This class represents a PCA-model that consists of: More...

#include <PcaModel.hpp>

Public Member Functions
	PcaModel (Eigen::VectorXf mean, Eigen::MatrixXf orthonormal_pca_basis, Eigen::VectorXf eigenvalues, std::vector< std::array< int, 3 > > triangle_list)

int	get_num_principal_components () const

int	get_data_dimension () const

const std::vector< std::array< int, 3 > > &	get_triangle_list () const

const Eigen::VectorXf &	get_mean () const

Eigen::Vector3f	get_mean_at_point (int vertex_index) const

template<class RNG >
Eigen::VectorXf	draw_sample (RNG &engine, float sigma=1.0f) const

Eigen::VectorXf	draw_sample (std::vector< float > coefficients) const

Eigen::VectorXf	draw_sample (std::vector< double > coefficients) const

const Eigen::MatrixXf &	get_rescaled_pca_basis () const

Eigen::MatrixXf	get_rescaled_pca_basis_at_point (int vertex_id) const

const Eigen::MatrixXf &	get_orthonormal_pca_basis () const

Eigen::MatrixXf	get_orthonormal_pca_basis_at_point (int vertex_id) const

const Eigen::VectorXf &	get_eigenvalues () const

float	get_eigenvalue (int index) const

std::vector< float >	project (const Eigen::VectorXf &instance) const

Friends
class	cereal::access

Detailed Description

This class represents a PCA-model that consists of:

a mean vector (y x z)
a PCA basis matrix (orthonormal and rescaled)
a PCA variance vector.

It also contains a list of triangles to built a mesh as well as a mapping from landmark points to the corresponding vertex-id in the mesh.

Constructor & Destructor Documentation

◆ PcaModel()

eos::morphablemodel::PcaModel::PcaModel	(	Eigen::VectorXf	mean,
		Eigen::MatrixXf	orthonormal_pca_basis,
		Eigen::VectorXf	eigenvalues,
		std::vector< std::array< int, 3 > >	triangle_list
	)

inline

Construct a PCA model from given mean, normalised PCA basis, eigenvalues and triangle list.

See the documentation of the member variables for how the data should be arranged.

Parameters

[in]	mean	The mean used to build the PCA model.
[in]	orthonormal_pca_basis	An orthonormal PCA basis (eigenvectors).
[in]	eigenvalues	The eigenvalues used to build the PCA model.
[in]	triangle_list	An index list of how to assemble the mesh.

Member Function Documentation

◆ draw_sample() [1/3]

template<class RNG >

Eigen::VectorXf eos::morphablemodel::PcaModel::draw_sample	(	RNG &	engine,
		float	sigma = `1.0f`
	)		const

inline

Draws a random sample from the model, where the coefficients are drawn from a standard normal (or with the given standard deviation).

Parameters

[in]	engine	Random number engine used to draw random coefficients.
[in]	sigma	The standard deviation.

Returns: A random sample from the model.

◆ draw_sample() [2/3]

Eigen::VectorXf eos::morphablemodel::PcaModel::draw_sample ( std::vector< double > coefficients ) const

inline

Returns a sample from the model with the given PCA coefficients. The given coefficients should follow a standard normal distribution, i.e. not be "normalised" with their eigenvalues/variances.

Parameters

[in] coefficients The PCA coefficients used to generate the sample.

Returns: A model instance with given coefficients.

◆ draw_sample() [3/3]

Eigen::VectorXf eos::morphablemodel::PcaModel::draw_sample ( std::vector< float > coefficients ) const

inline

Returns a sample from the model with the given PCA coefficients. The given coefficients should follow a standard normal distribution, i.e. not be "normalised" with their eigenvalues/variances.

Parameters

[in] coefficients The PCA coefficients used to generate the sample.

Returns: A model instance with given coefficients.

◆ get_data_dimension()

int eos::morphablemodel::PcaModel::get_data_dimension ( ) const

inline

Returns the dimension of the data, i.e. the number of shape dimensions.

As the data is arranged in a [x y z x y z ...] fashion, dividing this by three yields the number of vertices in the model.

Returns: The dimension of the data.

◆ get_eigenvalue()

float eos::morphablemodel::PcaModel::get_eigenvalue ( int index ) const

inline

Returns a specific eigenvalue.

Parameters

[in] index The index of the eigenvalue to return.

Returns: The eigenvalue.

