This class implements utilities function for the tracking library. More...

Static Public Member Functions
static ObjectPoint	backProjectImagePoint (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const Plane3 &plane, const ImagePoint &imagePoint, const bool useDistortionParameters, bool *frontObjectPoint=nullptr)
	Projects one image points onto a 3D plane and returns the resulting 3D object point. More...

static ObjectPoints	backProjectImagePoints (const AnyCamera &anyCamera, const HomogenousMatrix4 &world_T_camera, const Plane3 &plane, const ImagePoint imagePoints, const size_t numberImagePoints, Indices32 frontObjectPointIndices=nullptr)
	Projects a set of given image points onto a 3D plane and returns the resulting 3D object points. More...

static ObjectPoints	backProjectImagePoints (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const Plane3 &plane, const ImagePoint imagePoints, const size_t numberImagePoints, const bool useDistortionParameters, Indices32 frontObjectPointIndices=nullptr)
	Deprecated. More...

static ObjectPoints	backProjectImagePoints (const AnyCamera &anyCamera, const HomogenousMatrix4 &world_T_camera, const Cylinder3 &cylinder, const ImagePoint *imagePoints, const size_t numberImagePoints, Indices32 &intersectingPointIndices)
	Projects a set of given image points onto a 3D cylinder and returns only the resulting 3D object points for rays that intersect the cylinder. More...

static ObjectPoints	backProjectImagePoints (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const Cylinder3 &cylinder, const ImagePoint *imagePoints, const size_t numberImagePoints, const bool useDistortionParameters, Indices32 &intersectingPointIndices)
	Deprecated. More...

static ObjectPoints	backProjectImagePoints (const AnyCamera &anyCamera, const HomogenousMatrix4 &world_T_camera, const Cone3 &cone, const ImagePoint *imagePoints, const size_t numberImagePoints, Indices32 &intersectingPointIndices)
	Projects a set of given image points onto a 3D cone and returns only the resulting 3D object points for rays that intersect the cone. More...

static ObjectPoints	backProjectImagePoints (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const Cone3 &cone, const ImagePoint *imagePoints, const size_t numberImagePoints, const bool useDistortionParameters, Indices32 &intersectingPointIndices)
	Deprecated. More...

static ObjectPoints	backProjectImagePointsDamped (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const Plane3 &plane, const ImagePoint imagePoints, const size_t numberImagePoints, const bool useDistortionParameters, Indices32 frontObjectPointIndices=nullptr)
	Projects a set of given image points onto a 3D plane and returns the resulting 3D object points. More...

static Vectors3	createObjectPoints (const AnyCamera &camera, const HomogenousMatrix4 &world_T_camera, const ConstIndexedAccessor< Vector2 > &imagePoints, const Scalar distance)
	Creates a set of 3D object points for a set of given 2D image points. More...

static ObjectPoints	createObjectPoints (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const ConstIndexedAccessor< ImagePoint > &imagePoints, const bool useDistortionParameters, const Scalar distance)
	Deprecated. More...

static void	triangulateObjectPoints (const AnyCamera &camera0, const AnyCamera &camera1, const HomogenousMatrix4 &world_T_camera0, const HomogenousMatrix4 &world_T_camera1, const ConstIndexedAccessor< Vector2 > &imagePoints0, const ConstIndexedAccessor< Vector2 > &imagePoints1, Vectors3 &objectPoints, Indices32 &validIndices, const bool onlyFrontPoints=true, const Scalar maximalSqrError=Scalar(3 *3))
	Determines 3D object points by triangulating two sets of 2D image points from different camera poses. More...

static Triangles3	backProjectTriangles (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const Plane3 &plane, const Triangle2 *triangles, const size_t numberTriangles, const bool useDistortionParameters)
	Projects a set of given 2D image triangles onto a 3D plane and returns the resulting 3D object triangles. More...

static size_t	countFrontObjectPoints (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &pose, const ObjectPoint *objectPoints, const size_t numberObjectPoints)
	Counts the number of object points that are in front of a given camera. More...

static size_t	countFrontObjectPointsIF (const PinholeCamera &pinholeCamera, const HomogenousMatrix4 &invertedFlippedPose, const ObjectPoint *objectPoints, const size_t numberObjectPoints)
	Counts the number of object points that are in front of a given camera. More...

static size_t	countFrontObjectPoints (const PinholeCamera &cameraFirst, const PinholeCamera &cameraSecond, const HomogenousMatrix4 &poseFirst, const HomogenousMatrix4 &poseSecond, const ImagePoint imagePointsFirst, const ImagePoint imagePointsSecond, const size_t correspondences)
	Counts the number of object points that are visible in two individual camera frames and are located in front of both cameras. More...

static SquareMatrix2	covarianceMatrix (const ImagePoint *imagePoints, const size_t number, const Scalar minimalSigma=0)
	Creates the covariance matrix for a given set of image points. More...

static SquareMatrix2	covarianceMatrix (const ImagePoint *imagePoints, const size_t number, const ImagePoint &meanPoint, const Scalar minimalSigma=0)
	Creates the covariance matrix for a given set of image points. More...

static SquareMatrix2	covarianceMatrix (const ImagePoint imagePoints, const unsigned int indices, const size_t numberIndices, const Scalar minimalSigma, ImagePoint &meanPoint)
	Creates the covariance matrix for a given set of image points. More...

