gtsam::EssentialMatrix Class Reference

Detailed Description

An essential matrix is like a Pose3, except with translation up to scale It is named after the 3*3 matrix aEb = [aTb]x aRb from computer vision, but here we choose instead to parameterize it as a (Rot3,Unit3) pair.

We can then non-linearly optimize immediately on this 5-dimensional manifold.

Manifold
enum	{ dimension = 5 }
typedef OptionalJacobian< dimension, dimension >	ChartJacobian
static size_t	Dim ()
size_t	dim () const
EssentialMatrix	retract (const Vector5 &xi) const
	Retract delta to manifold.
Vector5	localCoordinates (const EssentialMatrix &other) const
	Compute the coordinates in the tangent space.

Advanced Interface
class	boost::serialization::access
	Serialization function.

Essential matrix methods
EssentialMatrix	operator* (const Rot3 &cRb, const EssentialMatrix &E)
	Given essential matrix E in camera frame B, convert to body frame C. More...
const Rot3 &	rotation () const
	Rotation.
const Unit3 &	direction () const
	Direction.
const Matrix3 &	matrix () const
	Return 3*3 matrix representation.
const Unit3 &	epipole_a () const
	Return epipole in image_a , as Unit3 to allow for infinity.
Unit3	epipole_b () const
	Return epipole in image_b, as Unit3 to allow for infinity.
GTSAM_EXPORT Point3	transformTo (const Point3 &p, OptionalJacobian< 3, 5 > DE=boost::none, OptionalJacobian< 3, 3 > Dpoint=boost::none) const
	takes point in world coordinates and transforms it to pose with |t|==1 More...
GTSAM_EXPORT EssentialMatrix	rotate (const Rot3 &cRb, OptionalJacobian< 5, 5 > HE=boost::none, OptionalJacobian< 5, 3 > HR=boost::none) const
	Given essential matrix E in camera frame B, convert to body frame C. More...
GTSAM_EXPORT double	error (const Vector3 &vA, const Vector3 &vB, OptionalJacobian< 1, 5 > H=boost::none) const
	epipolar error, algebraic

Constructors and named constructors
static GTSAM_EXPORT EssentialMatrix	FromRotationAndDirection (const Rot3 &aRb, const Unit3 &aTb, OptionalJacobian< 5, 3 > H1=boost::none, OptionalJacobian< 5, 2 > H2=boost::none)
	Named constructor with derivatives.
static GTSAM_EXPORT EssentialMatrix	FromPose3 (const Pose3 &_1P2_, OptionalJacobian< 5, 6 > H=boost::none)
	Named constructor converting a Pose3 with scale to EssentialMatrix (no scale)
template<typename Engine >
static EssentialMatrix	Random (Engine &rng)
	Random, using Rot3::Random and Unit3::Random.
	EssentialMatrix ()
	Default constructor.
	EssentialMatrix (const Rot3 &aRb, const Unit3 &aTb)
	Construct from rotation and translation.
virtual	~EssentialMatrix ()

Public Member Functions
Testable
GTSAM_EXPORT void	print (const std::string &s="") const
	print with optional string
bool	equals (const EssentialMatrix &other, double tol=1e-8) const
	assert equality up to a tolerance

Static Public Member Functions
static Vector3	Homogeneous (const Point2 &p)
	Static function to convert Point2 to homogeneous coordinates.

Friends
Streaming operators
GTSAM_EXPORT friend std::ostream &	operator<< (std::ostream &os, const EssentialMatrix &E)
	stream to stream
GTSAM_EXPORT friend std::istream &	operator>> (std::istream &is, EssentialMatrix &E)
	stream from stream

Member Function Documentation

rotate()

EssentialMatrix gtsam::EssentialMatrix::rotate	(	const Rot3 &	cRb,
		OptionalJacobian< 5, 5 >	HE = boost::none,
		OptionalJacobian< 5, 3 >	HR = boost::none
	)		const

Given essential matrix E in camera frame B, convert to body frame C.

Parameters

cRb	rotation from body frame to camera frame
E	essential matrix E in camera frame C

transformTo()

Point3 gtsam::EssentialMatrix::transformTo	(	const Point3 &	p,
		OptionalJacobian< 3, 5 >	DE = boost::none,
		OptionalJacobian< 3, 3 >	Dpoint = boost::none
	)		const

takes point in world coordinates and transforms it to pose with |t|==1

Parameters

p	point in world coordinates
DE	optional 3*5 Jacobian wrpt to E
Dpoint	optional 3*3 Jacobian wrpt point

Returns

point in pose coordinates

Friends And Related Function Documentation

operator*

EssentialMatrix operator* ( const Rot3 &  cRb, const EssentialMatrix &  E  )

friend

Given essential matrix E in camera frame B, convert to body frame C.

Parameters

cRb	rotation from body frame to camera frame
E	essential matrix E in camera frame C

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

• /Users/dellaert/git/github/gtsam/geometry/EssentialMatrix.h
• /Users/dellaert/git/github/gtsam/geometry/EssentialMatrix.cpp