#include <visp3/blob/vpDot.h>

Inheritance diagram for vpDot:

Public Types
enum	vpConnexityType { CONNEXITY_4, CONNEXITY_8 }

Public Member Functions
	vpDot ()

	vpDot (const vpImagePoint &ip)

	vpDot (const vpDot &d)

virtual	~vpDot ()

void	display (const vpImage< unsigned char > &I, vpColor color=vpColor::red, unsigned int thickness=1) const

vpColVector	get_nij () const

double	getArea () const

vpRect	getBBox () const

vpImagePoint	getCog () const

std::list< vpImagePoint >	getEdges () const

std::list< vpImagePoint >	getConnexities () const

double	getGamma () const

double	getGrayLevelPrecision () const

double	getMaxDotSize () const

double	getMeanGrayLevel () const

vpPolygon	getPolygon () const

unsigned int	getWidth () const

unsigned int	getHeight () const

void	initTracking (const vpImage< unsigned char > &I)

void	initTracking (const vpImage< unsigned char > &I, const vpImagePoint &ip)

void	initTracking (const vpImage< unsigned char > &I, const vpImagePoint &ip, unsigned int gray_level_min, unsigned int gray_level_max)

vpDot &	operator= (const vpDot &d)

bool	operator== (const vpDot &d) const

bool	operator!= (const vpDot &d) const

void	print (std::ostream &os)

void	setCog (const vpImagePoint &ip)

void	setComputeMoments (bool activate)

void	setConnexity (vpConnexityType type)

void	setMaxDotSize (double percentage)

void	setGrayLevelMin (const unsigned int &level_min)

void	setGrayLevelMax (const unsigned int &level_max)

void	setGrayLevelPrecision (const double &grayLevelPrecision)

void	setGraphics (bool activate)

void	setGraphicsThickness (unsigned int t)

void	track (const vpImage< unsigned char > &I)

void	track (const vpImage< unsigned char > &I, vpImagePoint &ip)

Public Member Functions Inherited from vpTracker
vpColVector	get_p () const

vpColVector	get_cP () const

Static Public Member Functions
static void	display (const vpImage< unsigned char > &I, const vpImagePoint &cog, const std::list< vpImagePoint > &edges_list, vpColor color=vpColor::red, unsigned int thickness=1)

static void	display (const vpImage< vpRGBa > &I, const vpImagePoint &cog, const std::list< vpImagePoint > &edges_list, vpColor color=vpColor::red, unsigned int thickness=1)

Public Attributes
double	m00

double	m01

double	m10

double	m11

double	m20

double	m02

double	mu11

double	mu20

double	mu02

Public Attributes Inherited from vpTracker
vpColVector	p

vpColVector	cP

bool	cPAvailable

Static Public Attributes
static const unsigned int	SPIRAL_SEARCH_SIZE = 350

Friends
VISP_EXPORT std::ostream &	operator<< (std::ostream &os, vpDot &d)

Detailed Description

This tracker is meant to track a dot (connected pixels with same gray level) on a vpImage.

The underground algorithm is based on a binarization of the image and a connex component segmentation to determine the dot characteristics (location, moments, size...).

The following sample code shows how to grab images from a firewire camera, track a blob and display the tracking results.

#include <visp3/blob/vpDot.h>
#include <visp3/gui/vpDisplayX.h>
#include <visp3/sensor/vp1394TwoGrabber.h>
int main()
{
#if defined(VISP_HAVE_DC1394)
  vpImage<unsigned char> I; // Create a gray level image container
  vp1394TwoGrabber g(false); // Create a grabber based on libdc1394-2.x third party lib
  g.acquire(I); // Acquire an image
#if defined(VISP_HAVE_X11)
  vpDisplayX d(I, 0, 0, "Camera view");
#endif
  vpDisplay::display(I);
  vpDisplay::flush(I);
  vpDot blob;
  blob.initTracking(I);
  blob.setGraphics(true);
  while(1) {
    g.acquire(I); // Acquire an image
    vpDisplay::display(I);
    blob.track(I);
    vpDisplay::flush(I);
  }
#endif
}

See also: vpDot2

Examples:: poseVirtualVS.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoAfma6Segment2DCamVelocity.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, testRobotAfma6Pose.cpp, testRobotViper850Pose.cpp, and trackDot.cpp.

