This class implements self-calibration for multiple views. More...

#include <MultipleViewGeometry.h>

Static Public Member Functions
static bool	findCommonIntrinsicsFromProjectionMatricesIF (const ConstIndexedAccessor< HomogenousMatrix4 > &iFlippedProjectionMatrices, SquareMatrix3 &cameraIntrinsics, SquareMatrix4 Q=nullptr, SquareMatrix3 omega=nullptr)
	Estimate the common intrinsic camera matrix based on an Absolute Conic omega (ω): omega = K * K^T — (ω_j = ω = KK^T).

static bool	findCommonIntrinsicsFromProjectionMatricesIF (const ConstIndexedAccessor< HomogenousMatrix4 > &iFlippedProjectionMatrices, const unsigned int imageWidth, const unsigned int imageHeight, SquareMatrix3 &cameraIntrinsics, SquareMatrix4 Q=nullptr, SquareMatrix3 omega=nullptr)
	Estimate a common intrinsic camera matrix based on an Absolute Conic ω: ω_j = ω = KK^T.

static bool	determineAbsoluteDualQuadricLinearIF (const ConstIndexedAccessor< HomogenousMatrix4 > &iFlippedProjectionMatrices, SquareMatrix4 &matrixQ, const unsigned int imageWidth, const unsigned int imageHeight, bool equalFxFy=true)
	Estimates the absolute dual quadric Q_infinity (Q∞) from several projection-pose matrices by solving a linear system: omega = P_j * Q_infinity * P_j^T — (ω_j = P_j * Q∞ * P_j^T).

static bool	intrinsicsFromAbsoluteDualQuadricIF (const SquareMatrix4 &symmetricQ, const ConstIndexedAccessor< HomogenousMatrix4 > &iFlippedProjectionMatrices, SquareMatrix3 *intrinsics)
	Determines individual intrinsic camera matrices from a known absolute dual quadric Q_infinity (Q∞) and corresponding camera-projection-pose matrices: omega_j = P_j * Q_infinity * P_J^T = K_j * K_j^T — (ω_j = P_j * Q∞ * P_J^T = K_j * K_j^T).

static bool	transformProjectiveToMetricIF (const SquareMatrix4 &Q, const ConstIndexedAccessor< HomogenousMatrix4 > &iFlippedProjectionMatrices, HomogenousMatrix4 iFlippedMetricProjectionMatrices, SquareMatrix4 transformation=nullptr)
	Transforms a projective reconstruction towards a metric reconstruction.

static bool	metricProjectionMatricesToPosesIF (const ConstIndexedAccessor< HomogenousMatrix4 > &metricProjectionsIF, const SquareMatrix3 &intrinsic, HomogenousMatrix4 *posesIF)
	Decomposes metric camera projection matrices all containing/sharing the same known camera matrix (intrinsic camera matrix) into (inverted and flipped) camera poses simply by applying the inverted intrinsic matrix.

Static Protected Member Functions
static bool	transformProjectionsZeroPrinciplePoint (const ConstIndexedAccessor< HomogenousMatrix4 > &iFlippedProjectionMatrices, const unsigned int imageWidth, const unsigned int imageHeight, HomogenousMatrix4 iFlippedNormalizedProjectionMatrices, SquareMatrix3 backTransformation=nullptr)
	Transforms an inverted and flipped camera projection matrix P = K * [R\|t] in a way that the principle point of the camera profile (the camera intrinsics) is zero.

static bool	getTransformProjectiveToMetricMatrix (const SquareMatrix4 &Q, SquareMatrix4 &transformation)
	Determines the perspective transformation to get a metric reconstruction.

Static Private Member Functions
static bool	upperTriangleCholeskyDecomposition (const SquareMatrix3 &omega, SquareMatrix3 &cameraIntrinsic)
	Performs the decomposition of an absolute conic omega (ω) into the intrinsic camera matrix: omega = K * K^T — (ω = K * K^T), where K is the camera matrix (which is a upper triangular matrix).

static Matrix	createLinearSystemForAbsoluteDualQuadric (const unsigned int omegaRowIndex, const unsigned int omegaColumnIndex, const HomogenousMatrix4 &iFlippedProjectionMatrix)
	Creates a line for the linear system for the zero condition of absolute conic ω(i, j).

Detailed Description

This class implements self-calibration for multiple views.

Member Function Documentation

◆ createLinearSystemForAbsoluteDualQuadric()

static Matrix Ocean::Geometry::AutoCalibration::createLinearSystemForAbsoluteDualQuadric	(	const unsigned int	omegaRowIndex,
		const unsigned int	omegaColumnIndex,
		const HomogenousMatrix4 &	iFlippedProjectionMatrix
	)

staticprivate

Creates a line for the linear system for the zero condition of absolute conic ω(i, j).

