Compute the maximal Feret diameter over a range of uniformly distributed orientations.

MaxFeretDiameter measure computes the maximum of Feret diameters measured on a shape over a uniform distribution of orientations. This measure is done on the polygonal (2d shapes) / polyhedral (3d shapes) approximations of the shapes. The number of orientations in the distribution can be specified by the user (it must be strictly greater than 0).

See FeretDiameter2d for more details about the 2d Feret diameters and FeretDiameter3d for more details about the 3d Feret diameters.

Chosen uniform distribution of orientations is defined as follows:

in 2d, each one of the N orientations is defined by its angle $\theta_i$ , that equals to $\theta_i=\frac{\pi}{N}$ with $i\in[[0; N-1]]$
in 3d, each one of the N orientations is defined by the couple of angles and (report to "ConventionsPoints3d" section in the Core documentation), that are defined as:
- if $N\leq400$ , the solutions of the Thomson problem
- if , $\phi_i = 2\times\pi\times u1$ and $\theta_i=acos(2\times u2-1)$ , with and uniformly distributed on range

Here is an example of maximal Feret diameter measurement on a 2d shape with a number of orientations of 180:

maximal Feret diameter over the range of orientations [0; PI[

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Generic	Length	MaxFeretDiameterMsrParams	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, "MaxFeretDiameterMsr")
    
    #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("MaxFeretDiameterMsr")
    
    # 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>();
    readFromXmlFile(inputShape2dCollPath, *pShape2dColl);
    // define a measure info set
    MeasureInfoSetPtr pMeasureInfoSet = MeasureInfoSet::create2dInstance();
    createMeasureInfo(pMeasureInfoSet, "MaxFeretDiameterMsr", createMaxFeretDiameterMsrParams(180));
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pMaxFeretDiameterOutMsr = pOutMeasureSet->getMeasure("MaxFeretDiameterMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pMaxFeretDiameterOutMsr->getMeasureResult());

https://en.wikipedia.org/wiki/Thomson_problem