static SquareMatrix2	covarianceMatrix (const Vector2 &direction0, const Scalar sigma0, const Vector2 &direction1, const Scalar sigma1)
	Creates a covariance matrix by two given orthogonal vectors. More...

static SquareMatrix2	covarianceMatrix (const Vector2 &direction0, const Vector2 &direction1)
	Creates a covariance matrix by two given orthogonal vectors. More...

static SquareMatrix2	covarianceMatrix (const Vector2 &majorDirection, const Scalar minimalSigma=1, const Scalar minorFactor=Scalar(0.01))
	Creates a covariance matrix by one given vector representing the major axis. More...

static bool	decomposeCovarianceMatrix (const SquareMatrix2 &covarianceMatrix, Vector2 &direction0, Vector2 &direction1)
	Decomposes a covariance matrix. More...

static bool	isPolygonConvex (const Vector2 *vertices, const size_t size, const bool strict=true)
	Returns whether a polygon of given 2D points is convex. More...

static Scalar	computePolygonArea (const Vector2 *vertices, size_t size)
	Compute the area of a polygon. More...

static Scalar	computePolygonArea (const Vectors2 &vertices)
	Compute the area of a polygon. More...

static Scalar	computePolygonAreaSigned (const Vector2 *vertices, size_t size)
	Compute the signed area of a polygon The value of the area will be positive if the vertices are in counter-clockwise order and negative if they are in clock-wise order. More...

static Scalar	computePolygonAreaSigned (const Vectors2 &vertices)
	Compute the signed area of a polygon The value of the area will be positive if the vertices are in counter-clockwise order and negative if they are in clock-wise order. More...

static bool	isInsideConvexPolygon (const Vector2 *vertices, size_t size, const Vector2 &point)
	Returns whether a given point lies inside a convex polygon. More...

static bool	isInsideConvexPolygon (const Vectors2 &vertices, const Vector2 &point)
	Returns whether a given point lies inside a convex polygon. More...

static bool	intersectConvexPolygons (const Vector2 vertices0, const size_t size0, const Vector2 vertices1, const size_t size1, Vectors2 &intersectedPolygon)
	Computation of the intersection of two convex polygons. More...

static bool	intersectConvexPolygons (const Vectors2 &vertices0, const Vectors2 &vertices1, Vectors2 &intersectedPolygon)
	Computation of the intersection of two convex polygons. More...

template<typename TAccessor >
static ImagePoint	meanImagePoint (const TAccessor &imagePointAccessor)
	Returns the mean position of a set of given 2D points. More...

template<typename TAccessor >
static ObjectPoint	meanObjectPoint (const TAccessor &objectPointAccessor)
	Returns the mean position of a set of given 3D points. More...

template<typename TAccessor >
static ImagePoint	medianImagePoint (const TAccessor &imagePointAccessor)
	Returns the median position of a set of given 2D points. More...

template<typename TAccessor >
static ObjectPoint	medianObjectPoint (const TAccessor &objectPointAccessor)
	Returns the median position of a set of given 3D points. More...

template<typename TAccessor >
static Scalar	medianDistance (const ImagePoint &imagePoint, const TAccessor &imagePointAccessor)
	Returns the median distance between a given 2D object point and a set of given 2D points. More...

template<typename TAccessor >
static Scalar	medianDistance (const ObjectPoint &objectPoint, const TAccessor &objectPointAccessor)
	Returns the median distance between a given 3D object point and a set of given 3D points. More...

static SquareMatrix3	createRandomHomography (const unsigned int width, const unsigned height, const Scalar maxTranslation)
	Create a random homography transformation The homography is created in such a way that points in an output image are mapped into the input image, i.e., inputPoints_i = homography * outputPoints_i. More...

static HomogenousMatrix4	randomCameraPose (const PinholeCamera &pinholeCamera, const Line3 &worldObjectPointRay, const Vector2 &distortedImagePoint, const Scalar distance)
	Deprecated. More...

static HomogenousMatrix4	randomCameraPose (const FisheyeCamera &fisheyeCamera, const Line3 &worldObjectPointRay, const Vector2 &distortedImagePoint, const Scalar distance)
	Deprecated. More...

static HomogenousMatrix4	randomCameraPose (const AnyCamera &anyCamera, const Line3 &worldObjectPointRay, const Vector2 &distortedImagePoint, const Scalar distance)
	Returns a random 6-DOF camera pose for any camera which observes a given 3D object point at a specified 2D image point location while having a specified distance to the 3D object point. More...

Detailed Description

This class implements utilities function for the tracking library.

Member Function Documentation

◆ backProjectImagePoint()

static ObjectPoint Ocean::Geometry::Utilities::backProjectImagePoint	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const Plane3 &	plane,
		const ImagePoint &	imagePoint,
		const bool	useDistortionParameters,
		bool *	frontObjectPoint = `nullptr`
	)

static

Projects one image points onto a 3D plane and returns the resulting 3D object point.

Beware: The back projected point may be located behind the camera due to the position and orientation of the given plane!
Beware: Ensure that the given plane is not parallel with the viewing direction of the camera.

