Measure allowing to compute energy of intensities for shape.

This measure computes the energy, also known as angular second moment, of image pixel/voxel intensity values associated to a 2d/3d shape. Its value equals to one for a constant signal and decreases with its unpredictability.

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

$E = \sum_{i=0}^{N-1}{p^2(b_i)}$

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 the bin of histogram,
is the intensity range (width) for the bin of histogram.

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

We could have predicted the behaviour of the results : the shape 3 has homogeneous intensity, thus, its energy equals 1. Moreover, the shapes 5 and 6 are the most noisy features, therefore their energies have the lowest values. Then, the noise intensity of the shapes 2 and 4, is close to the intensity noise intensity of the shapes 5 and 6. As a consequence, their energy have the same range. Finally, the shape 1 is less noisy than the shapes 2, 4, 5 and 6, which results in a higher energy value.

Moreover, the results are correlated with the ones obtained by the Entropy measure.

Measure allowing to compute energy of intensities for shape

Measure synthesis :

Measure Type	Measure Unit Type	Parameter Type	Result Type	Shape Requirements
Generic	None	EnergyMsrParams	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, "EnergyMsr")
    
    #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("EnergyMsr")
    
    # 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, "EnergyMsr")
    
    #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("EnergyMsr")
    
    # 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, "EnergyMsr");
    
    // compute measure on shape 2d collection
    MeasureSetPtr pOutMeasureSet = shapeAnalysis2d(pInGreyImg2d, pShape2dColl, pMeasureInfoSet);
    // retrieve associated results
    const MeasureConstPtr& pEnergyOutMsr = pOutMeasureSet->getMeasure("EnergyMsr");
    const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>& outResults = static_cast<const ipsdk::shape::analysis::ValueMeasureResult<ipsdk::ipReal64>&>(pEnergyOutMsr->getMeasureResult());