Measure eccentricity of the ellipse that has the same second moments as 2d shape.

Eccentricity 2d measure computes the eccentricity of the ellipse that has the same second moments as 2d shape.

The eccentricity of the ellipse (commonly denoted as either $e$ or $\varepsilon$ ) is given by :

$e = \varepsilon = \sqrt{\frac{\lambda_{max}^2 - \lambda_{min}^2}{\lambda_{max}^2}} = \sqrt{1 - \frac{\lambda_{min}^2}{\lambda_{max}^2}}$

where $\lambda_{max}$ and $\lambda_{min}$ are one-half of the ellipse's major and minor axes respectively (see InertiaLambdaMax and InertiaLambdaMin respectively).

Here is an example of eccentricity 2d measurement :

Measure eccentricity of the ellipse that has the same second moments as 2d shape

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Generic	None	None	Value (ipsdk::ipReal64)	Row Intersections

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, "Eccentricity2dMsr")
    
    #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("Eccentricity2dMsr")
    
    # 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, "Eccentricity2dMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pEccentricity2dOutMsr = pOutMeasureSet->getMeasure("Eccentricity2dMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pEccentricity2dOutMsr->getMeasureResult());