Parameters

pinholeCamera	The pinhole camera object
pose	Pose of the camera
plane	3D plane that is used to determine the position of the back-projected 3D object point
imagePoint	Image point that will be back-projected
useDistortionParameters	True, to use the distortion parameters of the camera
frontObjectPoint	Optional resulting statement whether the resulting object point is located in front of the camera; True, if so

Returns: Resulting 3D object point

◆ backProjectImagePoints() [1/6]

static ObjectPoints Ocean::Geometry::Utilities::backProjectImagePoints	(	const AnyCamera &	anyCamera,
		const HomogenousMatrix4 &	world_T_camera,
		const Cone3 &	cone,
		const ImagePoint *	imagePoints,
		const size_t	numberImagePoints,
		Indices32 &	intersectingPointIndices
	)

static

Projects a set of given image points onto a 3D cone and returns only the resulting 3D object points for rays that intersect the cone.

Parameters

anyCamera	The camera profile defining the projection and distortion
world_T_camera	The transformation from the camera coordinate system to world coordinates, `worldPoint = world_T_camera * cameraPoint`, must be valid
cone	3D cone that is used to determine the position of the back-projected 3D object points
imagePoints	Image points that will be back-projected
numberImagePoints	Number of given image points
intersectingPointIndices	Output indices of all 2D points whose rays actually intersect with the cone

Returns: Resulting 3D object points

◆ backProjectImagePoints() [2/6]

static ObjectPoints Ocean::Geometry::Utilities::backProjectImagePoints	(	const AnyCamera &	anyCamera,
		const HomogenousMatrix4 &	world_T_camera,
		const Cylinder3 &	cylinder,
		const ImagePoint *	imagePoints,
		const size_t	numberImagePoints,
		Indices32 &	intersectingPointIndices
	)

static

Projects a set of given image points onto a 3D cylinder and returns only the resulting 3D object points for rays that intersect the cylinder.

Parameters

anyCamera	The camera profile defining the projection and distortion
world_T_camera	The transformation from the camera coordinate system to world coordinates, `worldPoint = world_T_camera * cameraPoint`, must be valid
cylinder	3D cylinder that is used to determine the position of the back-projected 3D object points
imagePoints	Image points that will be back-projected
numberImagePoints	Number of given image points
intersectingPointIndices	Output indices of all 2D points whose rays actually intersect with the cylinder

Returns: Resulting 3D object points

◆ backProjectImagePoints() [3/6]

static ObjectPoints Ocean::Geometry::Utilities::backProjectImagePoints	(	const AnyCamera &	anyCamera,
		const HomogenousMatrix4 &	world_T_camera,
		const Plane3 &	plane,
		const ImagePoint *	imagePoints,
		const size_t	numberImagePoints,
		Indices32 *	frontObjectPointIndices = `nullptr`
	)

static

Projects a set of given image points onto a 3D plane and returns the resulting 3D object points.

Beware: The back projected points may be located behind the camera due to the position and orientation of the given plane!
Beware: Ensure that the given plane is not parallel with the viewing direction of the camera.

Parameters

anyCamera	The camera profile defining the projection and distortion
world_T_camera	The transformation from the camera coordinate system to world coordinates, `worldPoint = world_T_camera * cameraPoint`, must be valid
plane	3D plane that is used to determine the position of the back-projected 3D object points
imagePoints	Image points that will be back-projected
numberImagePoints	Number of given image points
frontObjectPointIndices	Optional resulting indices of all object points lying in front of the camera

Returns: Resulting 3D object points

See also: backProjectImagePointsDamped().

◆ backProjectImagePoints() [4/6]

static ObjectPoints Ocean::Geometry::Utilities::backProjectImagePoints	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const Cone3 &	cone,
		const ImagePoint *	imagePoints,
		const size_t	numberImagePoints,
		const bool	useDistortionParameters,
		Indices32 &	intersectingPointIndices
	)

static

Deprecated.

Projects a set of given image points onto a 3D cone and returns only the resulting 3D object points for rays that intersect the cone. Optional camera distortion will be clamped at the border of the camera's frame.

Parameters

pinholeCamera	The pinhole camera profile defining the projection and optional distortion
pose	Pose of the camera
cone	3D cone that is used to determine the position of the back-projected 3D object points
imagePoints	Image points that will be back-projected
numberImagePoints	Number of given image points
useDistortionParameters	True, to use the distortion parameters of the camera
intersectingPointIndices	Output indices of all 2D points whose rays actually intersect with the cone

Returns: Resulting 3D object points

◆ backProjectImagePoints() [5/6]

static ObjectPoints Ocean::Geometry::Utilities::backProjectImagePoints	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const Cylinder3 &	cylinder,
		const ImagePoint *	imagePoints,
		const size_t	numberImagePoints,
		const bool	useDistortionParameters,
		Indices32 &	intersectingPointIndices
	)

static

Deprecated.

Projects a set of given image points onto a 3D cylinder and returns only the resulting 3D object points for rays that intersect the cylinder. Optional camera distortion will be clamped at the border of the camera's frame.

