MomentCInvariant¶

class MomentCInvariant(self, flg_sxsynormalization: bool = false)¶

Bases: Moment

This class defines several 2D (translation+rotation+scale) invariants for both symmetric and non-symmetric objects. These moment-based invariants are described in the following papers [5] , [40] .

The descriptions for the invariants \(C_1\) to \(C_{10}\) can be found in [5] and for invariants \(P_x\) , \(P_y\) , \(S_x\) , \(S_y\) in [40] .

These invariants are classicaly used in visual servoing to control the out-of-plane rotations. The C-type or P-type invariants are used for non-symmetric objects whereas the S-type invariants are used for symmetric objects.

For most cases of non-symmetric objects, ( \(C_4\) , \(C_6\) ) or ( \(P_x\) , \(P_y\) ) couples are widely used to control x and y rotations. For symmetric objects \(S_x\) and \(S_y\) are the only choice.

There are 14 translation+rotation+scale invariants (10 C-type, 2 P-type and 2 S-type) that can be accessed from by vpMomentCInvariant::get or any of the get shortcuts.

The example below shows how to retrieve the \(C_2\) invariant:

#include <iostream>
#include <visp3/core/vpMomentCInvariant.h>
#include <visp3/core/vpMomentCommon.h>
#include <visp3/core/vpMomentObject.h>
#include <visp3/core/vpPoint.h>

int main()
{
  vpPoint p;
  std::vector<vpPoint> vec_p;

  p.set_x(6); p.set_y(-1); // coordinates in meters in the image plane (vertex 1)
  vec_p.push_back(p);
  p.set_x(2); p.set_y(3); // coordinates in meters in the image plane (vertex 2)
  vec_p.push_back(p);
  p.set_x(0); p.set_y(1.2); // coordinates in meters in the image plane (vertex 1)
  vec_p.push_back(p);
  p.set_x(-7); p.set_y(-4); // coordinates in meters in the image plane (vertex 2)
  vec_p.push_back(p);

  vpMomentObject obj(5); // Create an image moment object with 5 as maximum order
  obj.setType(vpMomentObject::DISCRETE); // Discrete mode for object
  obj.fromVector(vec_p);

  //initialisation with default values
  vpMomentCommon db(vpMomentCommon::getSurface(obj),vpMomentCommon::getMu3(obj),
                    vpMomentCommon::getAlpha(obj),1.);
  bool success;

  db.updateAll(obj); // Update AND compute all moments

  //get C-invariant
  const vpMomentCInvariant& C
    = static_cast<const vpMomentCInvariant&>(db.get("vpMomentCInvariant",success));
  if(success)
      std::cout << C.get(1) << std:: endl; // print C2 invariant
  else
      std::cout << "vpMomentCInvariant not found." << std::endl;

  return 0;
}

vpMomentCInvariant depends on vpMomentCentered (see vpMomentDatabase and vpMomentCommon ).

Default constructor. (option to use a different calculation mode for sx and sy)

Methods

`C1`	Shorcut for getting the value of \(C_1\) .
`C10`	Shorcut for getting the value of \(C_{10}\) .
`C2`	Shorcut for getting the value of \(C_2\) .
`C3`	Shorcut for getting the value of \(C_3\) .
`C4`	Shorcut for getting the value of \(C_4\) .
`C5`	Shorcut for getting the value of \(C_5\) .
`C6`	Shorcut for getting the value of \(C_6\) .
`C7`	Shorcut for getting the value of \(C_7\) .
`C8`	Shorcut for getting the value of \(C_8\) .
`C9`	Shorcut for getting the value of \(C_9\) .
`Px`	Shorcut for getting the value of \(P_x\) .
`Py`	Shorcut for getting the value of \(P_y\) .
`Sx`	Shorcut for getting the value of \(S_x\) .
`Sy`	Shorcut for getting the value of \(S_y\) .
`__init__`	Default constructor.
`compute`	Computes translation-plane-rotation-scale invariants.
`get`	Overloaded function.
`getC`	Access to partial invariant c (see [2]).
`getCN`	Getter for c (calculated from normalized 2nd and 3ord order moments)
`getI`	Access to partial invariants.
`getII`	Access to partial invariant I (see [2]).
`getIn1`	Getters for I (calculated from normalized 2nd and 3ord order moments)
`getK`	Access to partial invariant K (see [2]).
`getMomentVector`	To get all the invariant values as a whole.
`getS`	Access to partial invariant S (see [2]).
`getSN`	Getter for s (calculated from normalized 2nd and 3ord order moments)
`isSxSyfromNormalizedMoments`	To know if Sx and Sy were calculated from normalized moments or not
`name`	Moment name.
`printI`	Print partial invariant.
`printInvariants`	Print the moment invariants used to obtain the actual visual features

Inherited Methods

`linkTo`	Links the moment to a database of moment primitives.
`getObject`
`printDependencies`	Prints values of all dependent moments required to calculate a specific vpMoment .
`update`	Updates the moment with the current object.

Operators

`__doc__`
`__init__`	Default constructor.
`__module__`
`__repr__`

Attributes

`__annotations__`

C1(self) → float¶: Shorcut for getting the value of \(C_1\) .

