measure allowing to compute average of the change in the angles of the gradient vectors around the particle circumference

This measure allows to quantified the angularity of a shape using the change in the angles of the gradient vectors around the shape boundary.

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

$A_i = w_i \times \Delta\theta_i = \frac{l_i+l_{i-1}}{2}\left |\theta_{i}-\theta_{i-1}\right |$

where :

is the length of segment starting at considered top .
$\theta_{i}$ is the angle of the normal vector associated to segment starting at considered top .

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

$A=\frac{1}{W}\sum_{i=1}^{n}{A_i}=\frac{1}{\sum_{i=1}^{n}{\frac{l_i+l_{i-1}}{2}}}\sum_{i=1}^{n}{\frac{l_i+l_{i-1}}{2}\left |\theta_{i}-\theta_{i-1}\right |}$

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

See also: 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.; Masad, E., Al-Rousan, T., Button, J., Little, D. and Tutumluer, E. (2007). Test methods for characterizing aggregate shape, texture, and angularity. National Cooperative Highway Research Program (NCHRP) Report 555. Transportation Research Board, Washington, D.C.; Lees, G. (1964) A new method for determining the angularity of particles. Sedimentology, 3, pp. 2-21.; 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.; 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)

measure allowing to compute average of the change in the angles of the gradient vectors around the particle circumference

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Geometry 2d	Custom	None	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, "EdgeAngularity2dMsr")
    
    #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("EdgeAngularity2dMsr")
    
    # 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, "GradientAngularityIndex2dMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pGradientAngularityIndex2dOutMsr = pOutMeasureSet->getMeasure("GradientAngularityIndex2dMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pGradientAngularityIndex2dOutMsr->getMeasureResult());