alvar::TrifocalTensor Class Reference

Trifocal tensor works for three images like a fundamental matrix works for two images. More...

`#include <TrifocalTensor.h>`

## Public Member Functions

void computeTensor (const Pose &P1, const Pose &P2)
Initializes the tensor from identity pose and two other known poses. More...

void computeTensor (const Pose &P0, const Pose &P1, const Pose &P2)
Initializes the tensor from three known poses. More...

void project (const CvPoint2D64f &p0, const CvPoint2D64f &p1, CvPoint2D64f &p2)
Computes the projection of a point in the third pose. More...

double projectError (const CvPoint2D64f &p0, const CvPoint2D64f &p1, const CvPoint2D64f &p2)
Computes how much three points differ from the tensor. More...

TrifocalTensor ()

TrifocalTensor (const Pose &P1, const Pose &P2)
Constructs a tensor from identity pose and two other known poses. See computeTensor. More...

TrifocalTensor (const Pose &P0, const Pose &P1, const Pose &P2)
Constructs a tensor from three known poses. See computeTensor. More...

~TrifocalTensor ()

## Private Member Functions

double projectAxis (const CvPoint2D64f &p0, const CvPoint2D64f &p1, int l)

## Private Attributes

double T [3][3][3]

## Detailed Description

Trifocal tensor works for three images like a fundamental matrix works for two images.

Given three camera poses P0, P1, P2 and a 3D point X, we can calculate a trifocal tensor T(P0, P1, P2). The tensor relates projections of X in P0, P1 and P2 in such a way that when any two projections are known the third projection can be calculated.

This implementation of trifocal tensor assumes that the camera poses P0, P1 and P2 are known. When projections of X in P0 and P1 are known the projection in P2 can be computed using the tensor.

The current implementation cannot be used to directly compute the tensor from point correspondencies alone. The implementation can be used for example for optimizing three camera poses when point correspondences are known in the three images by minimizing the trifocal 'projection error' computed by projectError -method.

Pose P1, P2; // P0 is identity pose.
CvPoint2D64f proj0, proj1, proj2; // A 3D point projected with poses P0, P1 and P2.
TrifocalTensor T(P1, P2);
CvPoint2D64f test2;
T.project(proj0, proj1, test2);
assert(proj2.x == test2.x);
assert(proj2.y == test2.y);
assert(proj2.z == test2.z);

Definition at line 70 of file TrifocalTensor.h.

## Constructor & Destructor Documentation

 alvar::TrifocalTensor::TrifocalTensor ( )

Definition at line 28 of file TrifocalTensor.cpp.

 alvar::TrifocalTensor::TrifocalTensor ( const Pose & P1, const Pose & P2 )

Constructs a tensor from identity pose and two other known poses. See computeTensor.

Parameters
 P1 The second pose relative to the first pose. P2 The third pose relative to the first pose.

Definition at line 31 of file TrifocalTensor.cpp.

 alvar::TrifocalTensor::TrifocalTensor ( const Pose & P0, const Pose & P1, const Pose & P2 )

Constructs a tensor from three known poses. See computeTensor.

Parameters
 P0 The first camera pose. P1 The second pose relative to the first pose. P2 The third pose relative to the first pose.

Definition at line 35 of file TrifocalTensor.cpp.

 alvar::TrifocalTensor::~TrifocalTensor ( )

Definition at line 39 of file TrifocalTensor.cpp.

## Member Function Documentation

 void alvar::TrifocalTensor::computeTensor ( const Pose & P1, const Pose & P2 )

Initializes the tensor from identity pose and two other known poses.

The first pose is identity and the two other poses are relative translations/rotation between the first and the second pose and between the first and the third pose.

Parameters
 P1 The second pose relative to the first pose. P2 The third pose relative to the first pose.

Definition at line 42 of file TrifocalTensor.cpp.

 void alvar::TrifocalTensor::computeTensor ( const Pose & P0, const Pose & P1, const Pose & P2 )

Initializes the tensor from three known poses.

Parameters
 P0 The first camera pose. P1 The second pose relative to the first pose. P2 The third pose relative to the first pose.

Definition at line 74 of file TrifocalTensor.cpp.

 void alvar::TrifocalTensor::project ( const CvPoint2D64f & p0, const CvPoint2D64f & p1, CvPoint2D64f & p2 )

Computes the projection of a point in the third pose.

When we have three images, each a projection of a scene from the three different camera poses (identity and the two poses that were used to initialize the tensor) and a 2D point correspondence between the first and the second images, a position in the third image is computed.

Parameters
 p0 2D position in a image projected from the first pose. p1 2D position in a image projected from the second pose. p2 Computed 2D position in a image projected form the third pose.

Definition at line 183 of file TrifocalTensor.cpp.

 double alvar::TrifocalTensor::projectAxis ( const CvPoint2D64f & p0, const CvPoint2D64f & p1, int l )
private

Definition at line 94 of file TrifocalTensor.cpp.

 double alvar::TrifocalTensor::projectError ( const CvPoint2D64f & p0, const CvPoint2D64f & p1, const CvPoint2D64f & p2 )

Computes how much three points differ from the tensor.

When we have three images, each a projection of a scene from the three different camera poses (identity and the two poses that were used to initialize the tensor) and a 2D point correspondence between the first the second and the third images, we compute how well the three projections match with the trifocal tensor.

When the third point lies exactly where the tensor projects the first two points, the returned error is zero.

Parameters
 p0 2D position in a image projected from the first pose. p1 2D position in a image projected from the second pose. p2 2D position in a image projected form the third pose.
Returns
Squared projection error.

Definition at line 191 of file TrifocalTensor.cpp.

## Member Data Documentation

 double alvar::TrifocalTensor::T[3][3][3]
private

Definition at line 72 of file TrifocalTensor.h.

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

ar_track_alvar
Author(s): Scott Niekum
autogenerated on Mon Jun 10 2019 12:47:05