C10(self) → float¶: Shorcut for getting the value of \(C_{10}\) .

C2(self) → float¶: Shorcut for getting the value of \(C_2\) .

C3(self) → float¶: Shorcut for getting the value of \(C_3\) .

C4(self) → float¶: Shorcut for getting the value of \(C_4\) .

C5(self) → float¶: Shorcut for getting the value of \(C_5\) .

C6(self) → float¶: Shorcut for getting the value of \(C_6\) .

C7(self) → float¶: Shorcut for getting the value of \(C_7\) .

C8(self) → float¶: Shorcut for getting the value of \(C_8\) .

C9(self) → float¶: Shorcut for getting the value of \(C_9\) .

Px(self) → float¶: Shorcut for getting the value of \(P_x\) .

Py(self) → float¶: Shorcut for getting the value of \(P_y\) .

Sx(self) → float¶: Shorcut for getting the value of \(S_x\) .

Sy(self) → float¶: Shorcut for getting the value of \(S_y\) .

__init__(self, flg_sxsynormalization: bool = false)¶: Default constructor. (option to use a different calculation mode for sx and sy)

compute(self) → None¶: Computes translation-plane-rotation-scale invariants. Depends on vpMomentCentered . All possible invariants are computed here. The selection of the invariant is done afterwards.

get(*args, **kwargs)¶

Overloaded function.

get(self: visp._visp.core.MomentCInvariant, i: int) -> float

Gets the desired invariant.

Parameters:

i: given index. For invariants from C1 to C10 the corresponding index is from 0 to 9. For \(S_x\) , \(S_y\) the indexes are 10,11 and for \(P_x\) , \(P_y\) they are 12,13.

get(self: visp._visp.core.Moment) -> list[float]

Returns:: vector of values

getC(self, i: int) → float¶: Access to partial invariant c (see [2]).

getCN(self, i: int) → float¶: Getter for c (calculated from normalized 2nd and 3ord order moments)

getI(self, index: int) → float¶: Access to partial invariants. The index convention is the same as in [1].

getII(self, i: int) → float¶: Access to partial invariant I (see [2]).

getIn1(self) → float¶: Getters for I (calculated from normalized 2nd and 3ord order moments)

getK(self) → float¶: Access to partial invariant K (see [2]).

getMomentVector(self) → list[float]¶: To get all the invariant values as a whole.

getObject(self) → visp._visp.core.MomentObject¶

getS(self, i: int) → float¶: Access to partial invariant S (see [2]).

getSN(self, i: int) → float¶: Getter for s (calculated from normalized 2nd and 3ord order moments)

isSxSyfromNormalizedMoments(self) → bool¶: To know if Sx and Sy were calculated from normalized moments or not

linkTo(self, moments: visp._visp.core.MomentDatabase) → None¶

Links the moment to a database of moment primitives. If the moment depends on other moments, these moments must be linked to the same database.

Warning

Two moments of the same class cannot be stored in the same database

#include <visp3/core/vpMomentCentered.h>
#include <visp3/core/vpMomentDatabase.h>
#include <visp3/core/vpMomentGravityCenter.h>
#include <visp3/core/vpMomentObject.h>
#include <visp3/core/vpPoint.h>

int main()
{
  vpPoint p;
  std::vector<vpPoint> vec_p;

  p.set_x(1); p.set_y(1); // coordinates in meters in the image plane (vertex 1)
  vec_p.push_back(p);
  p.set_x(2); p.set_y(2); // coordinates in meters in the image plane (vertex 2)
  vec_p.push_back(p);

  vpMomentObject obj(2);
  obj.setType(vpMomentObject::DISCRETE); // Discrete mode.
  obj.fromVector(vec_p); // Init the dense object with the polygon

  vpMomentDatabase db;
  vpMomentGravityCenter G; // declaration of gravity center
  vpMomentCentered mc;     // mc contains centered moments

  G.linkTo(db);  // add gravity center to database
  mc.linkTo(db); // centered moments depend on gravity, add them to the
                 // database to grant access

  G.update(obj);  // specify the object for gravity center
  mc.update(obj); // and for centered moments

  G.compute();  // compute the moment
  mc.compute(); // compute centered moments AFTER gravity center

  return 0;
}

name(self) → str¶: Moment name.

printDependencies(self: visp._visp.core.Moment, os: std::ostream) → None¶: Prints values of all dependent moments required to calculate a specific vpMoment . Not made pure to maintain compatibility Recommended : Types inheriting from vpMoment should implement this function

printI(self, index: int) → None¶

Print partial invariant.

Prints the temporary invariants. Used for debug purposes only

Parameters:

index: int¶: index of the temporary invariant

printInvariants(self: visp._visp.core.MomentCInvariant, os: std::ostream) → None¶

Print the moment invariants used to obtain the actual visual features

Print out all invariants that were computed There are 15 of them, as in [Point-based and region based.ITRO05] [40]

update(self, object: visp._visp.core.MomentObject) → None¶: Updates the moment with the current object. This does not compute any values.