Radius angularity index 2d

sum of the distance difference between the outline of a shape in certain direction to that of an equivalent ellipse More...

Classes
class	ipsdk::imaproc::shape::analysis::RadiusAngularityIndex2dMsr
	Measurement object for measure RadiusAngularityIndex2d. More...
class	ipsdk::imaproc::shape::analysis::RadiusAngularityIndex2dMsrInfo
	Information object for measure RadiusAngularityIndex2d. More...
class	ipsdk::imaproc::shape::analysis::RadiusAngularityIndex2dMsrParams
	Parameter object for measure RadiusAngularityIndex2d. More...

Detailed Description

sum of the distance difference between the outline of a shape in certain direction to that of an equivalent ellipse

This measure allows to quantified the angularity of a shape using the difference between shape radius in a certain direction and that of its equivalent ellipse.

Note that equivalent ellipse associated to a shape is define such as :

• ellipse center is set at shape barycenter (see Barycenter2d)
• ellipse orientation is equal to orientation extracted from second order moment of shape (see Inertia Orientation 2d)
• ellipse dimensions are defined such that ellipse perimeter and area match with shape perimeter (see Perimeter2d) and shape area (see Area2d).

Given a set of orientations regularly sampled around unit circle (with number of orientation defined by parameter NbOrientations), we compute an angularity value given by :

where :

• is the angle associated to sample number ( with set to NbOrientations)
• is the radius of shape at angle , which is the length of segment starting at equivalent ellipse center, oriented and directed with respect to angle and ending at intersection with shape boundary (note that we retain farest intersection in case of non convex shape which may lead to several intersection points).
• is the radius of equivalent ellipse at angle .
  

Then the global shape angularity value is simply given by the sum of previous values over all sampled angles :

Here is an example of degree of angularity 2d computation on few caracteristic shapes :

See also

Taleb Al-Rousan, Eyad Masad, Erol Tutumluer, Tongyan Pan, Evaluation of image analysis techniques for quantifying aggregate shape characteristics, Construction and Building Materials 21 (2007) 978–990.

Al-Rousan, T., Masad, T., Tutumluer, E. and Pan T. (2007). Evaluation of image analysis techniques for quantifying aggregate shape characteristics.Construction and building materials21, pp. 978-990.

Dallas Little, Joe Button, Priyantha Jayawickrama, Mansour Solaimanian, Barry Hudson, Quantify shape, angularity and surface texture of aggregates using image analysis and study their effect on performance, Texas Department of Transportation, October 2003

Tafesse Solomon, Sun Wenjuan, Fernlund Joanne, and Linbing Wang, A new image analysis technique to quantify particle angularity, Engineering Geology and Geophysics Research Group Royal Institute of Technology (KTH)

Author

E.Noirfalise

Date

2017/07/18

Copyright

2017 Reactiv'IP, all right reserved.

sum of the distance difference between the outline of a shape in certain direction to that of an equivalent ellipse

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Geometry 2d	None	RadiusAngularityIndex2dMsrParams	Value (ipsdk::ipReal64)	Both

See Shape measurement for additional information on these pictograms

Measure Type :

This is a geometry 2d measure

• it use shape 2d data to compute a result
• it optionally can use dependencies to other measures to compute a result (see Measure Dependencies section)

This measure can only be used in 2d case

Measure Unit Type:

Measure RadiusAngularityIndex2d is not associated to any unit [ipsdk::shape::analysis::eMsrUnitFormat::eMUF_NoUnit]

Measure Parameter Type :

Measure RadiusAngularityIndex2d is associated to RadiusAngularityIndex2dMsrParams parameters

Measure Result Type :

Measure RadiusAngularityIndex2d is associated to ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64> results

Measure Shape Requirements :

Measure RadiusAngularityIndex2d requires row intersections and boundary approximation from shape data

Measure Dependencies :

Measure RadiusAngularityIndex2d depends on following measures :

Measure Mode	Measure Name	Measure Type	Measure Parameters
eMVP_2d	Perimeter2d	Perimeter2d	createHolesBasicPolicyMsrParams(_pMsrParams->getValue<RadiusAngularityIndex2dMsrParams::ProcessHoles>())
eMVP_2d	Area2d	PolygonArea2d	createHolesBasicPolicyMsrParams(_pMsrParams->getValue<RadiusAngularityIndex2dMsrParams::ProcessHoles>())
eMVP_2d	Barycenter2d	Barycenter2d
eMVP_2d	InertiaOrientation2d	InertiaOrientation2d
eMVP_2d	Shape2dRTree	Shape2dRTree

Note

See Shape Analysis 2d for more information on general shape 2d analysis and measurement usage.

Example of Python code :

Generic example in 2d case :

import PyIPSDK
import PyIPSDK.IPSDKIPLShapeAnalysis as shapeanalysis

    # Create the infoset
    inMeasureInfoSet2d = PyIPSDK.createMeasureInfoSet2d()
    PyIPSDK.createMeasureInfo(inMeasureInfoSet2d, "RadiusAngularityIndex2dMsr")
    
    #Perform the analysis
    outMeasureSet = shapeanalysis.labelAnalysis2d(inGreyImg, inLabelImg2d, inMeasureInfoSet2d)
    
    # save results to csv format
    PyIPSDK.saveCsvMeasureFile(os.path.join(tmpPath,  "shape_analysis_results.csv"), outMeasureSet)
    
    # retrieve measure results
    outMsr = outMeasureSet.getMeasure("RadiusAngularityIndex2dMsr")
    
    # retrieve measure values
    outMsrValues = outMsr.getMeasureResult().getColl(0)
    print("First label measurement equal " + str(outMsrValues[1]))

Example of C++ code :

Example informations

Associated library

IPSDKIPLShapeAnalysis

Code Example

    // opening grey level input image
    ImagePtr pInGreyImg2d = loadTiffImageFile(inputGreyImgPath);

    // read entity shape 2d collection used for processing
    Shape2dCollPtr pShape2dColl = boost::make_shared<Shape2dColl>();
    IPSDK_REQUIRE(readFromXmlFile(inputShape2dCollPath, *pShape2dColl) == true);

    // define a measure info set
    MeasureInfoSetPtr pMeasureInfoSet = MeasureInfoSet::create2dInstance();
    createMeasureInfo(pMeasureInfoSet, "RadiusAngularityIndex2dMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);

    // retrieve associated results
    const MeasureConstPtr& pRadiusAngularityIndex2dOutMsr = pOutMeasureSet->getMeasure("RadiusAngularityIndex2dMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pRadiusAngularityIndex2dOutMsr->getMeasureResult());