◆ get_eigenvalues()

const Eigen::VectorXf & eos::morphablemodel::PcaModel::get_eigenvalues ( ) const

inline

Returns the models eigenvalues.

Returns: The eigenvalues.

◆ get_mean()

const Eigen::VectorXf & eos::morphablemodel::PcaModel::get_mean ( ) const

inline

Returns the mean of the model.

Returns: The mean of the model.

◆ get_mean_at_point()

Eigen::Vector3f eos::morphablemodel::PcaModel::get_mean_at_point ( int vertex_index ) const

inline

Return the value of the mean at a given vertex index.

Parameters

[in] vertex_index A vertex index.

Returns: A 3-dimensional vector containing the values at the given vertex index.

◆ get_num_principal_components()

int eos::morphablemodel::PcaModel::get_num_principal_components ( ) const

inline

Returns the number of principal components in the model.

Returns: The number of principal components in the model.

◆ get_orthonormal_pca_basis()

const Eigen::MatrixXf & eos::morphablemodel::PcaModel::get_orthonormal_pca_basis ( ) const

inline

Returns the PCA basis matrix, i.e. the eigenvectors. Each column of the matrix is an eigenvector. The returned basis is orthonormal, i.e. the eigenvectors are not scaled by their respective eigenvalues.

Returns: Returns the orthonormal PCA basis matrix.

◆ get_orthonormal_pca_basis_at_point()

Eigen::MatrixXf eos::morphablemodel::PcaModel::get_orthonormal_pca_basis_at_point ( int vertex_id ) const

inline

Returns the PCA basis for a particular vertex, from the orthonormal basis.

Note: The function does not return the i-th basis vector - it returns all basis vectors, but only the block that is relevant for the vertex vertex_id.

Parameters

[in] vertex_id A vertex index. Make sure it is valid.

Returns: A 3 x num_principal_components matrix of the relevant rows of the original basis.

◆ get_rescaled_pca_basis()

const Eigen::MatrixXf & eos::morphablemodel::PcaModel::get_rescaled_pca_basis ( ) const

inline

Returns the PCA basis matrix, i.e. the eigenvectors. Each column of the matrix is an eigenvector. The returned basis is rescaled, i.e. every eigenvector is rescaled by multiplying it with the square root of its eigenvalue.

Returns: Returns the rescaled PCA basis matrix.

◆ get_rescaled_pca_basis_at_point()

Eigen::MatrixXf eos::morphablemodel::PcaModel::get_rescaled_pca_basis_at_point ( int vertex_id ) const

inline

Returns the PCA basis for a particular vertex, from the rescaled basis.

Note: The function does not return the i-th basis vector - it returns all basis vectors, but only the block that is relevant for the vertex vertex_id.

Todo: Can we return a const & view that points into the original data? I think it's not that easy - if we return e.g. "const auto&", then the compiler complains about returning a reference to a temporary. This will probably help: https://eigen.tuxfamily.org/dox/classEigen_1_1Block.html

Parameters

[in] vertex_id A vertex index. Make sure it is valid.

Returns: A 3 x num_principal_components matrix of the relevant rows of the original basis.

◆ get_triangle_list()

const std::vector< std::array< int, 3 > > & eos::morphablemodel::PcaModel::get_triangle_list ( ) const

inline

Returns a list of triangles on how to assemble the vertices into a mesh.

Returns: The list of triangles to build a mesh.

◆ project()

std::vector< float > eos::morphablemodel::PcaModel::project ( const Eigen::VectorXf & instance ) const

inline

Projects the given data instance into the model space, and returns the PCA coefficients.

Parameters

[in] instance A 3m x 1 col-vector (xyzxyz...)', where m is the number of model-vertices.

Returns: The PCA coefficients of the projected data.

The documentation for this class was generated from the following file:

include/eos/morphablemodel/PcaModel.hpp

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ PcaModel()

Member Function Documentation

◆ draw_sample() [1/3]

◆ draw_sample() [2/3]

◆ draw_sample() [3/3]

◆ get_data_dimension()

◆ get_eigenvalue()

◆ get_eigenvalues()

◆ get_mean()

◆ get_mean_at_point()

◆ get_num_principal_components()

◆ get_orthonormal_pca_basis()

◆ get_orthonormal_pca_basis_at_point()

◆ get_rescaled_pca_basis()

◆ get_rescaled_pca_basis_at_point()

◆ get_triangle_list()

◆ project()