The line contains values of the upper triangle entities of absolute dual quadric matrix Q_infinity — (Q∞): ω(i, j) = [P * Q∞ * P^T](i, j) = 0

Parameters

omegaRowIndex	Row index of absolute conic ω
omegaColumnIndex	Column index of absolute conic ω
iFlippedProjectionMatrix	The inverted and flipped camera projection matrix, must be valid

Returns: A line matrix [1x10] containing the values of the upper triangle entities of the symmetric matrix Q∞

◆ determineAbsoluteDualQuadricLinearIF()

static bool Ocean::Geometry::AutoCalibration::determineAbsoluteDualQuadricLinearIF	(	const ConstIndexedAccessor< HomogenousMatrix4 > &	iFlippedProjectionMatrices,
		SquareMatrix4 &	matrixQ,
		const unsigned int	imageWidth,
		const unsigned int	imageHeight,
		bool	equalFxFy = `true`
	)

static

Estimates the absolute dual quadric Q_infinity (Q∞) from several projection-pose matrices by solving a linear system:
omega = P_j * Q_infinity * P_j^T — (ω_j = P_j * Q∞ * P_j^T).

Here, we assume no skew and the principle point in the center of the camera frame.

Parameters

iFlippedProjectionMatrices	The inverted and flipped camera projection matrices [K \| P0], [K \| P1], [K \| P2], ..., with Pi = [Ri \| ti], at least 3
matrixQ	Resulting absolute dual quadric Q_infinity — (Q∞)
imageWidth	Width of the camera frame in pixel, with range [1, infinity)
imageHeight	Height of the camera frame in pixel, with range [1, infinity)
equalFxFy	Forces equal focal length in both dimension

Returns: True, if succeeded

See also: findCommonIntrinsicsFromProjectionMatricesIF()

◆ findCommonIntrinsicsFromProjectionMatricesIF() [1/2]

static bool Ocean::Geometry::AutoCalibration::findCommonIntrinsicsFromProjectionMatricesIF	(	const ConstIndexedAccessor< HomogenousMatrix4 > &	iFlippedProjectionMatrices,
		const unsigned int	imageWidth,
		const unsigned int	imageHeight,
		SquareMatrix3 &	cameraIntrinsics,
		SquareMatrix4 *	Q = `nullptr`,
		SquareMatrix3 *	omega = `nullptr`
	)

static

Estimate a common intrinsic camera matrix based on an Absolute Conic ω:
ω_j = ω = KK^T.

Solve a linear system by assuming zero skew, a known principle point (centered in the camera frame) and equal focal length for each ω

Parameters

iFlippedProjectionMatrices	Inverted and flipped camera projection matrices [K \| P0], [K \| P1], [K \| P2], ..., with Pi = [Ri \| ti], at least 3
imageWidth	Width of the camera frame in pixel, with range [1, infinity)
imageHeight	Height of the camera frame in pixel, with range [1, infinity)
cameraIntrinsics	Resulting camera intrinsics matrix
Q	Resulting absolute dual quadric Q∞, optionally
omega	Resulting absolute conic &omega, optionally

Returns: True, if succeeded

See also: findAbsoluteDualQuadricLinear()

◆ findCommonIntrinsicsFromProjectionMatricesIF() [2/2]

static bool Ocean::Geometry::AutoCalibration::findCommonIntrinsicsFromProjectionMatricesIF	(	const ConstIndexedAccessor< HomogenousMatrix4 > &	iFlippedProjectionMatrices,
		SquareMatrix3 &	cameraIntrinsics,
		SquareMatrix4 *	Q = `nullptr`,
		SquareMatrix3 *	omega = `nullptr`
	)

static

Estimate the common intrinsic camera matrix based on an Absolute Conic omega (ω):
omega = K * K^T — (ω_j = ω = KK^T).

Solve a linear system by assuming equal entities in each ω

Parameters

iFlippedProjectionMatrices	The inverted and flipped camera projection matrices [K * P0], [K * P1], [K * P2], ..., with Pi = [Ri \| ti], at least 3
cameraIntrinsics	Resulting intrinsic camera matrix
Q	Optional resulting absolute dual quadric Q∞
omega	Optional resulting absolute conic &omega

Returns: True, if succeeded

See also: findAbsoluteDualQuadricLinear()

◆ getTransformProjectiveToMetricMatrix()

static bool Ocean::Geometry::AutoCalibration::getTransformProjectiveToMetricMatrix	(	const SquareMatrix4 &	Q,
		SquareMatrix4 &	transformation
	)

staticprotected

Determines the perspective transformation to get a metric reconstruction.

Q∞ = H * Î * H^T, factorized by eigen decomposition.

Parameters

Q	Absolute dual quadric Q∞
transformation	Resulting perspective transformation H

Returns: True, if succeeded

See also: transformProjectiveToMetric()

◆ intrinsicsFromAbsoluteDualQuadricIF()

static bool Ocean::Geometry::AutoCalibration::intrinsicsFromAbsoluteDualQuadricIF	(	const SquareMatrix4 &	symmetricQ,
		const ConstIndexedAccessor< HomogenousMatrix4 > &	iFlippedProjectionMatrices,
		SquareMatrix3 *	intrinsics
	)

static

Determines individual intrinsic camera matrices from a known absolute dual quadric Q_infinity (Q∞) and corresponding camera-projection-pose matrices:
omega_j = P_j * Q_infinity * P_J^T = K_j * K_j^T — (ω_j = P_j * Q∞ * P_J^T = K_j * K_j^T).