Definition at line 115 of file vpDot.h.

Member Enumeration Documentation

◆ vpConnexityType

enum vpDot::vpConnexityType

Type of connexity 4, or 8.

Enumerator
CONNEXITY_4	For a given pixel 4 neighbors are considered (left, right, up, down)
CONNEXITY_8	For a given pixel 8 neighbors are considered (left, right, up, down, and the 4 pixels located on the diagonal)

Definition at line 121 of file vpDot.h.

Constructor & Destructor Documentation

◆ vpDot() [1/3]

vpDot::vpDot ( )

Definition at line 93 of file vpDot.cpp.

◆ vpDot() [2/3]

vpDot::vpDot ( const vpImagePoint & ip )

explicit

Constructor with initialization of the dot location.

Parameters

ip	: An image point with sub-pixel coordinates.

Definition at line 106 of file vpDot.cpp.

◆ vpDot() [3/3]

vpDot::vpDot ( const vpDot & d )

Copy constructor.

Definition at line 117 of file vpDot.cpp.

◆ ~vpDot()

vpDot::~vpDot ( )

virtual

Destructor.

Definition at line 129 of file vpDot.cpp.

Member Function Documentation

◆ display() [1/3]

void vpDot::display	(	const vpImage< unsigned char > &	I,
		vpColor	color = `vpColor::red`,
		unsigned int	thick = `1`
	)		const

Display in overlay the dot edges and center of gravity.

Parameters

I	: Image.
color	: The color used for the display.
thick	: Thickness of the displayed cross located at the dot cog.

Definition at line 826 of file vpDot.cpp.

References vpDisplay::displayCross(), and vpDisplay::displayPoint().

◆ display() [2/3]

void vpDot::display	(	const vpImage< unsigned char > &	I,
		const vpImagePoint &	cog,
		const std::list< vpImagePoint > &	edges_list,
		vpColor	color = `vpColor::red`,
		unsigned int	thickness = `1`
	)

static

Display the dot center of gravity and its list of edges.

Parameters

I	: The image used as background.
cog	: The center of gravity.
edges_list	: The list of edges;
color	: Color used to display the dot.
thickness	: Thickness of the dot.

Definition at line 880 of file vpDot.cpp.

References vpDisplay::displayCross(), and vpDisplay::displayPoint().

◆ display() [3/3]

void vpDot::display	(	const vpImage< vpRGBa > &	I,
		const vpImagePoint &	cog,
		const std::list< vpImagePoint > &	edges_list,
		vpColor	color = `vpColor::red`,
		unsigned int	thickness = `1`
	)

static

Display the dot center of gravity and its list of edges.

Parameters

I	: The image used as background.
cog	: The center of gravity.
edges_list	: The list of edges;
color	: Color used to display the dot.
thickness	: Thickness of the dot.

Definition at line 905 of file vpDot.cpp.

References vpDisplay::displayCross(), and vpDisplay::displayPoint().

◆ get_cP()

vpColVector vpTracker::get_cP ( ) const

inlineinherited

Return object parameters expressed in the 3D camera frame.

Definition at line 99 of file vpTracker.h.

◆ get_nij()

vpColVector vpDot::get_nij ( ) const

inline

Gets the second order normalized centered moment $n_{ij}$ as a 3-dim vector containing $n_{20}, n_{11}, n_{02}$ such as $n_{ij} = \mu_{ij}/m_{00}$

Returns: The 3-dim vector containing $n_{20}, n_{11}, n_{02}$ .

See also: getCog(), getArea()

Examples:: trackDot.cpp.

Definition at line 210 of file vpDot.h.

Referenced by vpFeatureBuilder::create().

◆ get_p()

vpColVector vpTracker::get_p ( ) const

inlineinherited

Return object parameters expressed in the 2D image plane computed by perspective projection.

Definition at line 97 of file vpTracker.h.