Parameters

pinholeCamera	The pinhole camera profile defining the projection and optional distortion
pose	Pose of the camera
cylinder	3D cylinder that is used to determine the position of the back-projected 3D object points
imagePoints	Image points that will be back-projected
numberImagePoints	Number of given image points
useDistortionParameters	True, to use the distortion parameters of the camera
intersectingPointIndices	Output indices of all 2D points whose rays actually intersect with the cylinder

Returns: Resulting 3D object points

◆ backProjectImagePoints() [6/6]

static ObjectPoints Ocean::Geometry::Utilities::backProjectImagePoints	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const Plane3 &	plane,
		const ImagePoint *	imagePoints,
		const size_t	numberImagePoints,
		const bool	useDistortionParameters,
		Indices32 *	frontObjectPointIndices = `nullptr`
	)

static

Deprecated.

Projects a set of given image points onto a 3D plane and returns the resulting 3D object points. Optional camera distortion will be clamped at the border of the camera's frame.
Beware: The back projected points may be located behind the camera due to the position and orientation of the given plane!
Beware: Ensure that the given plane is not parallel with the viewing direction of the camera.

Parameters

pinholeCamera	The pinhole camera profile defining the projection and optional distortion
pose	Pose of the camera
plane	3D plane that is used to determine the position of the back-projected 3D object points
imagePoints	Image points that will be back-projected
numberImagePoints	Number of given image points
useDistortionParameters	True, to use the distortion parameters of the camera
frontObjectPointIndices	Optional resulting indices of all object points lying in front of the camera

Returns: Resulting 3D object points

See also: backProjectImagePointsDamped().

◆ backProjectImagePointsDamped()

static ObjectPoints Ocean::Geometry::Utilities::backProjectImagePointsDamped	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const Plane3 &	plane,
		const ImagePoint *	imagePoints,
		const size_t	numberImagePoints,
		const bool	useDistortionParameters,
		Indices32 *	frontObjectPointIndices = `nullptr`
	)

static

Projects a set of given image points onto a 3D plane and returns the resulting 3D object points.

Optional camera distortion will be damped outside the border of the camera's frame.
Beware: The back projected points may be located behind the camera due to the position and orientation of the given plane!
Beware: Ensure that the given plane is not parallel with the viewing direction of the camera.

Parameters

pinholeCamera	The pinhole camera profile defining the projection and optional distortion
pose	Pose of the camera
plane	3D plane that is used to determine the position of the back-projected 3D object points
imagePoints	Image points that will be back-projected
numberImagePoints	Number of given image points
useDistortionParameters	True, to use the distortion parameters of the camera
frontObjectPointIndices	Optional resulting indices of all object points lying in front of the camera

Returns: Resulting 3D object points

See also: backProjectImagePoints().

◆ backProjectTriangles()

static Triangles3 Ocean::Geometry::Utilities::backProjectTriangles	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const Plane3 &	plane,
		const Triangle2 *	triangles,
		const size_t	numberTriangles,
		const bool	useDistortionParameters
	)

static

Projects a set of given 2D image triangles onto a 3D plane and returns the resulting 3D object triangles.

Parameters

pinholeCamera	The pinhole camera object
pose	Pose of the camera
plane	3D plane that is used to determine the position of the back-projected 3D object points
triangles	Triangles that will be back-projected
numberTriangles	Number of given image points
useDistortionParameters	True, to use the distortion parameters of the camera

Returns: Resulting 3D triangles

◆ computePolygonArea() [1/2]

Scalar Ocean::Geometry::Utilities::computePolygonArea	(	const Vector2 *	vertices,
		size_t	size
	)

inlinestatic

Compute the area of a polygon.

Parameters

vertices	The vertices of a polygon (can be convex or concave but must not be self-intersecting)
size	Number of vertices in the polygon, range: [0, infinity)

Returns: The absolute value of the area of the polygon (this value is undefined if the polygon is self-intersecting), range: [0, infinity)

◆ computePolygonArea() [2/2]

Scalar Ocean::Geometry::Utilities::computePolygonArea ( const Vectors2 & vertices )

inlinestatic

Compute the area of a polygon.

Parameters

vertices The vertices of a polygon (can be convex or concave but must not be self-intersecting)

Returns: The absolute value of the area of the polygon (this value is undefined if the polygon is self-intersecting), range: [0, infinity)

See also: CV::Segmentation::PixelContour::area()

◆ computePolygonAreaSigned() [1/2]

static Scalar Ocean::Geometry::Utilities::computePolygonAreaSigned	(	const Vector2 *	vertices,
		size_t	size
	)

static

Compute the signed area of a polygon The value of the area will be positive if the vertices are in counter-clockwise order and negative if they are in clock-wise order.

Parameters

vertices	The vertices of a polygon (can be convex or concave but must not be self-intersecting)
size	Number of vertices in the polygon, range: [0, infinity)

Returns: The area of the polygon (this value is undefined if the polygon is self-intersecting), range: (-infinity, infinity)

See also: CV::Segmentation::PixelContour::areaSigned()

◆ computePolygonAreaSigned() [2/2]

Scalar Ocean::Geometry::Utilities::computePolygonAreaSigned ( const Vectors2 & vertices )

inlinestatic

Compute the signed area of a polygon The value of the area will be positive if the vertices are in counter-clockwise order and negative if they are in clock-wise order.

