Compute the sphericity of a 3d shape.

Defined by Wadell in 1935, the sphericity of a shape is the ratio of the surface area of a sphere with the same volume as the shape to the surface area of the shape:

$Sphericity = \frac{\pi^{\frac{1}{3}} (6 V)^{\frac{2}{3}}}{A}$

Where $ A $ is the shape area, calculated with Area3d, and $ V $ is the shape volume, calculated with Volume3d.

Here is an example of sphericity measurement :

Compute the sphericity of a 3d shape

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Generic	None	Sphericity3dMsrParams	Value (ipsdk::ipReal64)	Both

See Shape measurement for additional information on these pictograms

Example of Python code :

Generic example in 3d case :

import PyIPSDK

import PyIPSDK.IPSDKIPLShapeAnalysis as shapeanalysis

    # Create the infoset
    inMeasureInfoSet3d = PyIPSDK.createMeasureInfoSet3d()
    PyIPSDK.createMeasureInfo(inMeasureInfoSet3d, "Sphericity3dMsr")
    
    #Perform the analysis
    outMeasureSet = shapeanalysis.labelAnalysis3d(inGreyImg, inLabelImg, inMeasureInfoSet3d)
    
    # save results to csv format
    PyIPSDK.saveCsvMeasureFile(os.path.join(tmpPath,  "shape_analysis_results.csv"), outMeasureSet)
    
    # retrieve measure results
    outMsr = outMeasureSet.getMeasure("Sphericity3dMsr")
    
    # 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 pInGreyImg3d = loadTiffImageFile(inputGreyImgPath, eTiffDirectoryMode::eTDM_Volume);
    // read entity shape 3d collection used for processing
    Shape3dCollPtr pShape3dColl = boost::make_shared<Shape3dColl>();
    readFromBinaryFile(inputShape3dCollPath, *pShape3dColl);
    // define a measure info set
    MeasureInfoSetPtr pMeasureInfoSet = MeasureInfoSet::create3dInstance();
    createMeasureInfo(pMeasureInfoSet, "Sphericity3dMsr", createHolesBasicPolicyMsrParams(bProcessHoles));
    
    // compute measure on shape 3d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis3d(pInGreyImg3d, pShape3dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pSphericity3dOutMsr = pOutMeasureSet->getMeasure("Sphericity3dMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pSphericity3dOutMsr->getMeasureResult());