◆ getArea()

double vpDot::getArea ( ) const

inline

Gets the area of the blob corresponding also to the zero order moment.

Returns: The blob area.

Examples:: trackDot.cpp.

Definition at line 225 of file vpDot.h.

◆ getBBox()

vpRect vpDot::getBBox ( ) const

inline

Return the dot bounding box.

See also: getWidth(), getHeight()

Definition at line 234 of file vpDot.h.

References vpRect::setRect().

◆ getCog()

vpImagePoint vpDot::getCog ( ) const

inline

Return the location of the dot center of gravity.

Returns: The coordinates of the center of gravity.

Examples:: servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, testRobotAfma6Pose.cpp, testRobotViper850Pose.cpp, and trackDot.cpp.

Definition at line 247 of file vpDot.h.

Referenced by vpFeatureBuilder::create(), operator!=(), operator=(), and operator==().

◆ getConnexities()

std::list<vpImagePoint> vpDot::getConnexities ( ) const

inline

Return the list of all the image points inside the dot.

Returns: The list of all the images points in the dot. This list is updated after a call to track().

Definition at line 265 of file vpDot.h.

◆ getEdges()

std::list<vpImagePoint> vpDot::getEdges ( ) const

inline

Return the list of all the image points on the border of the dot.

Warning: Doesn't return the image points inside the dot anymore. To get those points see getConnexities().

Examples:: trackDot.cpp.

Definition at line 255 of file vpDot.h.

◆ getGamma()

double vpDot::getGamma ( ) const

inline

Definition at line 267 of file vpDot.h.

◆ getGrayLevelPrecision()

double vpDot::getGrayLevelPrecision ( ) const

inline

Return the precision of the gray level of the dot. It is a double precision float witch value is in ]0,1]. 1 means full precision, whereas values close to 0 show a very bad precision.

Definition at line 275 of file vpDot.h.

◆ getHeight()

unsigned int vpDot::getHeight ( ) const

inline

Return the width of the dot.

See also: getHeight()

Examples:: trackDot.cpp.

Definition at line 303 of file vpDot.h.

References vpTracker::operator=().

◆ getMaxDotSize()

double vpDot::getMaxDotSize ( ) const

inline

Definition at line 276 of file vpDot.h.

◆ getMeanGrayLevel()

double vpDot::getMeanGrayLevel ( ) const

inline

Return the mean gray level value of the dot.

Definition at line 280 of file vpDot.h.

◆ getPolygon()

vpPolygon vpDot::getPolygon ( ) const

inline

Returns: a vpPolygon made from the edges of the dot.

Definition at line 285 of file vpDot.h.

◆ getWidth()

unsigned int vpDot::getWidth ( ) const

inline

Return the width of the dot.

See also: getHeight()

Examples:: trackDot.cpp.

Definition at line 294 of file vpDot.h.

◆ initTracking() [1/3]

void vpDot::initTracking ( const vpImage< unsigned char > & I )

Initialize the tracking with a mouse click and update the dot characteristics (center of gravity, moments).

Wait a user click in a gray area in the image I. The clicked pixel will be the starting point from which the dot will be tracked.

The threshold used to segment the dot is set with the grayLevelPrecision parameter. See the formula in setGrayLevelPrecision() function.

The sub pixel coordinates of the dot are updated. To get the center of gravity coordinates of the dot, use getCog(). To compute the moments use setComputeMoments(true) before a call to initTracking().

Warning: The content of the image modified since we call track() to compute the dot characteristics.

Parameters

I	: Image to process.

See also: track(), getCog()

Examples:: poseVirtualVS.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, testRobotAfma6Pose.cpp, testRobotViper850Pose.cpp, and trackDot.cpp.

Definition at line 635 of file vpDot.cpp.

References vpImagePoint::get_i(), vpImagePoint::get_j(), vpDisplay::getClick(), and track().

◆ initTracking() [2/3]

void vpDot::initTracking	(	const vpImage< unsigned char > &	I,
		const vpImagePoint &	ip
	)

Initialize the tracking for a dot supposed to be located at (u,v) and updates the dot characteristics (center of gravity, moments).