Parameters

vertices The vertices of a polygon (can be convex or concave but must not be self-intersecting)

Returns: The area of the polygon (this value is undefined if the polygon is self-intersecting), range: (-infinity, infinity)

◆ countFrontObjectPoints() [1/2]

static size_t Ocean::Geometry::Utilities::countFrontObjectPoints	(	const PinholeCamera &	cameraFirst,
		const PinholeCamera &	cameraSecond,
		const HomogenousMatrix4 &	poseFirst,
		const HomogenousMatrix4 &	poseSecond,
		const ImagePoint *	imagePointsFirst,
		const ImagePoint *	imagePointsSecond,
		const size_t	correspondences
	)

static

Counts the number of object points that are visible in two individual camera frames and are located in front of both cameras.

Parameters

cameraFirst	The camera profile of the first frame, optional distortion parameters of the camera will not be considered
cameraSecond	The camera profile of the first frame, optional distortion parameters of the camera will not be considered
poseFirst	Pose of the first camera
poseSecond	Pose of the second camera
imagePointsFirst	Image points located in the first frame
imagePointsSecond	Image points located in the second frame, each point corresponds to one point in the first frame (correspondence is defined by index)
correspondences	Number of given image point correspondences

Returns: Number of image points located in front of both camera

◆ countFrontObjectPoints() [2/2]

size_t Ocean::Geometry::Utilities::countFrontObjectPoints	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const ObjectPoint *	objectPoints,
		const size_t	numberObjectPoints
	)

inlinestatic

Counts the number of object points that are in front of a given camera.

Parameters

pinholeCamera	The pinhole camera profile to be used
pose	Pose of the camera (extrinsic camera matrix with viewing direction along the negative z-axis)
objectPoints	Object points for which the number of front object points will be determined
numberObjectPoints	The number of provided object points

Returns: Number of object points located in front of the camera

See also: countFrontObjectPointsIF().

◆ countFrontObjectPointsIF()

static size_t Ocean::Geometry::Utilities::countFrontObjectPointsIF	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	invertedFlippedPose,
		const ObjectPoint *	objectPoints,
		const size_t	numberObjectPoints
	)

static

Counts the number of object points that are in front of a given camera.

Parameters

pinholeCamera	The pinhole camera profile to be used
invertedFlippedPose	Inverted and flipped pose of the camera (not the default extrinsic camera matrix)
objectPoints	Object points for which the number of front object points will be determined
numberObjectPoints	The number of provided object points

Returns: Number of object points located in front of the camera

See also: countFrontObjectPoints().

◆ covarianceMatrix() [1/6]

static SquareMatrix2 Ocean::Geometry::Utilities::covarianceMatrix	(	const ImagePoint *	imagePoints,
		const size_t	number,
		const ImagePoint &	meanPoint,
		const Scalar	minimalSigma = `0`
	)

static

Creates the covariance matrix for a given set of image points.

Parameters

imagePoints	Image points for that the covariance will be determined
number	Number of image points
meanPoint	Already determined mean point of the provided image points
minimalSigma	Defining the minimal sigma that is applied, with range [0, infinity)

Returns: Resulting covariance matrix

◆ covarianceMatrix() [2/6]

SquareMatrix2 Ocean::Geometry::Utilities::covarianceMatrix	(	const ImagePoint *	imagePoints,
		const size_t	number,
		const Scalar	minimalSigma = `0`
	)

inlinestatic

Creates the covariance matrix for a given set of image points.

Parameters

imagePoints	Image points for that the covariance will be determined
number	Number of image points
minimalSigma	Defining the minimal sigma that is applied, with range [0, infinity)

Returns: Resulting covariance matrix

◆ covarianceMatrix() [3/6]

static SquareMatrix2 Ocean::Geometry::Utilities::covarianceMatrix	(	const ImagePoint *	imagePoints,
		const unsigned int *	indices,
		const size_t	numberIndices,
		const Scalar	minimalSigma,
		ImagePoint &	meanPoint
	)

static

Creates the covariance matrix for a given set of image points.

Parameters

imagePoints	Image points for that the covariance will be determined
indices	A set of indices that define a subset of the entire image points
numberIndices	Number of provided indices
minimalSigma	Defining the minimal sigma that is applied, with range [0, infinity)
meanPoint	Resulting mean point of the filtered image points

Returns: Resulting covariance matrix

◆ covarianceMatrix() [4/6]

static SquareMatrix2 Ocean::Geometry::Utilities::covarianceMatrix	(	const Vector2 &	direction0,
		const Scalar	sigma0,
		const Vector2 &	direction1,
		const Scalar	sigma1
	)

static

Creates a covariance matrix by two given orthogonal vectors.

Parameters

direction0	Direction of the major axis, with unit length
sigma0	Standard deviation of the major axis (equivalent to the square root of the first eigenvalue of the covariance matrix)
direction1	Direction of the minor axis, perpendicular to the main direction, with unit length
sigma1	Standard deviation of the second direction (equivalent to the square root of the second eigenvalue of the covariance matrix)

Returns: Resulting covariance matrix

◆ covarianceMatrix() [5/6]

static SquareMatrix2 Ocean::Geometry::Utilities::covarianceMatrix	(	const Vector2 &	direction0,
		const Vector2 &	direction1
	)

static

Creates a covariance matrix by two given orthogonal vectors.