The Cholesky decomposition is applied to factorize omega into K.

Parameters

symmetricQ	The absolute dual quadric q_infinity which is symmetric
iFlippedProjectionMatrices	The inverted and flipped camera projection pose matrices
intrinsics	The resulting intrinsic camera matrices, one for each projection pose matrix

Returns: True, if succeeded

See also: findAbsoluteDualQuadricLinear(); transformProjectionsZeroPrinciplePoint()

◆ metricProjectionMatricesToPosesIF()

static bool Ocean::Geometry::AutoCalibration::metricProjectionMatricesToPosesIF	(	const ConstIndexedAccessor< HomogenousMatrix4 > &	metricProjectionsIF,
		const SquareMatrix3 &	intrinsic,
		HomogenousMatrix4 *	posesIF
	)

static

Decomposes metric camera projection matrices all containing/sharing the same known camera matrix (intrinsic camera matrix) into (inverted and flipped) camera poses simply by applying the inverted intrinsic matrix.

Based on the following equation: P_metric = K * [R t] we can determine the camera poses by: [R t] = K^-1 * p_metric.

Parameters

metricProjectionsIF	The inverted and flipped metric camera projection matrices
intrinsic	The already known intrinsic camera matrix K
posesIF	The resulting inverted and flipped camera poses, one for each given camera projection matrix

Returns: True, if succeeded

See also: transformProjectiveToMetric().

◆ transformProjectionsZeroPrinciplePoint()

static bool Ocean::Geometry::AutoCalibration::transformProjectionsZeroPrinciplePoint	(	const ConstIndexedAccessor< HomogenousMatrix4 > &	iFlippedProjectionMatrices,
		const unsigned int	imageWidth,
		const unsigned int	imageHeight,
		HomogenousMatrix4 *	iFlippedNormalizedProjectionMatrices,
		SquareMatrix3 *	backTransformation = `nullptr`
	)

staticprotected

Transforms an inverted and flipped camera projection matrix P = K * [R|t] in a way that the principle point of the camera profile (the camera intrinsics) is zero.

P' = T * P.

Parameters

iFlippedProjectionMatrices	Inverted and flipped camera projection matrices, at least one
imageWidth	Width of image in pixel, with range [1, infinity)
imageHeight	Height of image in pixel, with range [1, infinity)
iFlippedNormalizedProjectionMatrices	Resulting normalized inverted and flipped camera projection matrices, one for each given camera projection matrix
backTransformation	Optional resulting back transformation matrix T^-1

Returns: True, if succeeded

See also: transformProjectiveToMetric()

◆ transformProjectiveToMetricIF()

static bool Ocean::Geometry::AutoCalibration::transformProjectiveToMetricIF	(	const SquareMatrix4 &	Q,
		const ConstIndexedAccessor< HomogenousMatrix4 > &	iFlippedProjectionMatrices,
		HomogenousMatrix4 *	iFlippedMetricProjectionMatrices,
		SquareMatrix4 *	transformation = `nullptr`
	)

static

Transforms a projective reconstruction towards a metric reconstruction.

Q∞ = H * Î * H^T.
P_metric = P * H.

Parameters

Q	Absolute dual quadric Q∞
iFlippedProjectionMatrices	The camera projection matrices (inverted flipped)
iFlippedMetricProjectionMatrices	Resulting metric projection matrices (inverted flipped)
transformation	Optional resulting perspective transformation matrix

Returns: True, if succeeded

See also: getTransformProjectiveToMetricMatrix()

◆ upperTriangleCholeskyDecomposition()

static bool Ocean::Geometry::AutoCalibration::upperTriangleCholeskyDecomposition	(	const SquareMatrix3 &	omega,
		SquareMatrix3 &	cameraIntrinsic
	)

staticprivate

Performs the decomposition of an absolute conic omega (ω) into the intrinsic camera matrix:
omega = K * K^T — (ω = K * K^T), where K is the camera matrix (which is a upper triangular matrix).

The Cholesky decomposition is applied.

Parameters

omega	The (symmetric) absolute conic to be decomposed (ω)
cameraIntrinsic	The resulting intrinsic camera matrix

Returns: True, if succeeded

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

MultipleViewGeometry.h

Static Public Member Functions

Static Protected Member Functions

Static Private Member Functions

Detailed Description

Member Function Documentation

◆ createLinearSystemForAbsoluteDualQuadric()

◆ determineAbsoluteDualQuadricLinearIF()

◆ findCommonIntrinsicsFromProjectionMatricesIF() [1/2]

◆ findCommonIntrinsicsFromProjectionMatricesIF() [2/2]

◆ getTransformProjectiveToMetricMatrix()

◆ intrinsicsFromAbsoluteDualQuadricIF()

◆ metricProjectionMatricesToPosesIF()

◆ transformProjectionsZeroPrinciplePoint()

◆ transformProjectiveToMetricIF()

◆ upperTriangleCholeskyDecomposition()