The threshold used to segment the dot is set to 80 percent of the gray level of the pixel (u,v).

The sub pixel coordinates of the dot are updated. To get the center of gravity coordinates of the dot, use getCog(). To compute the moments use setComputeMoments(true) before a call to initTracking().

Warning: The content of the image modified since we call track() to compute the dot characteristics.

Parameters

I	: Image to process.
ip	: Location of the starting point from which the dot will be tracked in the image.

See also: track()

Definition at line 686 of file vpDot.cpp.

References vpImagePoint::get_i(), vpImagePoint::get_j(), and track().

◆ initTracking() [3/3]

void vpDot::initTracking	(	const vpImage< unsigned char > &	I,
		const vpImagePoint &	ip,
		unsigned int	level_min,
		unsigned int	level_max
	)

Initialize the tracking for a dot supposed to be located at (u,v) and updates the dot characteristics (center of gravity, moments).

The sub pixel coordinates of the dot are updated. To get the center of gravity coordinates of the dot, use getCog(). To compute the moments use setComputeMoments(true) before a call to initTracking().

Warning: The content of the image modified since we call track() to compute the dot characteristics.

Parameters

I	: Image to process.
ip	: Location of the starting point from which the dot will be tracked in the image.
level_min	: Minimum gray level threshold used to segment the dot; value comprised between 0 and 255.
level_max	: Maximum gray level threshold used to segment the dot; value comprised between 0 and 255. gray_level_max should be greater than gray_level_min.

See also: track(), getCog()

Definition at line 740 of file vpDot.cpp.

References track().

◆ operator!=()

bool vpDot::operator!= ( const vpDot & d ) const

Definition at line 172 of file vpDot.cpp.

References getCog().

◆ operator=()

vpDot & vpDot::operator= ( const vpDot & d )

Copy operator.

Definition at line 134 of file vpDot.cpp.

References getCog(), m00, m01, m02, m10, m11, m20, mu02, mu11, and mu20.

◆ operator==()

bool vpDot::operator== ( const vpDot & d ) const

Definition at line 174 of file vpDot.cpp.

References CONNEXITY_8, vpDisplay::displayPoint(), vpTrackingException::featureLostError, vpImagePoint::get_u(), getCog(), vpImage< Type >::getHeight(), vpImage< Type >::getWidth(), vpTrackingException::initializationError, m00, m01, m02, m10, m11, m20, mu02, mu11, mu20, vpColor::red, vpImagePoint::set_u(), vpImagePoint::set_v(), and SPIRAL_SEARCH_SIZE.

◆ print()

void vpDot::print ( std::ostream & os )

inline

Definition at line 315 of file vpDot.h.

◆ setCog()

void vpDot::setCog ( const vpImagePoint & ip )

inline

Initialize the dot coordinates with ip.

Definition at line 320 of file vpDot.h.

◆ setComputeMoments()

void vpDot::setComputeMoments ( bool activate )

inline

Activates the dot's moments computation.

Parameters

activate true, if you want to compute the moments. If false, moments are not computed.

Computed moment are vpDot::m00, vpDot::m10, vpDot::m01, vpDot::m11, vpDot::m20, vpDot::m02 and second order centered moments vpDot::mu11, vpDot::mu20, vpDot::mu02 computed with respect to the blob centroid.

The coordinates of the region's centroid (u, v) can be computed from the moments by $u=\frac{m10}{m00}$ and $v=\frac{m01}{m00}$ .

Examples:: servoAfma6Ellipse2DCamVelocity.cpp, and trackDot.cpp.

Definition at line 337 of file vpDot.h.

◆ setConnexity()

void vpDot::setConnexity ( vpConnexityType type )

inline

Set the type of connexity: 4 or 8.

Examples:: trackDot.cpp.

Definition at line 342 of file vpDot.h.

◆ setGraphics()

void vpDot::setGraphics ( bool activate )

inline

Activates the display of all the pixels of the dot during the tracking. The default thickness of the overlayed drawings can be modified using setGraphicsThickness().

Warning: To effectively display the dot graphics a call to vpDisplay::flush() is needed.

Parameters

activate true to activate the display of dot pixels, false to turn off the display.