Parameters

direction0	Direction of the major axis, with standard deviation as length
direction1	Direction of the minor axis, perpendicular to the main direction, with standard deviation as length

Returns: Resulting covariance matrix

◆ covarianceMatrix() [6/6]

static SquareMatrix2 Ocean::Geometry::Utilities::covarianceMatrix	(	const Vector2 &	majorDirection,
		const Scalar	minimalSigma = `1`,
		const Scalar	minorFactor = `Scalar(0.01)`
	)

static

Creates a covariance matrix by one given vector representing the major axis.

Parameters

majorDirection	Direction of the major axis with standard deviation as length
minimalSigma	Minimal sigma that will be used (will be used if the length of the major direction is too small)
minorFactor	Ratio between the sigma of the minor and the major sigma, with range (0, 1]

Returns: Resulting covariance matrix

◆ createObjectPoints() [1/2]

static Vectors3 Ocean::Geometry::Utilities::createObjectPoints	(	const AnyCamera &	camera,
		const HomogenousMatrix4 &	world_T_camera,
		const ConstIndexedAccessor< Vector2 > &	imagePoints,
		const Scalar	distance
	)

static

Creates a set of 3D object points for a set of given 2D image points.

The 3D object points will lie on the ray which intersects the individual image points and the camera's center of projection.
The distance between 3D object points and the camera's center of projection defines the locations of the object points.

Parameters

camera	The camera profile defining the projection, must be valid
world_T_camera	The pose of the camera, with default camera pointing towards the negative z-space with y-axis upwards, must be valid
imagePoints	Image points that will be back-projected, at least one
distance	The distance between the camera's center of project and the resulting object points, with range (0, infinity)

Returns: The resulting 3D object points, defined in world

◆ createObjectPoints() [2/2]

static ObjectPoints Ocean::Geometry::Utilities::createObjectPoints	(	const PinholeCamera &	pinholeCamera,
		const HomogenousMatrix4 &	pose,
		const ConstIndexedAccessor< ImagePoint > &	imagePoints,
		const bool	useDistortionParameters,
		const Scalar	distance
	)

static

Deprecated.

Creates a set of 3D object points by a set of given 2D image points. The 3D object points are lying on the ray which intersect the individual image points and the camera's center of projection.
The distance between 3D object points and the camera's center of projection defines the locations of the object points.

Parameters

pinholeCamera	The pinhole camera profile defining the projection, must be valid
pose	Pose of the camera, must be valid
imagePoints	Image points that will be back-projected
useDistortionParameters	True, to use the distortion parameters of the camera
distance	The distance between the camera's center of project and the resulting object points, should be in range (0, infinity)

Returns: Resulting 3D object points

◆ createRandomHomography()

static SquareMatrix3 Ocean::Geometry::Utilities::createRandomHomography	(	const unsigned int	width,
		const unsigned	height,
		const Scalar	maxTranslation
	)

static

Create a random homography transformation The homography is created in such a way that points in an output image are mapped into the input image, i.e., inputPoints_i = homography * outputPoints_i.

Parameters

width	The width of the input image, range: [1, infinity)
height	The height of the input image, range: [1, infinity)
maxTranslation	A random global translation that is added to the random homography

Returns: A random homography

◆ decomposeCovarianceMatrix()

static bool Ocean::Geometry::Utilities::decomposeCovarianceMatrix	(	const SquareMatrix2 &	covarianceMatrix,
		Vector2 &	direction0,
		Vector2 &	direction1
	)

static

Decomposes a covariance matrix.

Parameters

covarianceMatrix	Covariance matrix that has to be decomposed
direction0	Resulting major axis, with standard deviation as length (the square root of the first Eigen value)
direction1	Resulting minor axis, with standard deviation as length (the square root of the second Eigen value)

Returns: True, if succeeded

◆ intersectConvexPolygons() [1/2]

static bool Ocean::Geometry::Utilities::intersectConvexPolygons	(	const Vector2 *	vertices0,
		const size_t	size0,
		const Vector2 *	vertices1,
		const size_t	size1,
		Vectors2 &	intersectedPolygon
	)

static

Computation of the intersection of two convex polygons.

Parameters

vertices0	The vertices of the first polygon
size0	The number of vertices in the first polygon, range: [3, infinity)
vertices1	The vertices of the second polygon
size1	The number of vertices of the second polygon, range: [3, infinity)
intersectedPolygon	The resulting intersection represented as a polygon

Returns: True, if succeeded

◆ intersectConvexPolygons() [2/2]

bool Ocean::Geometry::Utilities::intersectConvexPolygons	(	const Vectors2 &	vertices0,
		const Vectors2 &	vertices1,
		Vectors2 &	intersectedPolygon
	)

inlinestatic

Computation of the intersection of two convex polygons.

Parameters

vertices0	The vertices of the first polygon, size: [3, infinity)
vertices1	The vertices of the second polygon, size: [3, infinity)
intersectedPolygon	The resulting intersection represented as a polygon

Returns: True, if succeeded

◆ isInsideConvexPolygon() [1/2]

static bool Ocean::Geometry::Utilities::isInsideConvexPolygon	(	const Vector2 *	vertices,
		size_t	size,
		const Vector2 &	point
	)

static

Returns whether a given point lies inside a convex polygon.

