ratio of the bounding edge angles and the distance of the edges from the center of the particle which is defined by the largest inscribed circle to the radius of the maximum inscribed circle

This measure allows to quantified the angularity of a shape using its associated maximum inscribed circle (see MaxInscribedCircle2d).

For each tops of the polygonal approximation of shape, we compute an angularity value given by :

$A_i = (\pi-\theta_i)\frac{x_i}{r}$

where :

$\theta_i$ is the angle formed by polygonal approximation at considered top .
is the distance between maximum inscribed circle center and current top .
is the radius of maximum inscribed circle

Then the global shape angularity value is simply given by the mean of previous values over all tops of the polygonal approximation of shape :

$A=\frac{1}{n}\sum_{i=1}^{n}{A_i}=\frac{1}{n}\sum_{i=1}^{n}{(\pi-\theta_i)\frac{x_i}{r}}$

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

See also: 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); Lees, G. (1964) A new method for determining the angularity of particles. Sedimentology, 3, pp. 2-21.

ratio of the bounding edge angles and the distance of the edges from the center of the particle which is defined by the largest inscribed circle to the radius of the maximum inscribed circle

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Geometry 2d	Angle	DegreeOfAngularity2dMsrParams	Value (ipsdk::ipReal64)	Boundary Approximation

See Shape measurement for additional information on these pictograms

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, "DegreeOfAngularity2dMsr")
    
    #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("DegreeOfAngularity2dMsr")
    
    # 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, "DegreeOfAngularity2dMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pDegreeOfAngularity2dOutMsr = pOutMeasureSet->getMeasure("DegreeOfAngularity2dMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pDegreeOfAngularity2dOutMsr->getMeasureResult());