See also: setGraphicsThickness()

Examples:: poseVirtualVS.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, testRobotAfma6Pose.cpp, testRobotViper850Pose.cpp, and trackDot.cpp.

Definition at line 361 of file vpDot.h.

◆ setGraphicsThickness()

void vpDot::setGraphicsThickness ( unsigned int t )

inline

Modify the default thickness that is set to 1 of the drawings in overlay when setGraphics() is enabled.

See also: setGraphics()

Definition at line 368 of file vpDot.h.

References vpTracker::init(), and vpColor::red.

◆ setGrayLevelMax()

void vpDot::setGrayLevelMax ( const unsigned int & level_max )

inline

Definition at line 345 of file vpDot.h.

◆ setGrayLevelMin()

void vpDot::setGrayLevelMin ( const unsigned int & level_min )

inline

Definition at line 344 of file vpDot.h.

◆ setGrayLevelPrecision()

void vpDot::setGrayLevelPrecision ( const double & precision )

Set the precision of the gray level of the dot.

Parameters

precision

: It is a double precision float which value is in ]0,1]:

1 means full precision, whereas values close to 0 show a very bad accuracy.
Values lower or equal to 0 are brought back to an epsion>0
Values higher than 1 are brought back to 1 If the initial gray level is I, the gray levels of the dot will be between : $Imin=255*\big((\frac{I}{255})^{{\gamma}^{-1}}-(1-grayLevelPrecision)\big)^{\gamma}$ and $Imax=255*\big((\frac{I}{255})^{{\gamma}^{-1}}+(1-grayLevelPrecision)\big)^{\gamma}$ with $\gamma=1.5$ .

See also: setWidth(), setHeight(), setGrayLevelMin(), setGrayLevelMax()

Definition at line 854 of file vpDot.cpp.

◆ setMaxDotSize()

void vpDot::setMaxDotSize ( double percentage )

Maximal size of the region to track in terms of image size percentage.

Parameters

percentage : Image size percentage corresponding to the dot maximal size. Values should be in ]0 : 1]. If 1, that means that the dot to track could take up the whole image.

During the tracking, if the dot size if bigger than the maximal size allowed an exception is throwed : vpTrackingException::featureLostError.

Examples:: servoAfma6Ellipse2DCamVelocity.cpp.

Definition at line 601 of file vpDot.cpp.

References vpTRACE.

◆ track() [1/2]

void vpDot::track ( const vpImage< unsigned char > & I )

Track and compute the dot characteristics.

To get the center of gravity coordinates of the dot, use getCog(). To compute the moments use setComputeMoments(true) before a call to initTracking().

Warning: The image is modified (all the pixels that belong to the point are set to white (ie to 255).

Parameters

I	: Image to process.

See also: getCog()

Examples:: poseVirtualVS.cpp, servoAfma4Point2DArtVelocity.cpp, servoAfma4Point2DCamVelocity.cpp, servoAfma6Ellipse2DCamVelocity.cpp, servoAfma6FourPoints2DArtVelocity.cpp, servoAfma6Point2DArtVelocity.cpp, servoAfma6Point2DCamVelocity.cpp, servoAfma6Points2DCamVelocityEyeToHand.cpp, servoBiclopsPoint2DArtVelocity.cpp, servoViper850FourPoints2DArtVelocityLs_des.cpp, and trackDot.cpp.

Definition at line 770 of file vpDot.cpp.

References vpDisplay::displayCross(), vpImagePoint::get_u(), vpImagePoint::get_v(), m01, m02, m10, m11, m20, mu02, mu11, mu20, vpColor::red, vpImagePoint::set_u(), and vpImagePoint::set_v().

Referenced by initTracking(), and track().

◆ track() [2/2]

void vpDot::track	(	const vpImage< unsigned char > &	I,
		vpImagePoint &	ip
	)

Track and updates the new dot coordinates

To compute the moments use setComputeMoments(true) before a call to initTracking() or track().

Warning: The image is modified (all the pixels that belong to the point are set to white (ie to 255).