For polygons consisting of less than 3 points, this function always returns false. A point located on an edge of the polygon is considered as inside the polygon.

Parameters

vertices	The vertices of a convex polygon, can be nullptr if size == 0
size	The number of vertices in the polygon, range: [0, infinity)
point	The point to be tested

Returns: True, if the point is inside the polygon, otherwise false

◆ isInsideConvexPolygon() [2/2]

bool Ocean::Geometry::Utilities::isInsideConvexPolygon	(	const Vectors2 &	vertices,
		const Vector2 &	point
	)

inlinestatic

Returns whether a given point lies inside a convex polygon.

For polygons consisting of less than 3 points, this function always returns false. A point located on an edge of the polygon is considered as inside the polygon.

Parameters

vertices	The vertices of a convex polygon, can be nullptr if size == 0
point	The point to be tested

Returns: True, if the point is inside the polygon, otherwise false

◆ isPolygonConvex()

static bool Ocean::Geometry::Utilities::isPolygonConvex	(	const Vector2 *	vertices,
		const size_t	size,
		const bool	strict = `true`
	)

static

Returns whether a polygon of given 2D points is convex.

A polygon consisting of 0 to 2 vertices is considered to be convex.

Parameters

vertices	The vertices of the polygon, can be nullptr if size == 0
size	Number of vertices in the polygon, range: [0, infinity)
strict	If true, the polygon is tested for strict convexity (i.e. every internal angle is less than 180 degrees), otherwise internal angles can be up equal to 180 degrees

Returns: True if the polygon is convex, otherwise false

◆ meanImagePoint()

template<typename TAccessor >

ImagePoint Ocean::Geometry::Utilities::meanImagePoint ( const TAccessor & imagePointAccessor )

inlinestatic

Returns the mean position of a set of given 2D points.

Parameters

imagePointAccessor The accessor providing the image points, at least one

Returns: The resulting mean position

Template Parameters

TAccessor The data type of the accessor providing the image points

◆ meanObjectPoint()

template<typename TAccessor >

ObjectPoint Ocean::Geometry::Utilities::meanObjectPoint ( const TAccessor & objectPointAccessor )

inlinestatic

Returns the mean position of a set of given 3D points.

Parameters

objectPointAccessor The accessor for the object points, at least one

Returns: The resulting median position

Template Parameters

TAccessor The data type of the accessor providing the object points

◆ medianDistance() [1/2]

template<typename TAccessor >

Scalar Ocean::Geometry::Utilities::medianDistance	(	const ImagePoint &	imagePoint,
		const TAccessor &	imagePointAccessor
	)

inlinestatic

Returns the median distance between a given 2D object point and a set of given 2D points.

Parameters

imagePoint	The image point to which the median distance will be determined
imagePointAccessor	The accessor for the image points, at least one

Returns: The resulting median distance

Template Parameters

TAccessor The data type of the accessor providing the image points

◆ medianDistance() [2/2]

template<typename TAccessor >

Scalar Ocean::Geometry::Utilities::medianDistance	(	const ObjectPoint &	objectPoint,
		const TAccessor &	objectPointAccessor
	)

inlinestatic

Returns the median distance between a given 3D object point and a set of given 3D points.

Parameters

objectPoint	The object point to which the median distance will be determined
objectPointAccessor	The accessor for the object points, at least one

Returns: The resulting median distance

Template Parameters

TAccessor The data type of the accessor providing the object points

◆ medianImagePoint()

template<typename TAccessor >

ImagePoint Ocean::Geometry::Utilities::medianImagePoint ( const TAccessor & imagePointAccessor )

inlinestatic

Returns the median position of a set of given 2D points.

The resulting position is determined by a component-wise median determination.

Parameters

imagePointAccessor The accessor for the image points, at least one

Returns: The resulting median position

Template Parameters

TAccessor The data type of the accessor providing the object points

◆ medianObjectPoint()

template<typename TAccessor >

ObjectPoint Ocean::Geometry::Utilities::medianObjectPoint ( const TAccessor & objectPointAccessor )

inlinestatic

Returns the median position of a set of given 3D points.

The resulting position is determined by a component-wise median determination.

Parameters

objectPointAccessor The accessor for the object points, at least one

Returns: The resulting median position

Template Parameters

TAccessor The data type of the accessor providing the object points

◆ randomCameraPose() [1/3]

static HomogenousMatrix4 Ocean::Geometry::Utilities::randomCameraPose	(	const AnyCamera &	anyCamera,
		const Line3 &	worldObjectPointRay,
		const Vector2 &	distortedImagePoint,
		const Scalar	distance
	)

static

Returns a random 6-DOF camera pose for any camera which observes a given 3D object point at a specified 2D image point location while having a specified distance to the 3D object point.

Parameters

anyCamera	The camera profile defining the projection, must be valid
worldObjectPointRay	The 3D ray starting at the 3D object point and pointing towards the camera's center of projection, must be valid
distortedImagePoint	The 2D image point within the camera image, with range [0, anyCamera.width())x[0, anyCamera.height())
distance	The desired distance between 3D object point and camera (center of projection), with range (0, infinity)

Returns: The 6-DOF camera pose matching with the specified constraints, will be world_T_camera

◆ randomCameraPose() [2/3]

static HomogenousMatrix4 Ocean::Geometry::Utilities::randomCameraPose	(	const FisheyeCamera &	fisheyeCamera,
		const Line3 &	worldObjectPointRay,
		const Vector2 &	distortedImagePoint,
		const Scalar	distance
	)

static

Deprecated.

