<double> target_point1 = transform * source_point1; Coordinate<double> target_point2 = transform * source_point2; Coordinate<double> target_point3 = transform * source_point3; Coordinate<double> target_point4 = transform * source_point4; target_points.push_back(target_point1); target_points.push_back(target_point2); target_points.push_back(target_point3); target_points.push_back(target_point4); // Perform the transformation estimation. EstimateAffineTransformation3D<double> estimateAffineTransformation3D(source_points, target_points); estimateAffineTransformation3D.compute(); // Display the results. cout.precision(4); cout << std::fixed; cout << "Original transformation matrix:" << endl << endl << transform.getTransformationMatrix() << endl << endl; cout << "Estimated transformation matrix:" << endl << endl << estimateAffineTransformation3D.getTransformationMatrix() << endl << endl; // Example of how to use the result. Transform3D<double> transform2 = estimateAffineTransformation3D.getTransformationMatrix(); cout << "Source point 1: " << source_point1 << endl << "Target point 1: " << target_point1 << endl << "Target point 1: " << transform2 * source_point1 << endl; return 0; }
Output:
Original transformation matrix: 1.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 0.0000 2.0000 0.0000 1.0000 3.0000 0.0000 0.0000 0.0000 1.0000 Estimated transformation matrix: 1.0000 1.0000 -0.0000 1.0000 -0.0000 1.0000 0.0000 0.0000 2.0000 0.0000 1.0000 3.0000 0.0000 0.0000 0.0000 1.0000 Source point 1: (1.0000, 2.0000, 0.0000) Target point 1: (4.0000, 2.0000, 5.0000) Target point 1: (4.0000, 2.0000, 5.0000)
Definition at line 193 of file EstimateAffineTransformation3D.hpp.
enum TRTK::EstimateTransformation::Error [inherited] |
Definition at line 62 of file EstimateTransformation.hpp.
TRTK::EstimateAffineTransformation3D< T >::EstimateAffineTransformation3D | ( | ) |
Constructs a new instance of this class.
T | scalar type of the coordinates |
Definition at line 247 of file EstimateAffineTransformation3D.hpp.
TRTK::EstimateAffineTransformation3D< T >::EstimateAffineTransformation3D | ( | const std::vector< Coordinate< T > > & | source_points, |
const std::vector< Coordinate< T > > & | target_points | ||
) |
Constructs a new instance of this class.
T | scalar type of the coordinates |
[in] | source_points | The points can either be plain 3D or 4D homogeneous coordinates. |
[in] | target_points | The points can either be plain 3D or 4D homogeneous coordinates. |
No transformation estimation is done. To do so, please call compute().
ErrorObj | If there are any coordinates other than 3D or 4D coordinates, an error object is thrown and its error code is set to WRONG_POINT_SIZE . |
Definition at line 274 of file EstimateAffineTransformation3D.hpp.
TRTK::EstimateAffineTransformation3D< T >::EstimateAffineTransformation3D | ( | const std::vector< Vector3T > & | source_points, |
const std::vector< Vector3T > & | target_points | ||
) |
Constructs a new instance of this class.
T | scalar type of the coordinates |
[in] | source_points | 3D coordinates. |
[in] | target_points | 3D coordinates. |
No transformation estimation is done. To do so, please call compute().
Definition at line 296 of file EstimateAffineTransformation3D.hpp.
TRTK::EstimateAffineTransformation3D< T >::EstimateAffineTransformation3D | ( | const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > & | source_points, |
const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > & | target_points | ||
) |
Constructs a new instance of this class.
T | scalar type of the coordinates |
[in] | source_points | 4D homogeneous coordinates. |
[in] | target_points | 4D homogeneous coordinates. |
No transformation estimation is done. To do so, please call compute().
Definition at line 318 of file EstimateAffineTransformation3D.hpp.
TRTK::EstimateAffineTransformation3D< T >::~EstimateAffineTransformation3D | ( | ) | [virtual] |
Deletes the instance.
T | scalar type of the coordinates |
Definition at line 332 of file EstimateAffineTransformation3D.hpp.
void TRTK::EstimateAffineTransformation3D< T >::compute | ( | ) | [virtual] |
Computes the transformation estimation.
T | scalar type of the coordinates |
The transformation estimation uses a least square scheme. For a more detailed explanation of the algorithm, please have a look at the source code. (A link should be below.)