Parameters

I	: Image to process.
ip	[out] : Sub pixel coordinate of the tracked dot center of gravity.

Definition at line 812 of file vpDot.cpp.

References track().

Friends And Related Function Documentation

◆ operator<<

VISP_EXPORT std::ostream& operator<<	(	std::ostream &	os,
		vpDot &	d
	)

friend

Writes the dot center of gravity coordinates in the frame (i,j) (For more details about the orientation of the frame see the vpImagePoint documentation) to the stream os, and returns a reference to the stream.

Definition at line 921 of file vpDot.cpp.

Member Data Documentation

◆ cP

vpColVector vpTracker::cP

inherited

Feature coordinates expressed in the camera frame cP.

Definition at line 77 of file vpTracker.h.

Referenced by vpFeaturePoint3D::buildFrom(), vpSphere::changeFrame(), vpPoint::changeFrame(), vpCircle::changeFrame(), vpLine::changeFrame(), vpCylinder::changeFrame(), vpFeatureBuilder::create(), vpPoint::get_W(), vpPoint::get_X(), vpPoint::get_Y(), vpPoint::get_Z(), vpSphere::init(), vpCircle::init(), vpPoint::init(), vpLine::init(), vpCylinder::init(), vpMbtPolygon::isVisible(), vpTracker::operator=(), vpForwardProjection::print(), vpPose::printPoint(), vpForwardProjection::project(), vpSphere::projection(), vpCircle::projection(), vpPoint::projection(), vpLine::projection(), vpCylinder::projection(), vpPoint::set_W(), vpPoint::set_X(), vpPoint::set_Y(), and vpPoint::set_Z().

◆ cPAvailable

bool vpTracker::cPAvailable

inherited

Flag used to indicate if the feature parameters cP expressed in the camera frame are available.

Definition at line 83 of file vpTracker.h.

Referenced by vpTracker::init(), and vpTracker::operator=().

◆ m00

double vpDot::m00

Considering the general distribution moments for $ N $ points defined by the relation $m_{ij} = \sum_{h=0}^{N} u_h^i v_h^j$ , $m_{00}$ is a zero order moment obtained with $i = j = 0 $ .

See also: setComputeMoments()

Definition at line 135 of file vpDot.h.

Referenced by operator=(), and operator==().

◆ m01

double vpDot::m01

Considering the general distribution moments for $ N $ points defined by the relation $m_{ij} = \sum_{h=0}^{N} u_h^i v_h^j$ , $m_{01}$ is a first order moment obtained with $i = 0 $ and $ j = 1 $ .

See also: setComputeMoments()

Definition at line 142 of file vpDot.h.

Referenced by operator=(), operator==(), and track().

◆ m02

double vpDot::m02

Considering the general distribution moments for $ N $ points defined by the relation $m_{ij} = \sum_{h=0}^{N} u_h^i v_h^j$ , $m_{02}$ is a second order moment obtained with $i = 0 $ and $ j = 2 $ .

See also: setComputeMoments()

Definition at line 170 of file vpDot.h.

Referenced by operator=(), operator==(), and track().

◆ m10

double vpDot::m10

Considering the general distribution moments for $ N $ points defined by the relation $m_{ij} = \sum_{h=0}^{N} u_h^i v_h^j$ , $m_{10}$ is a first order moment obtained with $i = 1 $ and $ j = 0 $ .

See also: setComputeMoments()

Definition at line 149 of file vpDot.h.

Referenced by operator=(), operator==(), and track().

◆ m11

double vpDot::m11

Considering the general distribution moments for $ N $ points defined by the relation $m_{ij} = \sum_{h=0}^{N} u_h^i v_h^j$ , $m_{11}$ is a first order moment obtained with $i = 1 $ and $ j = 1 $ .

See also: setComputeMoments()

Definition at line 156 of file vpDot.h.

Referenced by operator=(), operator==(), and track().

◆ m20

double vpDot::m20

Considering the general distribution moments for $ N $ points defined by the relation $m_{ij} = \sum_{h=0}^{N} u_h^i v_h^j$ , $m_{20}$ is a second order moment obtained with $i = 2 $ and $ j = 0 $ .