Returns a random 6-DOF camera pose for a fisheye camera which observes a given 3D object point at a specified 2D image point location while having a specified distance to the 3D object point.

Parameters

fisheyeCamera	The fisheye camera profile defining the projection, must be valid
worldObjectPointRay	The 3D ray starting at the 3D object point and pointing towards the camera's center of projection, must be valid
distortedImagePoint	The 2D image point within the fisheye camera image, with range [0, fisheyeCamera.width())x[0, fisheyeCamera.height())
distance	The desired distance between 3D object point and camera (center of projection), with range (0, infinity)

Returns: The 6-DOF camera pose matching with the specified constraints, will be world_T_camera

◆ randomCameraPose() [3/3]

static HomogenousMatrix4 Ocean::Geometry::Utilities::randomCameraPose	(	const PinholeCamera &	pinholeCamera,
		const Line3 &	worldObjectPointRay,
		const Vector2 &	distortedImagePoint,
		const Scalar	distance
	)

static

Deprecated.

Returns a random 6-DOF camera pose for a pinhole camera which observes a given 3D object point at a specified 2D image point location while having a specified distance to the 3D object point.

Parameters

pinholeCamera	The pinhole camera profile defining the projection, must be valid
worldObjectPointRay	The 3D ray starting at the 3D object point and pointing towards the camera's center of projection, must be valid
distortedImagePoint	The 2D image point within the fisheye camera image, with range [0, fisheyeCamera.width())x[0, fisheyeCamera.height())
distance	The desired distance between 3D object point and camera (center of projection), with range (0, infinity)

Returns: The 6-DOF camera pose matching with the specified constraints, will be world_T_camera

◆ triangulateObjectPoints()

static void Ocean::Geometry::Utilities::triangulateObjectPoints	(	const AnyCamera &	camera0,
		const AnyCamera &	camera1,
		const HomogenousMatrix4 &	world_T_camera0,
		const HomogenousMatrix4 &	world_T_camera1,
		const ConstIndexedAccessor< Vector2 > &	imagePoints0,
		const ConstIndexedAccessor< Vector2 > &	imagePoints1,
		Vectors3 &	objectPoints,
		Indices32 &	validIndices,
		const bool	onlyFrontPoints = `true`,
		const Scalar	maximalSqrError = `Scalar(3 *3)`
	)

static

Determines 3D object points by triangulating two sets of 2D image points from different camera poses.

Parameters

camera0	The camera profile of the first camera, must be valid
camera1	The camera profile of the second camera, must be valid
world_T_camera0	The camera pose of the first camera, with default camera pointing towards the negative z-space with y-axis upwards, must be valid
world_T_camera1	The camera pose of the second camera, with default camera pointing towards the negative z-space with y-axis upwards, must be valid
imagePoints0	The 2D image points located in the first camera
imagePoints1	The 2D image points located in the second camera, each point must have a corresponding point in the first camera
objectPoints	The resulting valid 3D object points, does not provide invalid object points
validIndices	The resulting indices of the valid point correspondences for which a 3D object points could be determined, one index of reach resulting 3D object point
onlyFrontPoints	True, if only front object points are determined
maximalSqrError	The maximal squared projection pixel error for valid object points

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

geometry/Utilities.h

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ backProjectImagePoint()

◆ backProjectImagePoints() [1/6]

◆ backProjectImagePoints() [2/6]

◆ backProjectImagePoints() [3/6]

◆ backProjectImagePoints() [4/6]

◆ backProjectImagePoints() [5/6]

◆ backProjectImagePoints() [6/6]

◆ backProjectImagePointsDamped()

◆ backProjectTriangles()

◆ computePolygonArea() [1/2]

◆ computePolygonArea() [2/2]

◆ computePolygonAreaSigned() [1/2]

◆ computePolygonAreaSigned() [2/2]

◆ countFrontObjectPoints() [1/2]

◆ countFrontObjectPoints() [2/2]

◆ countFrontObjectPointsIF()

◆ covarianceMatrix() [1/6]

◆ covarianceMatrix() [2/6]

◆ covarianceMatrix() [3/6]

◆ covarianceMatrix() [4/6]

◆ covarianceMatrix() [5/6]

◆ covarianceMatrix() [6/6]

◆ createObjectPoints() [1/2]

◆ createObjectPoints() [2/2]

◆ createRandomHomography()

◆ decomposeCovarianceMatrix()

◆ intersectConvexPolygons() [1/2]

◆ intersectConvexPolygons() [2/2]

◆ isInsideConvexPolygon() [1/2]

◆ isInsideConvexPolygon() [2/2]

◆ isPolygonConvex()

◆ meanImagePoint()

◆ meanObjectPoint()

◆ medianDistance() [1/2]

◆ medianDistance() [2/2]

◆ medianImagePoint()

◆ medianObjectPoint()

◆ randomCameraPose() [1/3]

◆ randomCameraPose() [2/3]

◆ randomCameraPose() [3/3]

◆ triangulateObjectPoints()