The direction of the transformation is from the source points to the target points: \( p_{target} = \cal{T} \; \{ p_{source} \} \).
ErrorObj | If the point sets do not have the same cardinality, an error object is thrown and its error code is set to UNEQUAL_NUMBER_OF_POINTS . |
ErrorObj | If there are not enough points (at least four) to perform the transformation estimation, an error object is thrown and its error code is set to NOT_ENOUGH_POINTS . |
Implements TRTK::EstimateTransformation3D< T >.
Definition at line 358 of file EstimateAffineTransformation3D.hpp.
EstimateAffineTransformation3D< T >::Matrix3T TRTK::EstimateAffineTransformation3D< T >::getLinearTransformationMatrix | ( | ) | const |
T | scalar type of the coordinates |
Definition at line 477 of file EstimateAffineTransformation3D.hpp.
EstimateTransformation3D< T >::value_type TRTK::EstimateTransformation3D< T >::getRMS | ( | ) | const [virtual, inherited] |
Returns the root mean square (RMS) error of the estimated transformation.
T | scalar type of the coordinates |
It is assumed, that the computation was done before.
The value type T
must provide a function T sqrt(T value)
which yields the square root of value
.
ErrorObj | If the point sets do not have the same cardinality, an error object is thrown and its error code is set to UNEQUAL_NUMBER_OF_POINTS . |
Implements TRTK::EstimateTransformation< T >.
Definition at line 149 of file EstimateTransformation3D.hpp.
const EstimateTransformation3D< T >::Matrix4T & TRTK::EstimateTransformation3D< T >::getTransformationMatrix | ( | ) | const [virtual, inherited] |
T | scalar type of the coordinates |
Definition at line 195 of file EstimateTransformation3D.hpp.
EstimateAffineTransformation3D< T >::Vector3T TRTK::EstimateAffineTransformation3D< T >::getTranslationVector | ( | ) | const |
T | scalar type of the coordinates |
Definition at line 491 of file EstimateAffineTransformation3D.hpp.
void TRTK::EstimateTransformation3D< T >::setSourcePoints | ( | const std::vector< Vector3T > & | source_points ) | [inherited] |
Sets the source points.
T | scalar type of the coordinates |
[in] | source_points | 3D coordinates. |
Definition at line 247 of file EstimateTransformation3D.hpp.
void TRTK::EstimateTransformation3D< T >::setSourcePoints | ( | const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > & | source_points ) | [inherited] |
Sets the source points.
T | scalar type of the coordinates |
[in] | source_points | 4D homogeneous coordinates. |
Definition at line 265 of file EstimateTransformation3D.hpp.
void TRTK::EstimateTransformation3D< T >::setSourcePoints | ( | const std::vector< Coordinate< T > > & | source_points ) | [inherited] |
Sets the source points.
T | scalar type of the coordinates |
[in] | source_points | The points can either be plain 3D or 4D homogeneous coordinates. |
ErrorObj | If there are any coordinates other than 3D or 4D coordinates, an error object is thrown and its error code is set to WRONG_POINT_SIZE . |
Definition at line 215 of file EstimateTransformation3D.hpp.
void TRTK::EstimateTransformation3D< T >::setTargetPoints | ( | const std::vector< Coordinate< T > > & | target_points ) | [inherited] |
Sets the target points.
T | scalar type of the coordinates |
[in] | target_points | The points can either be plain 3D or 4D homogeneous coordinates. |
ErrorObj | If there are any coordinates other than 3D or 4D coordinates, an error object is thrown and its error code is set to WRONG_POINT_SIZE . |
Definition at line 293 of file EstimateTransformation3D.hpp.
void TRTK::EstimateTransformation3D< T >::setTargetPoints | ( | const std::vector< Vector3T > & | target_points ) | [inherited] |
Sets the target points.
T | scalar type of the coordinates |
[in] | target_points | 3D coordinates. |
Definition at line 325 of file EstimateTransformation3D.hpp.
void TRTK::EstimateTransformation3D< T >::setTargetPoints | ( | const std::vector< Vector4T, Eigen::aligned_allocator< Vector4T > > & | target_points ) | [inherited] |
Sets the target points.
T | scalar type of the coordinates |
[in] | target_points | 4D homogeneous coordinates. |
Definition at line 343 of file EstimateTransformation3D.hpp.
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