Measure allowing to compute entropy of intensities for shape.

This measure computes the entropy of image pixel/voxel intensity values associated to a 2d/3d shape. This is a measure of disorder of the state which value tends to zero for a constant signal and which increase with its unpredictability.

Entropy measure is based on the analysis of shape histogram (see Histogram). Given histogram parameters allowing to determine (among others) number of classes $N$ and a global range for histogram, this measure computes shape entropy as :

$H = -\sum_{i=0}^{N-1}{p(b_i)\log(p(b_i))}$

where $p(b_i)$ is the density of probability associated to bin $i$ of histogram :

$p(b_i) = \frac{P(b_i) \times R(b_i)}{\sum_{i=0}^{N-1}{P(b_i) \times R(b_i)}}$

and :

is the population for bin of histogram
is the intensity range (width) for bin of histogram

Here is an example of entropy measurement in 2d case :

Measure allowing to compute entropy of intensities for shape

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Generic	None	EntropyMsrParams	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, "EntropyMsr")
    
    #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("EntropyMsr")
    
    # retrieve measure values
    outMsrValues = outMsr.getMeasureResult().getColl(0)
    print("First label measurement equal " + str(outMsrValues[1]))

Generic example in 3d case :

import PyIPSDK

import PyIPSDK.IPSDKIPLShapeAnalysis as shapeanalysis

    # Create the infoset
    inMeasureInfoSet3d = PyIPSDK.createMeasureInfoSet3d()
    PyIPSDK.createMeasureInfo(inMeasureInfoSet3d, "EntropyMsr")
    
    #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("EntropyMsr")
    
    # 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, "EntropyMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pEntropyOutMsr = pOutMeasureSet->getMeasure("EntropyMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pEntropyOutMsr->getMeasureResult());