ImageDev

InertiaMoment2d

Measures the resistance of an object, defined by a two-dimensional binary image, to changes in its motion around a given axis of rotation.

Access to parameter description

For an introduction: This algorithm computes a measurement of an object's resistance to changes in its rotational motion.
The moment of inertia of an object on a given axis describes how difficult it is to change its angular motion around this axis.

For a point mass $m$, the moment of inertia $I$ is simply $m$ times the square perpendicular distance $r$ from the axis of rotation: $$ I = mr^2 $$ On a digital image, a pixel intensity can be considered as a mass.
Then, for an object of a binary image, $m$ is a constant equal to 1. Thus, the moment of inertia is the sum of the square perpendicular distances from the axis: $$ I = \sum_r r^2 = \sum_x(x-p(x))^2 $$ where: The rotation axis is defined by a point (rotationCenterX and rotationCenterY) and an orientation (rotationAngle), which are user-defined parameters.

For this measurement the image calibration is ignored. The coordinates used to calculate the moment of inertia are expressed in pixels.

See also

Function Syntax

This function returns outputMeasurement. 
// Function prototype
MeanInertiaMomentMsr::Ptr
inertiaMoment2d( std::shared_ptr< iolink::ImageView > inputBinaryImage,
                 int32_t rotationCenterX,
                 int32_t rotationCenterY,
                 double rotationAngle,
                 MeanInertiaMomentMsr::Ptr outputMeasurement = nullptr );
This function returns outputMeasurement. 
// Function prototype.
inertia_moment_2d(input_binary_image: idt.ImageType,
                  rotation_center_x: int = 1024,
                  rotation_center_y: int = 1024,
                  rotation_angle: float = 10,
                  output_measurement: Union[Any, None] = None) -> MeanInertiaMomentMsr
This function returns outputMeasurement. 
// Function prototype.
public static MeanInertiaMomentMsr
InertiaMoment2d( IOLink.ImageView inputBinaryImage,
                 Int32 rotationCenterX = 1024,
                 Int32 rotationCenterY = 1024,
                 double rotationAngle = 10,
                 MeanInertiaMomentMsr outputMeasurement = null );

Class Syntax

Parameters

Parameter Name Description Type Supported Values Default Value
input
inputBinaryImage
The input binary image. Image Binary nullptr
input
rotationCenterX
The X pixel coordinate of the rotation axis. Int32 >=1 1024
input
rotationCenterY
The Y pixel coordinate of the rotation axis. Int32 >=1 1024
input
rotationAngle
The orientation of the rotation axis in degrees. A positive value means that the angle is taken from the positive X axis to the positive Y axis. Float64 Any value 10
output
outputMeasurement
The output measurement result. MeanInertiaMomentMsr nullptr
Parameter Name Description Type Supported Values Default Value
input
input_binary_image
The input binary image. image Binary None
input
rotation_center_x
The X pixel coordinate of the rotation axis. int32 >=1 1024
input
rotation_center_y
The Y pixel coordinate of the rotation axis. int32 >=1 1024
input
rotation_angle
The orientation of the rotation axis in degrees. A positive value means that the angle is taken from the positive X axis to the positive Y axis. float64 Any value 10
output
output_measurement
The output measurement result. MeanInertiaMomentMsr None
Parameter Name Description Type Supported Values Default Value
input
inputBinaryImage
The input binary image. Image Binary null
input
rotationCenterX
The X pixel coordinate of the rotation axis. Int32 >=1 1024
input
rotationCenterY
The Y pixel coordinate of the rotation axis. Int32 >=1 1024
input
rotationAngle
The orientation of the rotation axis in degrees. A positive value means that the angle is taken from the positive X axis to the positive Y axis. Float64 Any value 10
output
outputMeasurement
The output measurement result. MeanInertiaMomentMsr null

Object Examples

auto polystyrene_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene_sep.vip" );

InertiaMoment2d inertiaMoment2dAlgo;
inertiaMoment2dAlgo.setInputBinaryImage( polystyrene_sep );
inertiaMoment2dAlgo.setRotationCenterX( 1024 );
inertiaMoment2dAlgo.setRotationCenterY( 1024 );
inertiaMoment2dAlgo.setRotationAngle( 10 );
inertiaMoment2dAlgo.execute();

std::cout << "meanMoment: " << inertiaMoment2dAlgo.outputMeasurement()->meanMoment( 0 ) ;

polystyrene_sep = imagedev.read_vip_image(imagedev_data.get_image_path("polystyrene_sep.vip"))

inertia_moment_2d_algo = imagedev.InertiaMoment2d()
inertia_moment_2d_algo.input_binary_image = polystyrene_sep
inertia_moment_2d_algo.rotation_center_x = 1024
inertia_moment_2d_algo.rotation_center_y = 1024
inertia_moment_2d_algo.rotation_angle = 10
inertia_moment_2d_algo.execute()

print("meanMoment: ", str(inertia_moment_2d_algo.output_measurement.mean_moment(0)))

ImageView polystyrene_sep = Data.ReadVipImage( @"Data/images/polystyrene_sep.vip" );

InertiaMoment2d inertiaMoment2dAlgo = new InertiaMoment2d
{
    inputBinaryImage = polystyrene_sep,
    rotationCenterX = 1024,
    rotationCenterY = 1024,
    rotationAngle = 10
};
inertiaMoment2dAlgo.Execute();

Console.WriteLine( "meanMoment: " + inertiaMoment2dAlgo.outputMeasurement.meanMoment( 0 ) );

Function Examples

auto polystyrene_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene_sep.vip" );

auto result = inertiaMoment2d( polystyrene_sep, 1024, 1024, 10 );

std::cout << "meanMoment: " << result->meanMoment( 0 ) ;

polystyrene_sep = imagedev.read_vip_image(imagedev_data.get_image_path("polystyrene_sep.vip"))

result = imagedev.inertia_moment_2d(polystyrene_sep, 1024, 1024, 10)

print("meanMoment: ", str(result.mean_moment(0)))

ImageView polystyrene_sep = Data.ReadVipImage( @"Data/images/polystyrene_sep.vip" );

MeanInertiaMomentMsr result = Processing.InertiaMoment2d( polystyrene_sep, 1024, 1024, 10 );

Console.WriteLine(  "meanMoment: " + result.meanMoment( 0 )  );