this measure allows to compute changes in the slope of the shape outline

This measure allows to quantified the angularity using the changes in the slope of of a shape outline.

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

$\Delta\theta_i = \left |\theta_{i}-\theta_{i-1}\right |$

where :

$\theta_i$ is angle between segments ending at considered top .

We then compute the histogram of these values using a number of orientation defined by parameter NbOrientations.

The global shape angularity value is then given by following formula :

$A=\sum_{i=1}^{m}{\theta_i \times P(i)}$

where :

is the requested number of orientations for histogram analysis (ie. parameter NbOrientations).
$\theta_i$ is the angle associated to center of class .
is the probability associated to class .

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

See also: Rao, C., Tutumluer, E. and Kim, I. T. (2002). Quantification of coarse aggregate angularity based on image analysis. In Transportation Research Record, Journal of the Transportation Research Board, No. 1787, Washington, D.C, pp. 117-124.; 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); Moaveni, Wang, Hart, Tutumluer, and Ahuja , Aggregate size and shape evaluation using segmentation techniques and aggregate image processing algorithms, Transportation Research Board Washington, DC, January 2013

this measure allows to compute changes in the slope of the shape outline

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Geometry 2d	Angle	OutlineSlopeAngularity2dMsrParams	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, "OutlineSlopeAngularity2dMsr")
    
    #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("OutlineSlopeAngularity2dMsr")
    
    # 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, "OutlineSlopeAngularity2dMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pOutlineSlopeAngularity2dOutMsr = pOutMeasureSet->getMeasure("OutlineSlopeAngularity2dMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pOutlineSlopeAngularity2dOutMsr->getMeasureResult());